Tiste

Luis

Cyril Mathilde Paul

Junah, Ilan Alice Owen

Nathalie Noël

Benoît, Julien Pierre Audrey

Cyrille Marc

Guillaume

Sophie

Stéphane

Gilbert

Pascal

Jean-Paul Pascal

Pierre Benjamin

Olivier Litaize

Abdel Chebboubi

Keywords:

Titre: Étude de la désexcitation radiative des fragments de fission du 252 Cf Mots clés: Fission -énergie d'excitation -émission γ -chambre d'ionisation -fonction de force gamma -densité de niveaux Résumé: La fission nucléaire est une réaction où un noyau se scinde en deux noyaux plus légers et émet une partie de l'énergie libérée sous forme de neutrons et gammas. Ce travail se concentre sur l'étude des photons émis après la fission spontanée du 252 Cf. La principale difficulté est d'identifier les fragments créés: une double chambre d'ionisation à grille de Frisch (FGTIC) a été utilisée avec un support ultra-mince qui permet d'observer des évènements rares sans émission de neutrons (fission froide). Dans ce régime, la résolution en masse de 0.68 a.m.u. permet une identification parfaite des masses. La FGTIC est couplée à 54 détecteurs NaI permettant de mesurer les gammas émis avec une grande efficacité. L'étude de cette émission de photons dans le cadre de la fission froide permet notam-ment d'identifier parfaitement deux fragmentations: 120 Cd/ 132 Sn et 118 Pd/ 134 Te. Dans la première 132 Sn est observé dans son état fondamental, ce qui implique que le spectre γ mesuré provient exclusivement du 120 Cd. La reproduction du spectre s'est montré très sensible à la distribution de spin initial, permettant sa détermination expérimentale pour la première fois dans la fission froide. Pour la seconde fragmentation étudiée ( 118 Pd/ 134 Te) la répartition en énergie d'excitation est la quantité la plus sensible pour reproduire le spectre. Elle a été déterminée pour la première fois à l'aide d'un algorithme génétique. Cette répartition est bien reproduite par une distribution statistique de l'énergie intrinsèque à la scission à l'aide de densités de niveaux microscopiques.

Introduction

La ssion est un mécanisme au cours duquel un noyau va se scinder en deux. Sous l'impulsion de la compétition entre la force nucléaire attractive, et la répulsion coulombienne, le noyau de 252 Cf va se déformer spontanément jusqu'à devenir une sorte d'haltère où deux préfragments sont liés par un cou mince. Rapidement après le début de cette déformation spontanée, (∼ 10 -21 s) le cou formé va se rompre, c'est le point de scission. À cet instant seule persiste la répulsion coulombienne, entraînant une forte accélération des fragments.

Bien plus tard, vers 10 -18 s les fragments accélérés vont émettre des neutrons puis des gammas. L'accélération des fragments et l'émission de neutrons et de gammas sont la preuve que le processus de ssion libère de l'énergie. Cette énergie libérée, notée Q, est partagée en deux. L'énergie totale d'excitation, d'abord, provient de l'énergie dissipée pendant la déformation du noyau ssionnant et de la relaxation des déformations des fragments à la scission.

En eet les fragments naissent très déformés à la scission et leur retour à leur déformation fondamentale libère de l'énergie sous forme d'excitation. L'énergie cinétique totale complète ce bilan. La cinétique des fragments a été une des premières observables étudié ce qui a permis de mettre en évidence que l'énergie cinétique totale s'élève en moyenne à 184 MeV pour la ssion du 252 Cf. L'énergie moyenne libérée pendant cette ssion est d'environ 218 MeV ce qui indique que la majeure partie (80 %) est sous forme cinétique. Les Cela montre que le mécanisme de répartition de l'énergie d'excitation est complexe et reste ix encore aujourd'hui une des problématiques ouvertes de la ssion. Ce travail adresse cette problématique par la suite. Les neutrons emportent 85 % de l'énergie totale d'excitation, le reste étant emporté par l'émission des gammas.

Les gammas emportent en moyenne 7 MeV comme montré ici par les mesures VESPA. Là où les neutrons emportaient beaucoup d'énergie, les gammas eux emportent la majeure partie du moment angulaire des fragments. De ce fait les expériences visant à déterminer le moment angulaire dans la ssion se sont concentrées sur l'étude des propriétés des gammas émis, que ce soit leur anisotropie, leur multiplicité, ou encore l'évolution de rapports isomériques avec l'énergie d'excitation, qui montre expérimentalement une dépendance entre les deux. Enn la mesure de l'alimentation directe des niveaux de la bande principale comme fait par Wilhelmy en 1972 mais surtout par Wilson en 2021 à permis de mesurer directement les distributions en moment angulaire après émission de neutrons. Ce après émission de neutrons est crucial puisque les neutrons emportent quand même du moment angulaire et les mesures doivent être corrigées an de remonter au moment angulaire à la scission pour essayer de comprendre son mécanisme de génération. À la suite du Nature de Wilson, un certain nombre de publications théoriques ont suivi an d'expliquer ces mesures.

La génération de ce moment angulaire dans la ssion ne fait, à ce jour, toujours pas l'objet d'un consensus. Ce travail adresse cette problématique sur une fragmentation spécique.

On comprend que pour le moment angulaire ou la répartition d'énergie, il est nécessaire d'accéder a ces quantités à la scission ainsi que de bien identier les fragments à la scission.

La mesure d'évènements de ssion sans émission de neutrons, ou froide, donne directement accès aux fragments créés à la scission et à leur propriétés. Les seules études se sont principalement concentrées sur l'identication de la ssion froide et ses rendements, ce qui est une performance dicile nécessitant une excellente résolution en énergie. Cette expérience s'est attelée à la dicile identication de la ssion froide et la mesurée corrélée des gammas émis. D'un point de vue macroscopique on peut voir la ssion froide comme deux fragments quasiment sphériques à la scission. De ce fait l'énergie cinétique totale prend la quasitotalité de l'énergie disponible, ne laissant pas assez d'énergie aux fragments pour émettre des neutrons. Ainsi les gammas émis sont les seuls vecteurs de l'énergie d'excitation et du moment angulaire, les mesurer donne simultanément accès a ces deux grandeurs. Ainsi nous arrivons à déterminer le moment angulaire et la répartition d'énergie d'excitation dans deux fragmentations froides parfaitement identiées.

Dispositif expérimental & analyse

Le dispositif expérimental utilisé se compose de 54 cristaux NaI (iodure de sodium) disposés de sorte à former un cube an de mesurer les gammas avec la plus grande ecacité possible.

Ce type de détecteur présente des bonnes résolution en temps, 5 ns, et en énergie, 6 % à 662 keV. Ces résolutions sont des largeurs à mi-hauteur. Au centre se trouve la double chambre d'ionisation à grille de Frisch qui permet de mesurer simultanément les deux énergies cinétiques des fragments, qui nous donne une mesure indirecte de leur masse. Ce détecteur à une excellente résolution intrinsèque en énergie de 160 keV, ce qui va nous permettre de mesurer précisément la ssion froide.

Il s'agit d'un détecteur gazeux au centre duquel est placé une électrode, la cathode, faisant face à une grille puis une anode de chaque côté. La source de 252 Cf est placée au centre de la cathode. Lorsqu'un évènement de ssion arrive, les deux fragments sont émis dos-à-dos donc de chaque coté de la cathode. Chaque fragment ionise le gaz sur son passage et est stoppé avant la grille.Les électrons crées vont dériver vers la grille puis l'anode dû au champ électrique appliqué. Le signal induit dépend du travail des charges, ainsi, sans grilles le signal de l'anode dépend de l'angle d'émission des fragments. Les grilles permettent d'isoler les x anodes de cette dépendance angulaire, assurant sa proportionnalité à l'énergie déposée. Ce type de détecteur permet de mesurer la masse avec la méthode 2E. Cette méthode se base sur la mesure des deux énergies cinétiques an de remonter aux masses grâce à la conservation de l'impulsion. Seulement cette conservation de l'impulsion n'est valable qu'en considérant les fragments avant émission de neutrons, alors que nous mesurons des quantités généralement après émission de neutrons. Nous devons donc faire un a priori sur le nombre de neutrons émis an de remonter aux grandeurs pré-neutrons. Seulement cet a priori dépend des quantités pré-neutrons qu'on essaie de déterminer. De fait une procédure itérative doit être mise en place pour reconstruire les masses et énergies avant émission des neutrons. La spécicité de l'analyse que j'ai conduite dans ce travail est le traitement de cet a priori an de pouvoir simultanément traiter la ssion standard et la ssion sans émission de neutrons.

Il s'agit, à ma connaissance, de la première étude le faisant. Dans cette méthode, la résolution en masse ne dépend que de la résolution en énergie. An d'identier deux masses en ssion froide à mi-hauteur, il nous faut atteindre une résolution en masse inférieure à 0.7 unités de masses. Cela se traduit par une dispersion en énergie cinétique qui doit être inférieure à 600 keV, c'est-à-dire environ 0.6%. An d'obtenir une si faible dispersion il faut correctement et précisément reconstruire l'énergie cinétique des fragments. Pour remonter à l'énergie cinétique depuis l'impulsion mesurée, deux corrections doivent être appliquées.

Chacune de ces corrections dépend de l'énergie cinétique que l'on essaie de déterminer et de la masse des fragments qui n'est pas encore connue. Il faut donc déterminer ces corrections de façon récursive. La première correction, allant de 3 à 6 % est le défaut d'impulsion qui prend en compte toutes les collisions non-ionisantes quand le fragment traverse le gaz. La seconde est la perte d'énergie dans le support. Un des deux fragments va devoir traverser ce support avant d'arriver dans le gaz, et donc perdre de l'énergie. C'est un des facteur les plus limitant pour la résolution en énergie, il a donc été minimisé et correspond environ à 0.3 %. Une fois ces corrections déterminées et la méthode 2E appliquée, les données sont en très bon accord avec la littérature. En eet les rendements en masse sont en excellent accord avec un ensemble de mesures utilisant diérents dispositifs et méthodes. En appliquant une correction moyenne du nombre de neutrons on obtient une excellente reproduction de l'évolution du TKE avec la masse, cependant ce traitement n'est pas correct pour les ssion froide. De ce fait un autre traitement permettant d'avoir la ssion à zéro neutron émis est utilisé.

Bien que les NaI soient surtout considéré comme des détecteurs gammas, ils ne sont pas insensibles aux neutrons. Ils interagissent dans le cristal induisant des gammas retardés.

On observe que ces gammas retardés baissent en intensité quand on augment en TKE, c'est-à-dire qu'on diminue le nombre de neutrons. Ainsi les pics à 57 keV et 200 keV sont les derniers à disparaître et leur disparition marque la n de l'émission des neutrons. Pour déterminer cette limite on utilise la distribution en TKE sélectionné par l'un de ces gammas.

La distribution ainsi obtenue est ajusté avec un paramétrisation de Brosa an de déterminer proprement la limite dans une zone avec peu de statistiques. La résolution en masse obtenue est de 0.68 unité de masse, contre 3.9 en ssion standard. Nous avons vérier qu'il n'y avait pas de décalage en masse.

Les isomères comme outils pour l'étude multi-paramétrique de la ssion Les premiers résultats de ce travail se concentre sur l'étude des propriétés des fragments isomériques. Dans un premier temps ce travail s'est penché sur les structures visibles dans le spectre γ prompt entre 3.5 et 7 MeV pour des masses proches de la symétrie. Bien que la première observation de ces structures ne soit pas récente, il n'existe pas de consensus dans la littérature sur l'origine de ces structures: viennent-elles de contributions discrètes xi ou continues du fragment lourd et/ou léger? Si elles viennent de la décroissance statistique, comment l'expliquer? Après avoir montré que ce travail observait tout aussi bien ces structures que les études précédentes, nous sommes allés plus loin en regardant des spectres prompt mieux sélectionnés (sélection grossière en masse dans la littérature) à l'aide d'isomères. Une quinzaine d'isomères ont été observés pour des fragments lourds proche de la symétrie. Ce faisant la quasi-totalité des spectres prompts associés montrent ces structures, nous permettant d'armer clairement que ces structures proviennent de la partie continue de la décroissance radiative des fragments et non de transitions discrètes limitées à quelques fragments spéciques. Le 134 Te possède deux isomères mesurés dans ce travail à des énergies d'excitation très diérentes: le spectre prompt associé à l'isomère 6+ à 1.691 MeV peut contenir des transitions allant jusqu'à un peu plus de 6 MeV (= S n -E * (6 + )), alors que l'isomère 12 + est lui à 5.804 MeV, ne pouvant contenir que des transitions sous 2 MeV. Lorsque l'on compare les deux spectres on remarque la disparition des structures au delà de 3.5 MeV en passant du 6 + au 12 + ce qui signe parfaitement que ces structures proviennent du fragment lourd. Nous nous sommes ensuite attelés à identier l'origine de ces structures dans la désexcitation de ces fragments lourds. La désexcitation radiative d'un noyau est globalement dirigée par deux quantités, la fonction de force γ et la densité de niveaux. La première va favoriser de "grandes" transitions tandis que la seconde va elle préférer faire des "petites" transitions. SI on regarde le cas d'une fragmentation Te/Pd, la probabilité d'une transition à une énergie donnée pour le Pd est maximale pour de transitions entre 2 et 3 MeV. Les transitions d'un état du continuum vers les niveaux discrets ont des taux de probabilités très faibles. La décroissance du Pd est ainsi plutôt dirigée par la densité de niveaux. Pour le Te, sa proximité avec la double fermeture de couche N=82 et Z=50 diminue fortement sa densité de niveaux, de ce fait la fonction de force va être la contributrice principale à la désexcitation du Te, venant favoriser les transitions entre le continuum et les niveaux discrets. Ainsi, comme l'on montré les calculs FIFRELIN, les structures proviennent majoritairement de la somme de deux spectres aux pentes très différentes, se croisant vers 3.5 MeV.

La deuxième partie de cette étude des isomères s'est concentrée sur la reproduction de leur distribution en énergie cinétique et TKE par les modèles GEF et FIFRELIN. Les distributions en énergie cinétique sont relativement bien décrites par le code GEF (mis à part un décalage global). FIFRELIN prédit des distributions plus structurées et incompatibles avec la résolution expérimentale. Ces structures sont associées à l'émission neutron. Pour les comparaison sur les distributions en TKE seul GEF est considéré. Pour les isomères A<100, la distribution prédite par GEF s'éloigne de la distribution expérimentale: cela est dû aux modes de ssion utilisés dans GEF. Pour ces masses, il y a un changement de mode qui s'opère dans GEF, entre le mode standard II et super-asymétrique. Ce dernier est associé à de fortes déformations qui se traduit par un TKE plus faible. Ainsi les données de ce travail permettent de questionner le choix de la déformation de ce mode dans GEF qui est peut-être trop importante.

Moment angulaire et répartition d'énergie dans la ssion froide

Pour la première fragmentation, on remarque que la fragmentation 132 Sn/ 120 Cd est la seule possible énergétiquement sur 5 MeV, et les suivantes sont forcément peu excités si elles sont signicativement présentes. De ce fait, la sélection en ssion froide faite ici favorise grandement la fragmentation 132 Sn/ 120 Cd. Pour s'en assurer on regarde la partie basse énergie du spectre où on identie clairement la structure basse énergie du Cd, et uniquement celle-ci ce qui nous permet de considérer que seule cette fragmentation est présente. 132 Sn est un noyau doublement magique donc son premier excité se trouve à 4.042 MeV. À cet endroit dans le xii spectre on ne remarque aucun sursaut statistiquement signicatif. On peut donc déterminer une limite supérieure de présence, nous disant qu'il peut vraiment être là au plus dans 1.76 % des évènements, autrement dit, quasiment jamais. On se trouve donc face à un cas exceptionnel où l'un des deux fragments se trouve dans son état fondamental. Puisque 132 Sn est dans son état fondamental ça veut dire que le TXE est simplement l'énergie d'excitation du Cd. Puisque TXE=Q-TKE, nous mesurons ici et pour la première fois la distribution en énergie d'excitation d'un fragment dans la ssion, ici le 120 Cd. Puisque l'énergie d'excitation est mesurée, la reproduction du spectre ne doit être sensible qu'à la distribution en moment angulaire. Ici la paramétrisation usuelle à l'aide d'un spin-cuto est utilisée. On observe des fortes variations du spectre simulé avec le choix du spin-cuto, surtout sur les intensités des transitions discrètes. En eet les 2 pics entre 800 keV et 1 MeV proviennent de niveaux avec des spins élevés (5,[START_REF] Hötzel | High-energy gamma-rays accompanying the spontaneous ssion of 252 Cf)[END_REF] pas nécessairement alimentés, au contraire du 2+. An de déterminer ce paramètre de spin-cuto, nous avons utilisé une méthode de chaîne de Markov Monte-Carlo. On obtient un distribution de spin-cuto centrée sur 3.7 avec un écart type de 0.2. Ce spin-cuto reproduit très bien le spectre expérimental. On détermine ainsi pour la première fois la distribution angulaire à la scission dans la ssion froide.

Passons maintenant à la seconde fragmentation froide qui va nous intéresser : 118/134. Ici aussi une fragmentation paire-paire possède un Q de réaction plus large que les fragmentations suivantes : 118 Pd/ 134 Te. Ces deux noyaux sont très proches de 120 Cd/ 132 Sn, de ce fait on s'attend à un comportement assez similaire à ce qu'on vient de voir en terme de répartition d'énergie d'excitation, de moment angulaire et de présence dans la sélection en ssion froide. De même que pour Cd/Sn, on identie clairement les structures basses énergies du 118 Pdmais aussi du 134 Te. Du point de vue de la reproduction du spectre, la distribution initiale en spin est xée. On mesure le TXE grâce au TKE mais maintenant que les deux fragments sont excités, il faut partager cette énergie entre les deux fragments. Ce partage est déterminé à l'aide d'un algorithme génétique. Il s'agit de la première détermination expérimentale de la répartition de l'énergie d'excitation entre deux fragments. La première chose à noter est que cette répartition est que le spectre expérimental est très bien reproduit par cette répartition en énergie d'excitation. Ensuite le partage de l'énergie est très structuré, selon les niveaux discrets du 134 Te. Comme le 134 Tene s'excite que dans ses niveaux discrets, le choix de spin-cuto pour décrire sa désexcitation statistique n'a aucun impact sur la répartition. En revanche le spin-cuto de 118 Pdpeut, lui, impacter la répartition. On peut voir ici que la répartition n'est pas très sensible aux variations du spin-cuto du Pd : les seules régions avec des variations notables sont des zones qui ont peu de sens physique puisque le Te reçoit une énergie entre son fondamental et son premier état excité. Cette répartition de l'énergie d'excitation est bien reproduite par tous les modèles disponibles, parfois opposés dans la littérature. This reaction, discovered in the last months of the year 1938 by O. Hahn and F. Strassmann [START_REF] Hahn | Über die entstehung von radiumisotopen aus uran durch bestrahlen mit schnellen und verlangsamten neutronen[END_REF], in which a nucleus will break into two smaller nuclei, called fragments, is still an active eld of research 85 years later. The nuclei produced in this phenomenon are exotic and possess high excitation energy which make them relevant candidates to study how nuclei de-excite themselves. This type of study is important in order to determine the abundance of the elements created during the nucleosynthesis. It is also required for the nuclear reactors in order to evaluate the heating induced by the photons in the core.

I Introduction

The experiment done in the present work was designed to measure the photon emission following the ssion of 252 Cf with great eciency while identifying the nuclei produced.

While the collected data was not conclusive on the ingredients describing the de-excitation of the fragments by photon emission, it showed great sensibility on the ssion mechanism.

This mechanism is hard to catch experimentally as it is hidden within multiple correlated quantities, therefore several models co-exist in order to describe the dierent ssion observables. The generation of angular momentum during the ssion and the excitation energy repartition between the fragments are two striking examples of such coexistence. While recent measurements [2] on the angular momentum marked a step towards a comprehensive description of its generation, the repartition of the excitation energy remains an open question with various descriptions [START_REF] Apalin | Neutron emission from u233, u235 and pu239 ssion fragments[END_REF] not always compatible. The present work displays additional data that can help to discriminate between them.

The present manuscript is divided in ve chapters. Chapter 1 will describe the ssion process and its relevance for the study of excited exotic nuclei. The ingredients required to describe the photon emission will be presented.

Chapter 2 will present the experimental setup used in the present work. Both the ionization chamber and the NaI array and their respective signals processing will be described. The twin ionization chamber will be highlighted as it is the detector that required the most care to detect the neutron-less ssion events.

Chapter 3 describes the analysis of the NaI array signals and especially the treatment of the neutron pollution mandatory to isolate the prompt γ cascade. A comprehensive description of the analysis of the twin ionization chamber is presented together with adjustments of the usual methods in order to treat correctly the neutron-less ssion events. The implemented algorithm to select the isomers from the massive collected data is nally presented.

Chapter 4 presents at rst, with the help of isomers, the results on the prompt γ spectra and especially the structure between 3.5 and 7 MeV observed near the symmetry [START_REF] Hötzel | High-energy gamma-rays accompanying the spontaneous ssion of 252 Cf)[END_REF] and the role of the strength function and level densities in it. In a second time the kinetic and total kinetic energy distributions gated by isomers are presented and confronted to predictions from ssion codes [START_REF] Schmidt | General description of ssion observables: Gef model code[END_REF][START_REF] Litaize | Fission modelling with frelin[END_REF]. This confrontation highlights potential improvements of those codes.

Finally Chapter 5 presents the results on cold ssion. Two fragmentations, 120 Cd/ 132 Sn and 118 Pd/ 134 Te, are investigated through their associated prompt spectrum, allowing to gain insights on the angular momentum and the sharing of the excitation energy between the two fragments.

Chapter 1

Radiative decay of the ssion fragments

This chapter will introduce the reader to the general concepts used in the following of this thesis. Fission will be described, especially the sharing of the energy between the two fragments. Then the usual description of the radiative decay of an excited nucleus will be presented.

Global description of ssion

Nuclear ssion was discovered almost 90 years ago by O. Hahn and F. Strassmann [START_REF] Hahn | Über die entstehung von radiumisotopen aus uran durch bestrahlen mit schnellen und verlangsamten neutronen[END_REF][START_REF] Hahn | Über den nachweis und das verhalten der bei der bestrahlung des urans mittels neutronen entstehenden erdalkalimetalle[END_REF] and interpreted later the same year by L. Meitner and O. Frisch [START_REF] Meitner | Disintegration of uranium by neutrons: a new type of nuclear reaction[END_REF] as a deforming nucleus, similar to a liquid drop, leading to its scission in two fragments and the release of roughly 200 MeV. In the following months N. Bohr and J. A. Wheeler produced the rst consistent theoretical description of the mechanism [START_REF] Bohr | The mechanism of nuclear ssion[END_REF] based on the liquid drop model (LDM) from N. Bohr [START_REF] Bohr | Neutron capture and nuclear constitution[END_REF].

The theoretical description of the ssion process has been greatly improved since the macroscopic description of a charged liquid drop undergoing deformation due to the Coulomb repulsion. Microscopic ingredients like shell corrections or pairing have been added [START_REF] Strutinsky | Shell eects in nuclear masses and deformation energies[END_REF][START_REF]Strutinsky : shells in deformed nuclei[END_REF] giving rise to macro-micro approaches. Fully microscopic descriptions were possible by applying the mean-eld approach of Hartree-Fock(-Bogoliubov) formalism. This section does not intend to describe the wide variety of models developed to describe the ssion, if the reader is interested in the theory of ssion, great reviews on the theory of ssion and its last advances can be found in [START_REF] Schunck | Theory of nuclear ssion[END_REF][START_REF] Bender | Future of nuclear ssion theory[END_REF].

Figure 1.1 shows a schematic description of the path to go from a single nucleus to two nuclei with large energies. It represents the potential energy as a function of a deformation degree of freedom, here the elongation is used. In the case of induced ssion (by a neutron, γ . . . ) the nucleus, in its ground state deformation, will be excited, then, with a certain probability it can deform itself. This deformation can be understood as a competition between the Coulomb repulsion of the protons and a surface tension. With the deformation it will overcome a rst barrier to go to a meta-stable state called a ssion isomer. From here it can either go back to the less-deformed ground state or continue to elongate itself. The two options are highly correlated to the heights of the two barriers surrounding it. If it continues to higher deformation it will cross a point of no-return: the saddle point. It is dened as the point of the highest potential energy, getting past it means that ssion is inevitable. One can note that a priori this point may not be at the top of the second barrier, in fact for some nuclei it is at the top of the rst barrier. After the saddle point the nucleus goes to higher and higher deformations and converges to a sort of dumbbell: the nucleus is similar to two pre-formed nuclei linked by a neck. Increasing the deformation leads to a thinner neck and the pre-fragments take shape. At some point the neck is so thin that it "snaps", this is the scission point. At this moment the nuclear force, or surface tension, that was holding the pre-fragments together, vanishes and only the Coulomb repulsion remains which greatly accelerate the fragments. This whole process takes around 10 -21 s. In the case of spontaneous ssion, which is the case 252 Cf, the nucleus has a certain probability to "cross" the barriers by quantum tunneling. It is also important to understand that the ssion path shown in Figure 1.1 is just the 1D-subspace of minimal energy along a deformation degree of freedom. In reality the ssion is described by a multi-dimensional potential energy surface and several ssion paths can co-exist.

Going from saddle to scission some potential energy is released and stored as excitation energy in the pre-fragments. Those fragments are born with a deformation at scission and, during their acceleration their shape is relaxed until they reach their ground state deformation. Such relaxation is accompanied by an energy release, transferred to the excitation energy.

Figure 1.2 shows the dierent steps of a fragment's life after the scission and how it can get rid of the excitation energy it possesses. The most cost-ecient way for the fragment to decrease its energy is by emitting neutrons. The neutron reduces the excitation energy by S n + E n where S n is the energy required to emit a neutron, the neutron separation energy, and E n is the energy of the neutron. Once the excitation energy does not allow to emit neutrons anymore, the nucleus will emit γ-rays to go all the way to the ground state. There is a competition between the two emissions []. During this cascade ( 10 -9 s) the nucleus can fall on an isomer: it is a state that has a "long" half-life, from several ns to µs. Then the decay of this specic state will be delayed compared to the cascade leading to it. Since the nuclei produced are neutron-rich they will decay towards more stable nuclei through β decay. Delayed neutron or γ emission can occur after β decay.

An exothermic binary reaction

In the following only the spontaneous ssion is considered. As discussed before the ssion reaction releases a tremendous amount of energy that needs to be conserved. In most cases ssion ends in a binary system, nonetheless a ternary particle can be emitted [START_REF] Wagemans | The nuclear ssion process[END_REF]. Working with a binary system allows to express conservation laws with simplicity.

The mass is conserved:

A F N = A L + A H = A post L + A post H + ν H + ν L (1.1)
where A F N is the mass of the ssioning nucleus. A L (A H ) is the mass of the primary light (heavy) fragment, the subscript post corresponds to the secondary fragments (after neutron emission) and ν L (ν H ) is the number of neutrons emitted by the light (heavy) fragment.

The charge is conserved:

Z F N = Z L + Z H (1.2)
where Z F N , Z L , Z H is the charge of the ssioning nucleus, light and heavy fragment respectively. The proton evaporation is neglected in ssion.

The momentum in the center-of-mass frame is conserved:

0 = p L + p H (1.3)
where p L (p H ) is the light (heavy) fragment's momentum. In the case of spontaneous ssion the center-of-mass frame is the laboratory frame.

the total angular momentum is conserved:

S 0 = S L + S H + L (1.4)
where S 0 is the angular momentum of the ssioning nucleus, S L (S H ) is the spin of the light (heavy) fragment and L the orbital momentum between the two fragments.

In the case of the spontaneous ssion of the even-even nucleus 252 Cf S 0 = 0.

Finally the total energy of the system is conserved:

Q = T KE + T XE = KE sci + V coul + E dis + E relax = KE L + KE H + E * L + E * H (1.5)
where KE sci is the kinetic energy acquired before scission, V coul is the kinetic energy gained by the acceleration of the fragments after scission due to Coulomb repulsion.

E dis is the dissipated energy due to level crossing between saddle and scission, while E relax is the fragments deformation potential energy converted in excitation energy by the shape relaxation of the fragments.Q is the total energy released by the splitting of the ssioning nucleus in two fragments:

Q = M (A F N , Z F N ) -M (A L , Z L ) -M (A H , Z H ) (1.6)
where

M (A F N , Z F N ), M (A L , Z L ), M (A H , Z H )
is the mass of the ssioning nucleus, light and heavy primary fragment, respectively. This available energy Q is shared between the total kinetic energy T KE = KE L + KE H , which is the sum of the two fragments kinetic energies (K E L and KE H ), and the total excitation energy T XE = E * L + E * H which is the sum of the two fragments excitation energies(E *

L and E * H ).

The two following subsections will describe the current knowledge and models on the angular momentum and the sharing of the excitation energy.

Angular momentum

In 1959 V. M. Strutinsky [START_REF] Strutinsky | Angular anisotropy of gamma quanta that accompany ssion[END_REF] showed that the γ emitted after the ssion of 239 Pu and 235 U present some angular anisotropy. It was interpreted as an eect of large angular momentum (AM) in the fully accelerated fragments, correlated with the ssion direction.

The generation of such AM was described using the macroscopic frame [1921] where the fragments are assumed to have collective rotational modes at scission. They are either transversal (wriggling and bending) or longitudinal (tilting and twisting) with respect to the ssion axis. Figure 1.3 shows the dierent collective modes, taken from [START_REF] Moretto | Equilibrium statistical treatment of angular momenta associated with collective modes in ssion and heavy-ion reactions[END_REF]. Because the wriggling and bending modes are in the transverse plane with respect to the ssion axis, they are degenerated modes.

The orbital AM origin was not described and it was mainly a quantity introduced to conserve the total AM. The experimental informations on the AM are extremely scarce, J.

B. Wilhelmy et al. [START_REF] Wilhelmy | Angular momentum of primary products formed in the spontaneous ssion of 252 Cf[END_REF] were the rst ones, and for a long time the only ones, to measure the AM for some nuclei in the spontaneous ssion of 252 Cf. Their results could not infer conclusions on the generation mechanism. It is only 50 years later that comprehensive data on the AM was measured by J. Wilson et al. [2]. It is worth noticing the work of Naik et al. [START_REF] Naik | Systematics of fragment angular momentum in low-energy ssion of actinides[END_REF] which presented systematics on the angular momentum from isomeric ration measurements. The work of Wilson et al. [2] showed a clear sawtooth pattern of the mean AM with the fragment's mass that showed to be rather independent of the ssioning system.

They also showed that the two angular momenta (light and heavy fragments) were almost uncorrelated. They concluded that such lack of correlations could be explained by a macroscopic post-scission generation mechanism. This article induced a succession of theoretical work [2427] on microscopic AM generation mechanism. They showed that, using dierent microscopic descriptions, the apparent uncorrelated AM are not incompatible with a pre-scission generation. In this case the large value of the orbital AM washes the possible correlations between the values of the AM. However the correlations remain in the relative orientation of the fragments AM with respect to each other. Also, the sawtooth pattern measured in [2] was also reproduced.

The experimental spin distributions measured in [2] are rather well described by a statistical spin distribution (Equation (1.15)). The sawtooth pattern of the AM was also reproduced by more phenomenological descriptions [START_REF] Travar | Experimental information on mass-and tke-dependence of the prompt ssion γ-ray multiplicity[END_REF][START_REF] Piau | Neutron and gamma multiplicities calculated in the consistent framework of the hauser-feshbach monte carlo code frelin[END_REF] in attempts to reproduce the measured sawtooth of the γ multiplicity. A recent work of I. Stetcu et al. [START_REF] Stetcu | Angular momentum removal by neutron and γ-ray emissions during ssion fragment decays[END_REF] showed that the sawtooth pattern observed in [2] might originate from an experimental bias and that the angular momentum removed by neutrons and statistical γ is, according to their model, larger than expected with a large standard deviation. This would shift upward the values found in [2] by several units.

To summarize, the angular momentum of ssion fragments arise naturally from microscopic calculation as uncorrelated but there is no real consensus on the mean value or width of the AM distribution. Nonetheless, the phenomenological approaches used in various codes [4,[START_REF] Schmidt | General description of ssion observables: Gef model code[END_REF]3133] to describe the AM as statistically distributed according to the level density shows convincing results on the ssion observables.

Excitation energy repartition

Probing the excitation energy repartition is rather dicult experimentally and no direct measurement exists. In order to understand this diculty let's start from Equation (1.5):

the total available energy is given to the fragments as kinetic energy (T KE = KE L + KE H ) and excitation energy (T XE = E * L + E * H ). While the distribution of the kinetic energies before neutron emission is quite straightforward:

0 = p L + p H ⇒ KE L KE H = A H A L (1.7)
it is harder for the excitation energies because there are dierent contributions:

E * = E intr + E def + E coll (1.8)
The intrinsic excitation energy E intr corresponds to excitations of individual nucleons before scission, E def is the deformation energy, gained by the nucleus by its shape relaxation to the ground state. The collective energy E coll corresponds to the possible low-energy collective excitations (rotations or vibrations) of the ssioning nucleus before scission. Each one of these three types of excitation energies has to be shared between the two fragments.

In the Madland-Nix model [START_REF] Madland | New calculation of prompt ssion neutron spectra and average prompt neutron multiplicities[END_REF] the assumption was made that the nascent fragments, still in contact through a neck are at thermal equilibrium, then the total excitation is shared according to the level density of the fragments. This is based on the Back-shifted Fermi gas model (BSFGM) of the level density where the temperature is dened as T = U/a which leads to E * = aT 2 . This description of thermal equilibrium T L = T H falls short to describe the neutron sawtooth ν(A) [4,[START_REF] Talou | Advanced monte carlo modeling of prompt ssion neutrons for thermal and fast neutron-induced ssion reactions on 239 Pu[END_REF]. In order to have a better description of the neutron sawtooth dierent temperature are assumed and the ratio R T = T L /T H is parametrized from experimental data of V. Apalin et al. [START_REF] Apalin | Neutron emission from u233, u235 and pu239 ssion fragments[END_REF] in [START_REF] Talou | Advanced monte carlo modeling of prompt ssion neutrons for thermal and fast neutron-induced ssion reactions on 239 Pu[END_REF]. For O. Litaize et al. [4] this R T is parametrized with 2 free parameters, chosen by the user. O. Litaize et al. [4] and A. Tudora et al. [] share T XE -E rot with E * = aT 2 , where E rot stands for the rotational energy of the two fragments, it is dened by the moment of inertia and the spin of the fragments.

Another approach was proposed by K.-H. Schmidt and B. Jurado in [3,[START_REF] Schmidt | Entropy driven excitation energy sorting in superuid ssion dynamics[END_REF] where the deformation energy comes from the shape relaxation of the fragments, the collective excitation is taken into account and supposed to be evenly shared between the two fragments. The intrinsic energy is then shared following the micro-canonical distribution:

E * L,H = E intr 0 E * L,H ρ L,H (E * L,H )ρ H,L (E intr -E * L,H )dE * L,H E intr 0 ρ L,H (E * L,H )ρ H,L (E intr -E * L,H )dE * L,H (1.9)
This approach is based on similar assumptions as the previous two but instead of taking the BSFGM for the whole excitation energy it uses a parametrization similar to the Composite Gilbert-Cameron Model (CGCM, see Sec. 1.2.1 for more details on the level densities models) which is a better description of the level density at low excitation energy. Equation (1.9) tends to the same energy sharing as [4,[START_REF] Talou | Advanced monte carlo modeling of prompt ssion neutrons for thermal and fast neutron-induced ssion reactions on 239 Pu[END_REF] above a dozen MeV. Figure 1.4 shows the comparison of the two phenomenological approaches, taken from [3].

A new microscopic approach to share the intrinsic energy was introduced by M. Albertsson et al. in [5,[START_REF] Albertsson | Correlation studies of ssion-fragment neutron multiplicities[END_REF]. It consists in determining the shape evolution of the ssioning system along the ssion path by performing a random walk on the potential energy surface, guided by the deformed microscopic level densities. Such method allows to determine the sharing of the intrinsic energy and the deformation energies microscopically, it is in excellent agreement with the dierent data-sets on the neutron emission with respect to the TKE and neutron sawtooth at dierent neutron energies. It is worth noticing that all the presented approaches reproduce the measurement from Naqvi et al. [START_REF] Naqvi | Fission fragment properties in fast-neutron-induced ssion of 237 Np[END_REF], shown in Figure 1.5, even if their approaches parametrizations are radically dierent. This gure shows the evolution of 140 Xe, the blue ones to 94 Sr. The dotted lines corresponds to the approach of [START_REF] Schmidt | Entropy driven excitation energy sorting in superuid ssion dynamics[END_REF], the full lines to Equation (1.9) and [3] and the dashed lines represent the repartition following E * = aT 2 . The arrows represent the neutron separation energies. Taken from [3].

the mean number of neutron emitted in the neutron-induced ssion of 237 Np at two incident neutron energies. An increase in the neutron energy is translated by more neutrons emitted only from the heavy fragments, meaning that almost all the additional energy given by the incident neutron is transferred as excitation energy to the heavy fragment. Data from [START_REF] Naqvi | Fission fragment properties in fast-neutron-induced ssion of 237 Np[END_REF], Figure taken from [3].

Codes predicting ssion observables

In the next chapters the dierent results of the present work are compared with two codes that aim at describing the ssion observables, GEF [START_REF] Schmidt | General description of ssion observables: Gef model code[END_REF] and FIFRELIN [START_REF] Litaize | Fission modelling with frelin[END_REF]. They are briey described here.

GEF

It is a semi-empirical code developed by K.-H. Schmidt and B. Jurado [START_REF] Schmidt | General description of ssion observables: Gef model code[END_REF], it aims at describing the whole ssion through several empirical models and various parameters to get a systematic and consistent description of a large range of ssioning nuclei. These parameters are adjusted on various experimental data. The Z distribution is determined from the macroscopic potential of the ssioning nucleus, with shell eects determined empirically.

The relative yields of the Brosa [START_REF] Brosa | Multimodal ssion and neutron evaporation[END_REF] ssion modes are adjusted to the experimental mass yields. The excitation of the fragments is then calculated: the intrinsic energy available before scission is shared according to an energy sorting mechanism [3,[START_REF] Schmidt | Entropy driven excitation energy sorting in superuid ssion dynamics[END_REF], a deformation energy is given to each fragment from the relaxation of their deformation at scission. From this determination of the TXE, the TKE is extracted from Equation (1.5), where the fragments scission deformations will play a role in the determination of the Coulomb repulsion.

The neutron emission is based on the statistical Weisskopf model [START_REF] Weisskopf | Statistics and nuclear reactions[END_REF] where the emission spectrum is proportional to exp(n /T d ) with n the neutron energy and T d the temperature of the daughter nucleus. The γ/n competition is empirically parametrized. The γ decay is fully statistical divided in an E1 cascade to the yrast band, followed by an E2 cascade to the ground state. The discrete level scheme is not taken into account and instead parametrized following [START_REF] Batra | Reformulation of the variable moment of inertia model in terms of nuclear softness[END_REF][START_REF] Mariscotti | Phenomenological analysis of ground-state bands in even-even nuclei[END_REF]. The angular momentum is carried away only by the E2 cascade. The GEF version 2023.1.2 was used for the present work.

FIFRELIN

It is a code developed by O. Litaize and O. Serot [START_REF] Litaize | Fission modelling with frelin[END_REF], it is based on the Hauser-Feshbach (HF) formalism [START_REF] Hauser | The inelastic scattering of neutrons[END_REF] which allow to calculate the neutron and γ partial widths of all the possible transitions. Then the neutron and γ emission is determined from these widths, which intrinsically hold the γ/n competition. The low-lying structure of the nuclei is also taken from the RIPL database [START_REF] Capote | Ripl reference input parameter library for calculation of nuclear reactions and nuclear data evaluations[END_REF], but an intermediate region is introduced between the statistical description and the discrete transitions: in this intermediate region the experimentally known levels are completed according to the level density through nuclear realizations [START_REF] Be£vá° | Simulation of γ cascades in complex nuclei with emphasis on assessment of uncertainties of cascade-related quantities[END_REF]. The masses and TKE of the fragments are taken from the experimental distributions or from GEF otherwise. An iterative procedure allows to determine the intrinsic and rotational energy of the fragments. The rst one is shared according to E * = a(E * )T 2 under the assumption that there is no thermal equilibrium, then the temperature ratio R T = T L /T H is parametrized with 2 parameters.

The ssion process can be summarized as a nucleus undergoing shape deformation, spontaneously or with external help, that lead to the formation of two primary fragments after the scission. The two highly excited fragments are accelerated due to the Coulomb repulsion and de-excite themselves by emitting neutrons and photons. Therefore one can consider the ssion as a huge factory producing a variety of excited exotic nuclei, it is in fact one of the starting points for exotic beams [4648]. Studying the electromagnetic decay of such excited nuclei is of high interest for fundamental studies like the r-process [START_REF] Arnould | The r-process of stellar nucleosynthesis: Astrophysics and nuclear physics achievements and mysteries[END_REF] or application like γ-heating in the reactors core [START_REF] Rimpault | Needs of accurate prompt and delayed γ-spectrum and multiplicity for nuclear reactor designs[END_REF]. This was the original goal of this study. The following section will present the main ingredients to describe the photon emission and the challenges of their measurements in the ssion.

Theory of the photon emission

The emission of photons by a nucleus is categorized according to its multipolarity L and its type X, either electric, E, or magnetic, M . The electromagnetic transition between an initial state s i and a nal state s f satises certain selection rules: the total angular momentum (multipolarity) taken by the transition is constrained by

|J i -J f | L J i + J f ,
the change of parity is governed by:

π i π f = (-1) L (electric) (-1) L+1 (magnetic) (1.10)
where the index i, f represent the initial or nal state, respectively. Above a few MeV of excitation energy the electromagnetic decay of a nucleus can be treated as statistical and is governed by the radiative width Γ γ . Then the probability to do a transition of type X and multipolarity L from a state

s i = {J i , π i , E i } of energy E γ = E i -E f (E f is not xed) is
expressed as:

P XL (E γ ) = Γ γXL (E γ , J i , π i , J f , π f ) X,L,λ Γ γXL (E i -E λ , J i , π i , J λ , π λ ) (1.11)
where the radiative width Γ γXL associated to a transition of energy E γ from a well dened initial state s i = {J i , π i , E i } is expressed as:

Γ γXL (E γ , J i , π i , J f , π f ) = E 2L+1 γ f XL (E γ , J i , π i , J f , π f )ρ J f ,π f (E f ) (1.12) ρ J f ,π f (E f
) represents the number of levels per energy range, or level density, of spin J f and parity π f at the nal energy

E f = E i -E γ . f XL (E γ , J i , π i , J f , π f )
is the strength function that depends on the initial and nal states.

Nuclear level density

The present subsection describes the dierent phenomenological and microscopic description of the nuclear level density (NLD). All the models are adjusted to reproduce two quantities:

the number of low-lying discrete levels and density of levels at S n (neutron separation energy) populated by thermal neutron capture, ie s-wave (l = 0). This mean level spacing at S n , denoted D 0 , is dened as:

1 D 0 = J+1/2 j=|J-1/2| ρ F (S n , j, Π) (1.13)
where J, Π are the spin and parity of the target nucleus and ρ F the density of the compound nucleus.

CT (Constant Temperature)

This model is purely empirical and is based on the observation that the cumulative number of levels can be describe by an exponential increase for excitation energy below a few MeV [START_REF] Gilbert | A composite nuclear-level density formula with shell corrections[END_REF].

It is parametrized as:

ρ CT (E * ) = 1 T exp (E * -E 0 ) T (1.14)
E * is the excitation energy, E 0 and T are constant parameters adjusted on the experimental data which, for exotic nuclei, is mostly the discrete levels. E 0 is an energy shift and T corresponds to the temperature of the nucleus. The spin distribution of the levels is assumed to be statistical and follows:

P (J, σ) = 2J + 1 2σ 2 exp(- (J + 1/2) 2 2σ 2 ) (1.15)
where σ is the spin-cuto. The parity distribution is assumed to be equiprobable.

CGCM (Composite Gilbert-Cameron Model)

This model oers a more precise description of the NLD than the CT model that quickly overestimates the number of levels. It is a mix between a constant temperature behavior at low excitation energy and a Fermi gas above:

ρ CGCM (E * ) = ρ CT (E * ) for E * E M ρ F GM (E * ) for E * E M (1.16)
E M is the matching energy between the two descriptions. The Fermi gas NLD is dened as [5153]:

ρ F GM (E * ) = 1 12 √ 2σ exp 2 √ aU a 1/4 U 5/4
(1.17)

where U = E * -∆ is the eective excitation energy which takes into account the pairing energy ∆, σ is the spin-cuto of Equation (1.15). The level density parameter a is dened as [START_REF] Ignatyuk | Phenomenological description of energy dependence of the level density parameter[END_REF]:

a(E * ) = ã 1 + δW U exp(-γU ) (1.18)
with the shell correction energy δW , the shell damping parameter γ and the asymptotic level density parameter ã. These parameters are well dened as a function of the nucleus.

The three parameters E 0 , T and E M are determined by the following conditions:

the continuity in E * = E M , the continuity of the derivative in E * = E M , and by adjusting the level density to the discrete levels.

Microscopical description

The Hartree-Fock(-Bogoliubov) formalism allows to calculate the position in energy of the proton and neutron orbitals, then, through a combinatorial approach [START_REF] Hilaire | Combinatorial nuclear level densities based on the gogny nucleon-nucleon eective interaction[END_REF][START_REF] Goriely | Improved microscopic nuclear level densities within the hartree-fock-bogoliubov plus combinatorial method[END_REF] one can determine the number of states corresponding to a given energy, spin and parity. This state density is related to the level density by dierent relations, described in [START_REF] Hilaire | Combinatorial nuclear level densities based on the gogny nucleon-nucleon eective interaction[END_REF][START_REF] Goriely | Improved microscopic nuclear level densities within the hartree-fock-bogoliubov plus combinatorial method[END_REF]. The level densities determined through this combinatorial approach still need to be adjusted to the data on the D 0 and the discrete levels, therefore they are normalized with two parameters to scale and shift the tabulated densities. In the following two microscopic NLD are used [START_REF] Goriely | Further explorations of skyrme-hartreefock-bogoliubov mass formulas. vii. simultaneous ts to masses and ssion barriers[END_REF][START_REF] Goriely | Péru : First gogny-hartree-fock-bogoliubov nuclear mass model[END_REF], they originate from two interactions, Skyrme and Gogny-D1M, respectively.

They are referred as "Skyrme" or "D1M" in the following chapters.

Figure 1.6 shows the dierent models for NLD presented here for the case of 134 Te. They are extracted from TALYS [START_REF] Koning | Talys 1.0. International Conference on Nuclear Data for Science and Technology[END_REF]. One clearly sees that all the level densities have roughly the same behavior below 8 MeV, induced by the tting on the discrete levels. The NLD from microscopic calculations show more structured shapes at low excitation energy because of the small deformation of 134 Te (N=82). 134 Te has strong shell eects that greatly reduce its NLD and increase the energy range for which the concept of "level density" is less valid. where the neutrons are protons oscillate with respect to each other [START_REF] Harakeh | Giant resonances: fundamental high-frequency modes of nuclear excitation[END_REF]. D. Brink [START_REF] Brink | Some aspects of the interaction of light with matter[END_REF] and P. Axel [START_REF] Axel | Electric dipole ground-state transition width strength function and 7-mev photon interactions[END_REF] showed that the strength function for photoabsorption was well described by a lorentzian shape, depending only on the energy of the photon. This approximation to consider the strength function independent of the spin and parity of both initial and nal states and excitation energy of the initial state is also known as the Brink-Axel hypothesis. Following this approximation the two main empirical formulae are presented along microscopic calculations.

SLO

The Standard LOrentzian model express the γSF as a lorentzian:

f SLO E1 (E γ ) = 1 3 * (π c) 2 σ 0 Γ 2 r E γ (E 2 γ -E 2 r ) 2 + Γ 2 r E 2 γ (1.19)
where σ 0 , E r and Γ r are respectively the intensity, energy and width of the resonance. This parametrization follows the work of D. Brink [START_REF] Brink | Some aspects of the interaction of light with matter[END_REF] and P. Axel [START_REF] Axel | Electric dipole ground-state transition width strength function and 7-mev photon interactions[END_REF] and their approximation stating that the strength function depends only on the photon energy. The resonances other than E1 are usually described using the SLO model, as per RIPL recommendation [START_REF] Capote | Ripl reference input parameter library for calculation of nuclear reactions and nuclear data evaluations[END_REF].

EGLO

The Enhanced Generalized LOrentzian introduces a dependence on the initial excitation energy of the nucleus through its temperature [START_REF] Kopecky | Observation of the m1 giant resonance by resonance averaging in 106pd[END_REF][START_REF] Kadmenskij | Radiative widths of neutron resonances and giant dipole resonances[END_REF]:

f EGLO E1 (E γ ) = σ 0 Γ r 3 * (π c) 2 E γ Γ K (E γ , T f ) (E 2 γ -E 2 r ) 2 + E 2 γ Γ K (E γ , T f ) 2 + 0.7Γ K (0, T i ) E 3 r (1.20)
where T i and T f are the initial and nal state temperatures. Γ K (E γ , T ) is the empirically corrected, temperature dependent resonance width dened as:

Γ K (E γ , T ) = k 0 + (1 -k 0 ) E γ -ε 0 E r -ε 0 Γ(E γ , T ) with Γ(E γ , T ) = Γ r E r E 2 γ + 4πT 2 (1.21)
with k 0 and ε 0 the empirical parameters adjusted on experimental data [START_REF] Kopecky | Gamma-ray strength functions[END_REF]. This description improves the overall description of the data [START_REF] Capote | Ripl reference input parameter library for calculation of nuclear reactions and nuclear data evaluations[END_REF] and the second term in Equation (1.20) signicantly improves the low energy description [START_REF] Capote | Ripl reference input parameter library for calculation of nuclear reactions and nuclear data evaluations[END_REF].

QRPA

The Quasi-particle Random Phase Approximation (QRPA) is a microscopic model that treats the collective excitations (phonons) in the nucleus, completing the HFB method that describes the independent quasi-particle excitations. Such collective description is extremely ecient when the potential can be approximated with a parabola. The most complete base of such strength function [6668] is provided using the Gogny-D1M interaction. The strength functions created through the QRPA are adjusted to the experimental data [START_REF] Goriely | Gogny-hfb+qrpa dipole strength function and its application to radiative nucleon capture cross section[END_REF].

Figure 1.7 shows the comparison of the γSF models for the E1 strength function of 134 Te.

Here also the microscopic calculations show more structured shapes. All the γSF are tuned to reproduce the GDR, this energy range is irrelevant for the study of radiative decay below S n . It is important to notice that the prompt γ spectra will only be sensible to the relative variation (ie. the slope) of the γSF with the transition energy since only the emission probability is relevant. In regard of that matter both microscopic and EGLO γSF show similar trend below 8 MeV, contrary to the SLO γSF.

In-house code: DEGA

In order to master the dierent ingredients useful for the reproduction of the prompt γ spectrum, the laboratory developed a de-excitation code called DEGA. It is a stochastic [START_REF] Koning | Talys 1.0. International Conference on Nuclear Data for Science and Technology[END_REF] or RIPL [START_REF] Capote | Ripl reference input parameter library for calculation of nuclear reactions and nuclear data evaluations[END_REF] databases are used, and a continuum part above the threshold where the decay of states is treated as statistical, according to Equation (1.11).

A simplied description of a cascade done with DEGA is shown in Figure 1.8. DEGA was validated by comparing it with FIFRELIN calculations.

Statistical decay

The continuum region is divided in bins of excitation energy, the bin width is given by the user. A width of 50 keV oers a good compromise between the precision needed for the decay and the computation time. Each bin can decay either to another bin of the continuum or to the discrete levels. A multi-dimensional matrix is created for the continuum-continuum transitions as well as continuum-discrete transitions.

Continuum-continuum transitions For each matrix element, determined by E i , E f , J i , J f , π i and π f , the partial width Γ cc γ (E i , E f , J i , J f , π i , π f ) is computed according to Equation (1.12). All the models of γSF and NLD presented previously are implemented in DEGA. For the γSF only the E1 and M1 strength functions are used since they are the main contributors. I implemented the microscopic tables for both NLD and γSF during this thesis, they are read from the TALYS libraries. The spin distribution is parametrized as in Equation (1.15) and the parity is taken as equiprobable, unless specied (HFB tables).

Every parameter needed for the γSF or NLD is calculated as in [START_REF] Koning | Talys 1.0. International Conference on Nuclear Data for Science and Technology[END_REF].

G.S. E cut S n

Discrete levels γSF + NLD Continuum-discrete transitions Similarly to the continuum-continuum transitions the partial width to decay directly to the discrete part of the level scheme

Γ cd γ (E i , E d , J i , J d , π i , π d )
is computed according to Equation (1.12). In this case the nal state is perfectly dened so

ρ J d ,π d (E d ) = 1.
Normalization For every initial bin dened by {E i , J i , π i } the corresponding matrix elements of both matrices are normalized by:

N i = Ωc={E f ,J f ,π f } Γ cc γ (E i , J i , π i , Ω c ) + ω d ={E d ,J d ,π d } Γ cd γ (E i , J i , π i , ω d ) (1.22)
with J f , J d , π f , π d constrained by the selection rules mentioned previously.

THEORY OF THE PHOTON EMISSION

Decay of the discrete levels

As stated before the discrete levels are taken from the RIPL [START_REF] Capote | Ripl reference input parameter library for calculation of nuclear reactions and nuclear data evaluations[END_REF] or TALYS [START_REF] Koning | Talys 1.0. International Conference on Nuclear Data for Science and Technology[END_REF] database.

The decay of those states follows the intensities given by the database. The lifetime of the states is not yet considered in DEGA.

The theoretical description of the photon emission was presented along the dierent models of the required ingredients. The next subsection is focused on the challenges to measure the γSF and NLD in nuclei created in the ssion.

Challenges in the study of photon emission in ssion

Even though ssion creates a large variety of exotic nuclei several challenges arise in order to exploit the measured γ spectrum in terms of γSF and NLD. First of all the nuclei have to be identied in mass and charge. In general such identication is performed with a mass spectrometer like VAMOS++ [START_REF] Pullanhiotan | Performance of vamos for reactions near the coulomb barrier[END_REF][START_REF] Rejmund | Performance of the improved larger acceptance spectrometer: Vamos++[END_REF] or SOFIA [START_REF] Boutoux | The soa experiment[END_REF] and usually only for one fragment, except in SOFIA. The spectroscopic studies done with mass spectrometers are usually focused on the low-lying structure of the fragments and not on the detection of the full cascade.

Such measurements require large geometrical and intrinsic eciency in order to detect the high energy component of the cascade. The idea of the present experiment was to couple a twin ionization chamber (FGTIC) [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF] to Sodium-Iodide crystals allowing a geometrical eciency near 100% when using spontaneous ssion. When working with twin ionization chambers the typical resolution is 4 mass units, this can be improved by looking at rare events where no neutrons are emitted and the masses are unambiguously identied [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF].

The charge identication can be done by looking at isomeric delayed decays, at the cost of reducing statistics. To get the γSF and NLD from the measured prompt spectrum the excitation energy and initial spin distribution of the nucleus of interest have to be known.

The FGTIC gives access to the TKE distribution and in the case of isomers in cold ssion it gives access to the TXE distribution (Q = T KE + T XE). The sharing of this energy between the two identied fragments cannot be inferred from the measured quantities therefore a modelisation is required. As it was discussed previously, dierent approaches exist that can induce large variations in the fragments excitation energy below 10 MeV of TXE.

Similarly there is no consensus on the choice of the initial spin distribution. Since neither the excitation energy nor the angular momentum can be properly determined they are additional parameters to take into account to reproduce the measured prompt-γ spectra. In the present work the measured spectra showed in the end little dependence on both γSF and NLD. Unexpectedly though, the data on neutron-less ssion yield interesting results on the angular momentum and the excitation energy repartition at low TXE.

The present chapter has presented the initial goal of the present work and introduced the relevant observables and quantities to understand the rest of this thesis. The next chapters are focused on detailing the experimental setup and the data analysis as well as the presentation and interpretation of the results.

Part II

Experimental setup and signal processing Chapter 2

Experimental Setup

This chapter will focus on the detection system used for this work. At rst the philosophy of the experiment will be presented. Then a quick presentation on the setup will be followed by a more detailed discussion on the two detectors used. An emphasis will be put on a description of the FGTIC signal processing that tries to be complete. The dierent characteristics of the NaI array will be discussed, nally the acquisition system will be described.

Experimental method

Let's recall that the initial goal of this work was to measure the γ decay of ssion fragments to test the γSF and NLDs. Then the main constraint for the experimental setup was the identication of the ssion fragments as precisely as possible while having a γ detection as complete as possible. The use of a Frisch-Gridded Twin Ionization Chamber (FGTIC) is well suited for this type of study. It is a gaseous detector composed of a central cathode, on which the source or target is placed, facing two anodes on both sides. A Frisch grid [73] is placed between the cathode and anode to allow fast detection and proportionality between the deposited energy and the anode signal (see Sec.

0 = ±A L • E L ∓ A H • E H A i = A F N E j E i + E j i, j = (L, H) (2.1)
where A F N = A L + A H is the mass of the ssioning system and A L,H are the masses of the ssion fragments at scission. It allows multi-observables study since it gives access to (A L , A H , KE L , KE H , T KE) coincident measurements. In the case of ssion without neutron emission, the mass resolution solely depends on the energy resolution. As shown in [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF][START_REF] Oed | High resolution axial ionization chamber for ssion products[END_REF] the main limiting factor of this resolution is the straggling and energy loss inside the source backing. Therefore a thin backing is mandatory to get the best resolution in this regime.

Obviously when neutrons are emitted Equation (2.1) is not valid anymore. In order to reconstruct the pre-neutron quantities the ν (A, T KE) (dependence of the neutron emission on the fragments' masses and total kinetic energy, TKE) distribution must be assumed.

The resulting resolutions are 4 u.a for hot ssion (with neutron emission) and 0.54 for cold (neutron-less) ssion [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF]. Such resolution for cold fragmentation allows great selectivity on the mass but it is not sucient to perfectly identify the nuclei since the fragments charges remain unknown. This aw can be partially lifted by the detection of isomers with the γ-array. Isomers are meta-stable levels that produce a unique delayed decay allowing its identication in mass and charge.

The γ-array is made from thallium-doped Sodium-Iodide (NaI-Tl or NaI in the following) crystals. It was designed to cover the maximum of the solid angle around the FGTIC while having large detection volumes to detect the whole cascade , especially the high energy γ rays and use the prompt γ-spectra for comparison with simulations. Most of the γ-rays are emitted below S n but due to the γ-n competition [7880] some γ-rays of energies higher than S n can be produced. the NaI crystal caps were sitting on these crossing bars. Threaded rods were screwed through the bars from on end to the other to create quartering and maintain the distance between each bar with lock nuts. The most delicate part was to maintain the ceiling of NaI without putting any matter below the entrance side of the detectors. The solution found was to use a quartering similar to the one used for the oor. This time two bars were put in compression on the photomultiplier aluminum encapsulation (see Figure 2.1c). On each side of the NaI cube, aluminum bars were screwed together (or to the platform for walls) to maintain the integrity of the cube. The FGTIC was placed inside. Its centering was ensured by a 3Dprinted plastic support. The chamber was made compact to t inside the NaI cube, it is 13.5 cm long and 16.2 cm wide. The available space inside the cube was too small to put the charge pre-amplier of the FGTIC inside so they were placed outside. One NaI detector was slightly pulled out to leave space for the high-voltage of the FGTIC and the gas tubes.

All the output signals were sent to a FASTER [81] rack. Details on the acquisition system can be found at the end of this chapter.

Frisch-Gridded Twin Ionization Chamber

A Frisch-Gridded Twin Ionization Chamber is rather simple by design. It is a gaseous

detector composed of a central cathode facing an anode on each side with a Frisch grid [73] located close to each anode (a photo is shown in Figure 2.2a). Such design was rst described by O. Bunemann [START_REF] Bunemann | Design of grid ionization chambers[END_REF]. In the present work a 252 Cf source is placed between the two coppertapped electrodes making the cathode as can be seen in Figures 2.2b and 2.2c where a test 252 Cf source was placed in the cathode. This allows the two emitted fragments to travel separately in the gas in each side of the chamber and fully stopped before the grids. This section will discuss the interaction mechanism, the signal generation as well as the dierent eects that can reduce the signal amplitude and how to correct them.

Interaction of a heavy charged particles in a gas

A ssion fragment or an α-particle will interact in a medium mainly by Coulomb interaction with the electron clouds within the medium's atoms. The electrons will be pulled towards the charged particle and depending on the distance between the two, the electron might be moved to a higher-lying orbital (excitation) or teared completely from the atom (ionization).

Obviously the energy needed for the electron to be ripped o of the atom is taken from the charged particle, reducing its velocity. As stated in [START_REF] Knoll | Radiation detection and measurement 2 nd edition chapter 5[END_REF] the maximum energy E max that can be transferred to an electron of mass m e by a charged particle of energy E and mass m is:

E max = 4 m e m • E = 4 m e m n • E/A 1 500 • E/A (2.2)
With A the number of nucleons and m n the mass of a nucleon. One deduces that to lose all its energy the charge particle will have many such interactions. The quantity of interest for the electrical signals produced by an ionization chamber is the number of ion-pair (electronion pair) created along the track of the charged particle. The number of ion-pair created after the full stop of a charged particle is proportional to the kinetic energy and dened by the W-value. It is the average energy lost by the charged particle per ion-pair formed. At a minimum the charged particle must transfer an energy equal to the rst ionization potential to produce an ion-pair. For typical gases it is of the order of 10 to 20 eV. The W-value is systematically higher since the charged particle may lose its energy without ionizing the gas, one example being an excitation in the electron cloud. W-values for Argon, CH The fundamental limit in energy resolution for such detector will be given by the statistical uncertainty on the number of ion pairs created. The Fano factor is an empirical constant that translates this uncertainty. From the Fano factor and the W-value one can estimate this minimal energy resolution. Let us consider 5.5 MeV α-particles interacting in a P-10 gas. The Fano factor was measured for such gas mixture [START_REF] Kase | Fano factor in gas mixture of ar+10% ch4[END_REF] and is equal to 0.18. The mean number of ion-pairs n 0 is given by:

n 0 = E dep W = 5.5 • 10 6 26.6 = 2.068 • 10 5 (2.3)
The variance v is just n 0 multiplied by the Fano factor, and the energy resolution is:

FWHM α = 2.35 • √ v • W = 2.35 • √ 0.18 • n 0 • 26.6 = 12.06 keV (2.4)
Figure 2.3 shows the results of the response of one side of the chamber to a 3α-source. Each bump corresponds to the alphas of each nuclei ( 239 Pu, 241 Am, 244 Cm). To get the energy resolution each bump was tted with one gaussian per α energy. An additional peak is added for the 241 Am decay since its main α decay feeds a highly converted level of 237 Np, mixing this conversion electron to the deposited energy. It creates a shouldering near 5.53

MeV that needs to be taken into account. The standard deviation was considered constant over the short energy range. The resolutions measured were 36.4 and 35 keV for the two sides of the chamber for E α ∼ 5 MeV. There is clearly an additional eect than just the statistical uncertainty from the number of ion pair produced. Such eects are discussed in [START_REF] Kase | Fano factor in gas mixture of ar+10% ch4[END_REF] where they measured an energy resolution of 11.7 keV for 5.3 MeV α-particles. The main dierence between the two resolution is that in their work, Kase et al. worked with cryogenic electronics to reduce the electronic noise. From these α resolutions one can extrapolate them to the ssion fragment region. Indeed the resolution is proportional to √ E. The kinetic energy of a ssion fragment is of the order of 100 MeV which lead to an estimated resolution of FWHM FF ∼ 150 keV.

Signal induction

In order to pick up these ion-pairs, an electric eld is applied to the volume in which the charged particle has been stopped. This eld will separate the electron from the ion and the movement of both of them will induce a signal on the electrodes. A schematic view of the FGTIC is shown in Figure 2.4. There is two volumes to dene for a proper description of the FGTIC, namely the interaction volume (between the cathode and the grid) and the drifting volume (between the grid and the anode). In the ideal case the grid can be considered as a conductor plate but fully transparent to electrons. Let us derive the induced charges for the dierent electrodes.

Signal induction in the interaction volume

One can consider that the gas ionization by the charged particle (here a ssion fragment or α-particles) is instantaneous. Indeed the ionization time is of the order of a few nanoseconds whereas the drift velocity of electrons is a few cm • µs -1 [82], so their total drift time will θ: the angle between the track and the normal of the cathode. X = x/ cos θ the distance between the ionization point and the grid. ρ 0 (X): the charge density along the track. n 0 = ρ 0 (X)dX: number of ion-pairs created along the track.

V C : the cathode voltage.

-

→ E = V C D • - → u x :
the electric eld between the grid (grounded) and the cathode.

i g,C (t): the current induced by a moving electron on the grid and cathode respectively. Q g,C (t): the charge induced by a moving electron on the grid and cathode respectively.

-

→ v e : the electron drift velocity, its norm will be denoted v e .

t e = (D -x)/v e : the time for the electrons to get to the grid.

Finally, given the mass dierence between the electron and the ion, one can consider the ion to be static during the drift time of the electrons. Then only the movement of the electrons will be considered. The Shockley-Ramo theorem [START_REF] Shockley | Currents to conductors induced by a moving point charge[END_REF][START_REF] Ramo | Currents induced by electron motion[END_REF] states that the current on an electrode induced by a single moving electron is:

i = -e - → v e • - → E (2.5)
For the case of innite parallel plates, which can be applied here [START_REF] Ramo | Currents induced by electron motion[END_REF], Equation (2.5) be-

comes: i = - ev e D (2.6)
The complete derivation can be found in [START_REF] North | Analysis of the eect of space charge on grid impedance[END_REF] and will not be exposed here because, as it is said in [START_REF] Ramo | Currents induced by electron motion[END_REF] : "In [START_REF] North | Analysis of the eect of space charge on grid impedance[END_REF] it is stated that this same result is deduced from image theory. This involves the setting up of an innite series of image charges on each side of the plates for a given position of the electron and a consideration of the total ux crossing one of the planes due to the series of charges, a method which is lengthy and requires no little familiarity with methods of handling innite series.". Then the induced current on both the grid and the cathode can be expressed as (-for the grid, + for the cathode):

i g,C (t) =    ∓e v e D for t < t e 0 for t t e (2.7)
where t e is the time for the electron to reach the grid. By integrating this current one can obtain the induced charge over time:

q g,C (t) =    ∓e v e D t for t < t e ∓e 1 - x D for t t e (2.

8)

The charge increases linearly with time until the electrons are captured by/pass through the grid. Then the total charge induced by a single electron on both electrodes is:

q tot g,C = ∓e 1 - x D (2.9)
To get the charge induced by the whole track one needs to integrate q tot g,c over X:

Q g,C = ∓ ρ 0 (X) e 1 - X D cos θ dX = ∓n 0 e 1 - X D cos θ (2.10)
where X = 1/n 0 Xρ 0 (X)dX. The total charge induced by electrons moving in this volume is dependent on the track direction. Therefore those signals are not directly proportional to the deposited energy.

Signal induction in the drifting volume

The electrons created in the interaction volume drift towards the grid and, as stated before, the grid is considered to be transparent to electrons. Then, to describe the induction in the drifting volume, one can consider that these electrons are generated at the surface of the grid with a density ρ 0 . This means that the induced charge on the grid and the anode is the same as Equation (2.10) but with θ = 90°(electrons generated parallel to the grid). The charges on the anode and grid are:

Q A = -n 0 e Q g = n 0 e (2.

11)

Finally the total charges induced on all three electrodes are:

             Q A = -n 0 e Q G = Q g + Q g = n 0 e X D cos θ Q C = n 0 e 1 - X D cos θ (2.12)
This highlights the importance of the Frisch grid that shields the anode from angular correlation on the anode's induced charge. Indeed without the grid the detector only corresponds to the interaction volume and the charge induced on the anode would be Q A = n 0 eX cos θ/D.

Obviously Equation (2.12) only works in a perfect setup where no electrons are lost in their migration and where the grid can perfectly shield the anode. The following sections will discuss the various phenomena that can induce a loss of information, starting with the natural imperfections of the grid used.

Grid transparency and ineciency

When discussing the signal induction in Sec. 2.3.2 two assumptions were made on the grid: it is fully transparent to electrons and it is perfectly shielding the anode from anything happening between the grid and the cathode.

While the former can be obtained, the full shielding is not possible and needs to be corrected.

Grid Transparency

It is essential for the good operation of the FGTIC that all electrons created along the track induce all their charge on the anode. It means that none should be caught by the grid wires. The optical transparency of the grid is a great asset but not sucient. The grid used in this study was made with wires of 30 µm diameter and a spacing of 470 µm. Then an elementary mesh will have (30 × 470 + 30 × 500) / (500 2 ) = 12% of its total area covered by wires. Considering that electrons follow the electric eld lines upstream, if the electric eld is the same on both sides of the grid then 12% of the electrons would end up on the grid and not induce a signal on the anode. To avoid such capture one must nullify the crossing of electric eld lines with the grid wires. This was studied in [START_REF] Bevilacqua | A procedure for the characterization of electron transmission through frisch grids[END_REF] for two types of mesh grids with one (mesh 2 in [START_REF] Bevilacqua | A procedure for the characterization of electron transmission through frisch grids[END_REF]) extremely similar to the ones used in this FGTIC. They measured the evolution of alpha peaks with respect to the eld ratio R:

R = V A -V G V G -V C • D CG D AG (2.13)
with:

V A , V G and V C the anode, grid and cathode voltage respectively, the grid is grounded, D CG and D AG the cathode-grid and anode-grid distance respectively.

They found that the nominal pulse height was attained for R > 2.5. A similar work was done for this chamber with a 3α-source and is shown in Figure 2.5: the cathode voltage was xed at -1600 V and the anode voltage was increased, displaying a plateau above V A = +1000 V, corresponding to a eld ratio of 2.6 which is consistent with [START_REF] Bevilacqua | A procedure for the characterization of electron transmission through frisch grids[END_REF].

Grid Ineciency

By construction the grid cannot provide a perfect shielding. O. Bunemann et al. [START_REF] Bunemann | Design of grid ionization chambers[END_REF] were the rsts to theorize the concept of "grid ineciency" (GI, noted as σ) which characterizes the imperfection of the grid's shielding. They dene this ineciency as how much the induced charge on the anode depends on the electric eld at the charge creation point, x 0 . By supposing that the number of collected electrons is equal to the surface density of eld lines crossing through the grid, E A , one can express the grid ineciency σ as:

σ = dE A dE x 0 for V A -V G constant (2.14)
From their derivations [START_REF] Bunemann | Design of grid ionization chambers[END_REF] they obtained an expression depending only on geometrical parameters of the FGTIC: δ is the distance between two wires, r the radius of a wire, ρ the linear wire density.

σ = l l + p (2.
This expression was derived for a wire grid, but nowadays mesh-grids are more commonly used and it is not trivial how to change Equation (2.15) and Equation (2.16) to describe a mesh grid. R. Bevilacqua et al. [START_REF] Bevilacqua | A procedure for the characterization of electron transmission through frisch grids[END_REF] did measurements in this objective and concluded that the only change was on ρ according to this empirical relation (for the same δ and r on the wire and mesh grids):

ρ mesh ρ grid 2 (2.17)
This can also be interpreted via symmetry conservation. Usually FGTIC are cylindrical meaning that they are invariant to rotations around their axis. Then the same goes for the mesh-grid. One can describe a mesh-grid as a superposition of two wire-grids with one rotated by 90°. Then the properties of the FGTIC should be unchanged whether one is rotated or not. This leads to consider that a mesh-grid can be described by a wire-grid with a linear density twice larger. The linear wire density for the grid used here is 0.8. This results in a grid ineciency σ of 4.75 • 10 -3 .

The way to consider this ineciency and properly correct it was just recently formalized by A. Göök et al. [START_REF] Göök | Application of the shockleyramo theorem on the grid ineciency of frisch grid ionization chambers[END_REF] and experimentally conrmed the same year by A. Al-Adili et al. [START_REF] Al-Adili | Ambiguities in the gridineciency correction for frisch-grid ionization chambers[END_REF].

They applied the Shockley-Ramo theorem while considering the GI eect on the anode.

This changes Equation (2.7) (only in the drifting volume) to (+ for the grid,for the anode):

i GI g ,A (t) =            ±σe v e D for t < t e ± (1 -σ) e v e p
for t e t < t e 0 for t t e

where t e is the time for the electron to reach the grid, t e the time for the electron to reach the anode. The (1 -σ) factor ensures that the induced charge is at most equal to e. Then the induced charges are:

q GI g ,A (t) =              ±σe v e D t for t < t e ± (1 -σ) e v e p t + σe 1 - x D for t e t < t e ±e 1 -σ x D for t t e (2.

19)

After integration over the charge density one gets the following changes to Equation (2.12):

                 Q GI A = -n 0 e 1 -σ X D cos θ Q G = Q g + Q GI g = n 0 e (1 -σ) X D cos θ Q C = n 0 e 1 - X D cos θ (2.20)
This description formalizes the angular dependence of the anode signal. This dependence must be removed if one wants to preserve the proportionality between the deposited energy and the anode signal. Note that the cathode signal holds the same dependence as the anode if multiplied by σ. Then:

Q GI A -σQ C = -n 0 e (1 -σ) (2.21)
By dening Q corr A = -n 0 e one gets the nal expression for the GI corrected anode signal:

Q corr A = Q GI A -σQ C 1 -σ (2.22)
When two particles are emitted from the source simultaneously the cathode signal will hold the angular dependence of the two particles, which cannot be disentangled. It cannot be used to correct the anode signal. Fortunately the individual induced charges can be reconstructed from the grid and anode signals:

Q Σ = Q GI A + Q G = -n 0 e 1 -σ X D cos θ + n 0 e (1 -σ) X D cos θ = -n 0 e 1 -σ X D cos θ + (σ -1) X D cos θ = -n 0 e 1 - X D cos θ = -Q C (2.23)
So Equation (2.22) becomes:

Q corr A = Q GI A + σQ Σ 1 -σ (2.24)
However if the grid signals are not saved during the acquisition (which was the case for this experiment) such correction is not possible. The only choice available is to use an approximate correction: as stated before, the grid ineciency is of the order of few 10 -3 then:

Q corr A = -n 0 e = Q GI A 1 -σX/D cos θ σ 1 Q GI A 1 + σ X D cos θ (2.25)
The cos θ is not an observed quantity so Equation (2.25) can be written dierently to depend only on measured quantities. Let ∆T be the time dierence between the cathode and the anode signals. One can consider that the induction of a signal on the cathode is instantaneous. The anode signal will kick o when the rst electron crosses the grid. This electron is the one created furthest away from the cathode since the electron drift velocity is constant in each volume. Then if the range of the emitted particle is denoted R:

v e ∆T = R cos θ (2.26)
From this Equation (2.25) can be rewritten as:

Q corr A σ 1 Q GI A 1 + σ X R v e D ∆T (2.27)
where each ingredient can be measured, except for X. However, A. Göök et al. [START_REF] Göök | Particle emission angle determination in frisch grid ionization chambers by electron drift-time measurements[END_REF] proposed to approximate the ratio X/R with a constant, equal to 0.34. SRIM [START_REF] Ziegler | Srim -the stopping and range of ions in matter[END_REF] calculations were made to verify this approximation by calculating the energy lost by dierent ions in the range of ssion fragments as a function of the distance traveled in the gas. Figure 2.6

shows dierent energy loss computed with SRIM for a light and a heavy fragment. The total distance traveled is simply the last bin where the fragment has deposited some energy.

Since the number of charge carriers is proportional to the deposited energy, the charge barycentre is equal to the deposited energy barycentre. This mean position will depend on the energy deposition prole in the gas, that can greatly change according to the nucleus, as depicted in Figure 2

σ X D cos θ = σ X D cos θ = 6 • 10 -4
(2.28)

In this experiment the mean energy lost in the backing is around 300 keV (see Sec. 3.2.2), which means that for an average kinetic energy close to 100 MeV for ssion fragment the energy loss correction will be of the order of 3 • 10 -3 whereas the grid ineciency account for ve times less. Therefore in the present work the grid ineciency is negligible and not corrected for.

Time measurement

From Equation (2.26) the cos θ distribution can be extracted from the cathode-anode time dierence. This is the only option in this work since the grid signal was not in the acquisition.

Otherwise one could extract the cosine from:

cos θ = D X • Q corr A -Q Σ Q corr A (2.29)
Therefore the experimental uncertainty on the cosine distribution will come from the time measurement of the cathode and the anode. The way to derive the R/v e ratio will be explained in details later on (see subsubsection 3.2.2.1). There are two main categories of eects leading to timing uncertainties namely the walk and jitter eects. The walk eect mainly originates from the amplitude changes of the input signal. Figure 2.7a (from [START_REF] Knoll | Radiation detection and measurement 2 nd edition chapter 5[END_REF]) describes this eect: for a given threshold two signals with dierent amplitudes will get a (a) 86 Se.

(b) 158 Sm. dierent time measured since the lower one will exceed the threshold value at a later time.

The jitter usually comes from the electric noise picked-up in the dierent components, as shown in Figure 2.7b the threshold can be momentarily exceeded inducing a random broadening of the measured time. Jitter eects are always present (unless working with cryogenic electronics) but can be reduced to some extent (∼ 1.5% of the amplitude for this work) mainly by shielding the electric components. Depending on the characteristics of the signal, the walk eect can be greatly reduced by using a constant fraction discriminator (CFD). A CFD creates a bipolar signal from the input one that crosses zero when the signal is at a given amplitude fraction. Therefore this zero-crossing point is independent of the signal amplitude. This is true only if the signal rise time is constant for all pulses. This is the case for the cathode signal which timing was taken with a CFD, but it does not apply to the anodes signals. Indeed the rise time of the anode is schematically given by the time dierence between the rst electron arrival at the grid and the arrival of the last one at the grid. This time dierence is obviously longer for tracks perpendicular to the grid than for parallel ones. Then only a leading edge timing is reasonable. Leading edge timing is quite sensible to the signal amplitude, therefore the trigger level needs to be as close to the baseline as possible while being in a region of steep slope. Here the level was at 2 mV, just above the baseline.

Energy-loss in the source backing

As discussed before, the FGTIC only measures induced currents and charges that are proportional to the deposited energy. Then all other observables that can be reconstructed will be based on the deposited energy and its resolution. The latter will be one of the determining factors for the resolution of the other observables [START_REF] Oed | High resolution axial ionization chamber for ssion products[END_REF].

It is not possible to build a freestanding 252 Cf source due to its high activity therefore the 252 Cf needs to be deposited on a backing. As described in Figure 2.8, during the spontaneous ssion of 252 Cf, the two fragments end up on both sides on the chamber, meaning one has to go through the backing. By traveling through it the fragment will interact and lose some of its energy. This is a quantity that cannot be measured by the FGTIC but it can be corrected afterwards with the help of a SRIM [START_REF] Ziegler | Srim -the stopping and range of ions in matter[END_REF] calculation for example. However trying to reduce this oine correction can be useful as described by L. Gaudefroy et al. in [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF]:

thanks to an ultra-thin backing (10µg/cm 2 ) they were able to see ssion events with no neu- tron emission on the raw data. In the case without neutron emission (or cold ssion), the momentum conservation law straightforwardly gives a relation between the kinetic energies and the masses of both fragments:

- → 0 = -→ p L + -→ p H (2.30) ⇒ m L E L = m H E H (2.31) ⇔ E L E H = m H m L (2.32)
Equation (2.32) can be graphically translated by straight lines when looking at the 2Dhistogram Anode vs Anode (see Figure 2.9). One clearly sees that such lines are well dened and separated. Here the mass resolution depends only on the energy resolution leading to a FWHM of 0.54 a.m.u. [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF]. This encouraged the laboratory to pursue its eorts in making an even thinner backing.

Manufacturing of the source

The source was manufactured in the same way as [START_REF] Pauker | Transfer properties of 252cf and their use for source preparation[END_REF]. A carbon foil of 5 µg/cm 2 was prepared. It was reinforced by 5 to 10 nm of Formvar (a polymer) to gain in sturdiness. This backing (twice thinner than in [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF]) yielded promising results. The cold ssion can now be seen on both side of the anode vs anode histogram (see Figure 2.9). In [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF] the cold ssion was seen on the raw data for events where the light fragment pass through the backing (less energy lost than for the heavy one). Here even when the heavy fragment travels through the ultra-thin backing the energy lost is suciently small to still see the lines. One can translate this in terms of resolution. In both [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF] and this work the α-resolution is 35 keV, giving an energy resolution of 150 keV for the ssion fragments. For simplicity the sample will be considered on the surface, meaning that one fragment will travel through the whole thickness of the backing whereas the other will immediately travel through the gas. Then the uncertainty on the energy of the fragment going through the backing will be:

σ E H,L = σ α + ∆E H,L (2.33)
Where σ α = 67 keV corresponds to the energy uncertainty for ssion fragments extrapolated from the α-resolution and ∆E H,L is the energy lost in the backing. From Equation (2.1) one can evaluate the mass uncertainty as :

σ A L,H A L,H = σ E H,L E L + E H 2 + σ 2 E L,H • 1 E 2 L,H + 1 (E L + E H ) 2 - 2 E L,H • (E L + E H ) (2.34)
Then this mass uncertainty can be computed for both fragments traveling through the backing and for both backings. The results are summarized in Table 2.3. It is clear that the reduction of the backing thickness has an important eect on the mass resolution. Moreover if one consider that two gaussian peaks G 1 (x, m 1 , σ) and G 2 (x, m 1 +1, σ) are distinguishable when the sum of the two is at most at half-maximum for m = m 1 + 0.5, then it imposes σ A 0.3. This criteria is almost satised in [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF] when the light fragment passes through the backing but fully satised in this work for both cases. It highlights the need to reduce the energy lost in the backing. In reality both sides will be corrected for energy loss because the 252 Cf atoms migrates through the backing.

Electron recombination

Loss of information can also occur by the capture of electrons in the gas. There are mainly two recombination eects that need to be looked at for tuning the FGTIC: the columnar recombination and the capture by impurities.

Columnar recombination

This phenomenon was rst theorized by G. Jaé [START_REF] Jaffé | Zur theorie der ionisation in kolonnen[END_REF] in 1913. When a charged particle travels through a gas (or a liquid) the ion-pairs form a column along the track. The width EDIFIS [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF] This work of this column is given by the mean free path of the electrons. It will diuse in the gas and the number of ion-pair will decrease due to recombination. This eect is limited due to the electric eld, but the eld intensity might not be able to prevent all the recombination.

Indeed depending on the angle between the eld and the track the recombination will be more or less important (see Figure 2.12). If the track is perpendicular to the electric eld then the interaction probability between the ions and the electrons is minimized. On the opposite when they are parallel the probability is maximum since the electrons created upstream will be drifting towards the anode, following the ionization track where the positive ions are (see the left hand side of Figure 2.12). This recombination eect can be suppressed by increasing the eld intensity.

Gas impurities

If the gas possesses electronegative impurities such as O 2 they can capture the drifting electrons. Obviously such eect depends on the impurities concentration and the distance traveled by the electron in the gas. This will induce a higher decrease in pulse height for electrons created close to the cathode than for those created close to the anode. Similarly to the columnar recombination, by increasing the eld strength one can avoid the electrons attachment to the impurities.

(a

) V C = -500 V (b) V C = -2300 V

4π-NaI array

Coupled to the FGTIC is the set of 54 NaI detectors that will measure the γ-rays produced by the decay of the ssion fragments. The dierent characteristics of such array are discussed in the following.

Description

This array was developed to maximize the detection eciency while having all the detectors facing the source. This array is made of [START_REF] Ignatyuk | Phenomenological description of energy dependence of the level density parameter[END_REF]

Calibration

A calibration of the array was performed by putting several radioactive sources in the center of the array ( 22Na, 60 Co, 65 Zn, 137 Cs, 139 Ce, 152 Eu, 207 Bi, 241 Am). Each detector was calibrated independently: an example for the NaI n°102 is shown in Figure 2.14a. The resolution for all the detectors is between 6 -7% for the 137 Cs 662 keV γ-ray, usual for NaI crystals and in agreement with the constructor data. This type of scintillator is known to have a good linearity [START_REF] Knoll | Radiation detection and measurement 2 nd edition chapter 5[END_REF], as can be seen in Figure 2.14c. The highest calibration point is From these calibrated spectra one can determine the energy resolution for the various discrete γ-rays. As always the standard deviation varies similarly to the square root of the energy. Still for scintillators detectors a more accurate description is given by [START_REF] Knoll | Radiation detection and measurement 2 nd edition chapter 5[END_REF]:

σ = α • E β + γ (2.35)
Such tting procedure was done with this data set for its implementation in the simulation code and is shown in Figure 2.15. The green dots are the standard deviations for reference peaks and the purple line is the t using Equation 2.35. The nal value for the β is 0.42.

Time resolution

The time resolution was determined with the coincident measurement of the two γ emitted by a 22 Na source between the NaI and a LaBr 3 detector, known for its excellent time resolution. The full width of the time distribution is 5.4 ns as shown in Figure 2.16.

Geant4 simulation

In the following, γ cascades will be computed with various de-excitation codes. To compare it with the measurements the choice was made to convolute the calculated spectra with the detector response. The whole detection setup was simulated with Geant4. It is a Monte-Carlo code (C++) dedicated to the simulation of various interactions between radiations and materials [START_REF] Agostinelli | Geant4a simulation toolkit[END_REF]. Very little work was done with this simulation tool since O. Roig had already implemented the full geometry of the NaI and the setup . Simulated responses for usual sources are shown in Figure 2.17. The simulated spectra are an overall good reproduction of the experiment. However a systematic shift is observed between the experimental compton edge and the simulation, it was previously seen in [START_REF] Tam | Optimization of the monte carlo simulation model of nai(tl) detector by geant4 code[END_REF][START_REF] Grozdanov | Semi-empirical gamma-ray response function of bgo, nai(tl) and labr3(ce) scintillation detectors[END_REF]. Here it will not be corrected since the γ-spectra that will be compared will come from multi-cascade events where the continuum part of the cascade will dominate, erasing such discrepancies. Running Geant4 is quite costly so to limit this time consumption a convolution matrix was done. It was realized on a basis of 10 keV and compared, for the same input le, with a full Geant4 computation. Figure 2.18a shows the result for a 152 Eu cascade using the convolution matrix and the Geant4 simulation. A pretty good agreement is obtained with a slight shift from the matrix use due to the bin size of this matrix. This can be overcome be linearly interpolating the matrix elements: the intensity of a γ of 105 keV will be equally divided between the bin of 100 keV and the bin of 110 keV, whereas a γ of 107.5 keV will contribute at 75% to the bin of 110 keV and only 25% to the bin of 100 keV. Then by including this weighting in the product of the raw spectrum with the matrix in Figure 2.18b one can perfectly reproduce the full Geant4 simulation. show the relative dierence and its dispersion between the two convolution methods. This dierence is contained within 5% with a gaussian-like distribution as highlighted by the red curve in Figure 2.18d. It translates the fact that the Geant4 simulation mimics the physical process for a given statistic while the matrix convolution is an averaged one, smoothing the statistical errors. One can now convolve within a second using the interpolation of the matrix when it takes around 10 min for the full Geant4 simulation (for 10 6 events).

Acquisition system 2.5.1 FASTER

The FASTER [81] system is developed at LPC Caen by D. Etasse and his collaborators. It is meant to be modular and versatile for nuclear physics experiment. It is a fully digitized acquisition system allowing diverse triggering conditions and online basic data visualization.

The modularity of the system is due to the two types of cards (MOSAHR and CARAS) developed, that can be connected to a single motherboard allowing clock synchronization between the daughterboards.

The daughterboards used in this experiment were MOSAHR ones. It is a 14-bit digitizer designed to process signals from charge pre-ampliers (CPA). It is mainly used in nuclear spectroscopy with silicon, HpGe detectors or ionization chambers. It specializes in precise energy measurement. Two lters are implemented, a CR-RC 4 and a trapezoidal one, espe- cially ecient on detectors with a ballistic decit. It corresponds to detectors for which a

Trigger system

The FASTER acquisition possess a near-online triggering module. The computer sorts the signals from the daughterboards by their synchronized timestamps and keeps this ow in a buer. A triggering condition is either a boolean expression (e.g. "(channel 1 AND channel 2) OR channel 3 " ) or a multiplicity trigger (e.g. "AT LEAST/EXACTLY/AT MOST 2 in channel 1, 2, 3 "). One can dene follower labels that are channels not present in the triggering condition but that still need to be grouped with it. Once a triggering condition is met in the ow, FASTER will group together every follower data that is within a userdened time window (e.g. -100 ns to 10 µs) and the triggering channels and write it on disk. If one wants to write all the data ow on disk and not just the triggered ones one needs to use the so-called "lossless trigger" mode. It groups the events that needs to (ie.

triggered ones) and write them, along all the other ungrouped events. In this experiment the triggering condition was the FGTIC, all the NaI were followers and the lossless trigger mode was used.

Electronics and gas handling

Each FGTIC electrode was connected to CAEN MOD 1422 charge pre-ampliers (CPA).

The output signals from the CPAs were sent to the faster acquisition. Since the FGTIC is quite compact, the gas pressure inside had to be higher than the atmospheric one. Moreover two pressures and voltages setups were used to measure either the ssion fragments or the α-particles: the longer the track, the better the cosine resolution. The gas used was a P-10 mixture (90% Ar, 10% CH 4 ) at 1.5 bars for the ssion fragments (V C = -1800V, V A = +1500V) and 2 bars for the detection of α-particles (V C = -1700V, V A = +1400V).

The gas was owing with a speed of 0.1L.min -1 , ensuring a permanent renewing of the gas in the chamber.

Chapter 3

Data analysis

The previous chapter focused on the presentation of the experimental setup and the signal processing of the FGTIC. This chapter is its continuation where the complete analysis of both NaI and FGTIC will be described. At rst the discussion will focus on the corrections implemented to conserve the time and energy alignments of the NaI detectors between each other and through the whole acquisition time. Then the analysis of the FGTIC will be extensively described. A general description of the goal and diculty of such analysis will be presented followed by the description of the dierent corrections that need to be taken into account before calibrating the kinetic energies. Then the estimation of the neutron evaporation and its impact on the observables will be discussed. The way to isolate the ssion events without any neutron emitted will be addressed afterwards followed by a comparison of the observables measured in this experiment with the literature. Lastly, the isomer identication process will be presented.

NaI analysis

This section will discuss the time and energy alignment procedures of the NaI crystals which are mandatory requirements to treat the whole array as a single detector.

Time alignment

From this point onward all the detectors time will be the time dierence between the timestamp for the detector of interest and the timestamp of the FGTIC cathode. The choice of such reference is explained by the fact that the cathode signal kicks o as soon as fragments are emitted and mark the t 0 of the ssion event. Then the rst step of the analysis of the NaI-array is to align the prompt γ-peak with the ssion t 0 . Indeed the emission of prompt particles (γ or neutrons) is done in a mere 10 -17 s, which is instantaneous considering the resolution of a few nanoseconds of the NaI. The evolution of the mean position of this prompt γ-peak during the whole experiment is shown in

Gain monitoring

The last chapter described the calibration procedure done prior to the experiment. However in a data acquisition of six months it is inevitable for the gains to change over time, be it from electronic instabilities, temperature dependence or aging of the detectors. As for two channels from the same daughterboard, relative to a reference one (channel 1). This retrace the life of the experiment, especially all the issues that occurred. One can see that for almost half of the time the gains were steadily drifting but at some point channels were detectors have a drift within 5% while a few go up to 10%. This drift will induce minimal loss in resolving power on each channel. Figure 3.4b displays the same drift but this time with a common reference for every channel. This highlights the systematic shifts between the NaI. It is understandable since all detectors were calibrated independently. This mismatching may reduce the resolving power when adding all individual spectra. Therefore this procedure of gain matching was mainly a way to align the dierent NaI detectors together since the variations for a single detector is small for 6 months of acquisition. The red curve in Figure 3.4b is a great example to see the temperature dependence of the NaI crystals [START_REF] Moszy«ski | Temperature dependences of labr3(ce), lacl3(ce) and nai(tl) scintillators[END_REF].

The room temperature was never properly monitored therefore day-night temperature variations can be seen as oscillations of the gains around the mean drifting tendency, however they are negligible. The eect of this gain matching is represented in Figure 3.5. Figure 3.5a shows the evolution of the neutron delayed peaks without gain correction for a single crystal between the rst and last day. A displacement of the mean position of the peak is observed, slightly reducing the resolution power. The spectra shown in Figure 3.5b are gated on the delayed radiation, where the room background can be seen, for the whole array. The gain matching has little eects except for the 2.7 MeV peak for which a small increase of the resolving power is seen.

Neutron pollution

NaI detectors are known to be sensitive to neutrons [START_REF] Häusser | The prompt response of bismuth germanate and nai(tl) scintillation detectors to fast neutrons[END_REF]. Due to the compact geometry of the setup a mixing between the prompt γ and the neutrons can occur, it needs to be quantied. The delayed bump in Then the neutrons interact in the NaI crystals mainly by inelastic scattering on 127 I. The neutron and prompt γ peaks are rather distinct above 400-500 keV but there is a clear mixing below, due to the broadening of both peaks. The prompt peak will be selected by a time window, so this window needs to be properly tuned to minimize the neutron mixing. The time distribution can be described with a gaussian shape (prompt γ), a maxwellian distribution (neutrons), expressed as:

M (t) = a • (t -m ) 2 • e -(t-m ) 2 /2σ 2 M σ 3 M (3.1)
and an exponential decay for the delayed radiations. To help the convergence of this tting procedure the exponential parameters were xed via a t on the time range [30; 60] ns or [20; 40] ns. Each parameter was constrained to avoid any divergences or nonphysical solutions. The total t function used was:

f (x) =                      a • e - (t -m) 2 2σ 2 + c for t < 0 ns a • e - (t -m) 2 2σ 2 + M (t) + c for 0 t < 3 ns a • e - (t -m) 2 2σ 2 + M (t) + b • e λt + c otherwise (3.2)
This quite simplistic description does not really describe the reality but oers a good estimate with only 7 free parameters (b, λ previously determined). Such tting procedure is shown in Figures 3.8a3.8d for 500 keV intervals. The neutron bump is unambiguously identied above 500 keV but the lower the γ energy, the harder it is to distinguish a clear separation between the neutron bump and the prompt peak. Obviously the tail above 20-25 ns is not well reproduced by this t, even more at high γ energy since the neutron bump is more pronounced and that a maxwellian is too simple to describe it. The region of interest is between 0 and 15 ns where the mixing will occur. In this region the t displays a rather good description of the data for every selection made. Of course the addition of the exponential introduces a discontinuity at t = 3 ns. However this does not have any signicant impact on the t quality in the prompt γ and neutron region. From this t one can extract the percentage of prompt γ and neutrons selected by a given time window. The evolution of this ratio of neutrons present in the time window, referred as neutron mixing is shown in Figure 3.9a for dierent time selections. The increase of this mixing with the decrease of the γ energy is conrmed and quantied for the dierent time windows. The mixing is below 10% for every selection but a reduction by a factor 2 can be achieved by going from |T | < 5 ns to |T | < 4 ns while keeping the rejection of prompt γ below 10% for the majority of the spectrum, with a maximum around 20% for E γ < 150 keV as shown in Figure 3.9b. Going from |T | < 4 ns to |T | < 3.5 ns reduces the neutron mixing by a quarter while signicantly increasing the prompt γ rejection. The use of the time window of 4 ns was judged as the optimal one since it allows a correct neutron rejection (94% on average) and a great prompt γ selection (95% on average). Therefore in the following the prompt γ spectra will correspond to a time selection of 0 ± 4 ns. Finally the detection eciency due to this time selection is energy dependent so it will need to be taken into account for the convolution of calculated spectra with the Geant4 matrix.

FGTIC analysis

This section will focus on the dierent methods and procedures used in the present work to extract the observables of interest (KE, TKE and masses of the ssion fragments) from the FGTIC signals. Firstly a brief overview of the analysis will be given, highlighting the dierent cruxes of such work. Then the determination of the energy lost in the source backing will be discussed with the help of the cold ssion regime. After that the calibration procedure will be extensively developed as well as the way to estimate the number of neutrons emitted where dierent methods will be confronted. Finally the present work will be compared to the literature on a various set of observables.

Analysis procedure

The challenge of using a FGTIC is not in its design but in the treatment of the data mainly because one needs to correct eects that depends on the fragment's properties on an eventby-event basis without measuring them. The main observable that needs to be reconstructed is the mass of the fragments. The 2E-method is based on:

A pre L,H = 252 • KE pre H,L KE pre H + KE pre L (3.3)
where the pre labels corresponds to observables before the neutron emission. These quantities cannot be measured since the neutrons are emitted around 10 -17 s after the scission.

Then:

KE pre H,L = KE post H,L A pre H,L A pre H,L -ν H,L (3.4)
with ν H,L the number of neutrons emitted by the heavy or light fragment, and KE post H,L its kinetic energy after the neutron emission. The latter is the quantity that can be measured in the FGTIC. However the fragment travels through a backing and in a gas so the energy deposited by ionization is:

E ion. H,L = KE post H,L -∆E H,L A post H,L , KE post H,L -P HD A post H,L , KE post H,L (3.5)
with E ion. being the deposited energy in the FGTIC, δE the energy lost in the backing. The Pulse Height Defect, P HD, originates from all the non-ionizing collisions that do not contribute to the deposited energy but take some energy from the fragment. Finally E ion. is measured by the charge induced on the anodes by the drift of the electrons in the gas. The measured quantity is then a pulse height P i proportional to E ion. . Therefore this analysis needs to start from P i and reconstruct pieces by pieces the pre-neutron masses. This is quite challenging since the data only contains this pulse height and nothing else. All the corrections that need to be done are impossible to determine event-by-event, only mean quantities can be used. = P i + δE/ cos θ) and then calibrate the deposited energies on the literature (K E app i = i P corr i + β i ). From these apparent energies KE app one can estimate the pulse height defect that creates a rst estimate of the post-neutron energies and masses. Then comes a real crux: taking care of the neutron emission. Here a ν (A) or ν (A, T KE) dependence must be assumed. This step is recursive and will be extensively described and discussed in the following. Then the last step is to check the consistency of this whole procedure with the literature or other requirements which can induce changes at several steps, making this analysis inter-dependent and recursive. These interactions are an aftermath of the inter-dependence of the dierent corrections: both neutron emission and PHD hold mass and kinetic energy dependencies. Since they are needed ingredients as well as what is determined through the analysis a lot of back and forth checks and recursions are required. Each step will be thoroughly discussed, starting with the energy lost in the backing.

Calibration

Energy lost in the backing

From the Bethe-Block formula [START_REF] Knoll | Radiation detection and measurement 2 nd edition chapter 5[END_REF] the energy lost in a given material depends mainly on the charges of both the particle and the material, the distance traveled inside and the initial energy of the particle. The ssion fragments will be emitted at a certain angle from the normal of the cathode, meaning that the distance traveled in the backing will be inversely proportional to the cosine of this angle.

Cosine distribution

From Equation (2.26) the way to reconstruct the cosine distribution is via the electron drift time. It was emitted by the source and traveled a distance R (its range) in the interaction volume with an angle θ from the normal. The fragment will continuously ionize the gas along its trajectory and be fully stopped in mere nanoseconds. As soon as the electrons start drifting, an induced signal is generated on the cathode. The electrons created at the end of the track will be the rst ones to reach the grid since the electron drift velocity is constant (∼ 5 cm • µs -1 ) and the ionization is regarded as instantaneous. Once they attained the grid they immediately induce a signal on the anode. Therefore the time dierence between the cathode and the anode, ∆T is a measure of the distance d:

∆T = d v e (3.6)
with v e being the electron drift velocity. Therefore ∆T can also be related to the angle θ:

D = d + R • cosθ (3.7) ⇔ v e • ∆T = D -R • cosθ (3.8) ⇔ ∆T = D -R • cosθ v e (3.9)
Because of the geometry on the cathode, depicted schematically in Figure 3.12, there exists a maximum angle of emission. Indeed if the fragments are emitted at a greater angle they will hit and interact with the cathode, losing all or a part of their energy before reaching the interaction volume. In this experiment the two values are θ max

2 82°and θ max 1 86°. θ 1 max θ 2 max { Cathode Backing
Figure 3.12: Schematic view of the cathode, centered on the part where the source is laying.

The two limit conditions to Equation (3.9) are then:

       ∆T (θ = 0) = D -R v e ∆T (θ = θ max ) = D -R • cosθ max v e (3.10)
D v e can be expressed as T 0 , the time needed for an electron emitted on the cathode to drift all the way to the grid. Therefore:

cosθ = v e R • (T 0 -∆T ) (3.11)
The cosine distribution is well dened if R/v e and T 0 are known. From Equation (3.10), R/v e and T 0 can be expressed only with time measurements between the cathode and the anode. The drift velocity is xed by the electric eld applied and the gas pressure in the system. The range of a fragment in a gas is dened through the Bethe-Block formula [START_REF] Knoll | Radiation detection and measurement 2 nd edition chapter 5[END_REF] and is dependent of the mass and the charge of the fragment and the medium it is traveling in. The mass and charge of the medium is xed since the fragments are traveling through a single gas mixture. The range will then only depend on the fragment's kinetic energy and charge.

Figure 3.13a shows the anode pulse height versus the cathode-anode time, with the two angular limits represented as red curves. The two bumps come from the light and heavy fragments that have dierent mean kinetic energies. For angles grazing the cathode (close to ∆T ∼ 500 ns) one sees the pulse height reduced. In this case the distance traveled in the backing is increased several folds and the fragment may hit the cathode losing even more energy. A small correlation between the pulse height and the ∆T is seen in Figure 3.13a.

This correlation is not understood. It could be due to electron capture on impurities, however the electric eld was already increased until a plateau in the pulse height was achieved, as described in Sec. 2.3.6. The energy loss depends on the ssion emission angle, therefore on the time between the cathode and the anode. However such slope is not consistent with just this eect, as detailed later. Properly and systematically identifying the ∆T (θ = 0) and ∆T (θ = θ max ) limits will allow the cosine calibration. To do so for each pulse height value the half-maximum values for N < N max /2 and N > N max /2 are determined as in Figure 3.13b. These two points then determines ∆T (θ = 0) and ∆T (θ = θ max ). Time alignment The time dierence between the cathode and the anode depends on the fragment's properties but also on the properties of the gas itself. Then if the purity of the gas is changing during the experiment it will aect the electron drift velocity and the T 0 and R/v e . Therefore the evolution of the cathode-anode time was followed throughout the experiment by selecting on a pulse height region where a mean position could be well-dened. This region is highlighted in Figure 3.15a. One can also see a line at low pulse height that corresponds to fortuitous α events. To reduce the data saved on disk, a minimum on the anode pulse height was set at 40. The evolution of the mean other bumps can also be aliated to this reaction. Then the time position is shown in Figure 3.15b. Clear distinctions can be made between the dierent gas bottle used during the experiment. This reects the small discrepancies in gas purity of the bottles. On rst approximation a constant shift was taken for each gas bottle, this approximation may be too simplistic. With this the limit conditions of the cosine distribution are known and the angular distribution can be extracted. Figure 3.16 shows the cosine build from this procedure as well as the dierence between the two cosines extracted for both sides of the chamber. The cosine is expected to be isotropic since the fragment emission is isotropic in the rest frame (the laboratory frame here since it is spontaneous ssion). Figure 3.16a displays a small anisotropy where the large angles seem to be slightly favored. This type of anisotropy is on par with similar experiments [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF][START_REF] Göök | Particle emission angle determination in frisch grid ionization chambers by electron drift-time measurements[END_REF], while being less than what was measured in [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF]. This bias is probably an eect of the timing measurement but its origin is unclear. The distributions for each side of the chamber are highly correlated, as expected. As shown in Figure 3.16b their dierence is zero on average, with a FWHM of 0.216. Rejecting events that have cosine values below 0.2 and with a ∆ cos above 0.255 reduces the fortuitous coincidences and false trigger. As depicted in Figure 3.16c adding a selection on the cosine distributions reduces the low pulse height tail. It also increase the peak-to-valley ratio between the heavy and light bumps.

Fitting procedure of the δE on the cold ssion lines

The previous chapter introduced the notion of cold ssion and showed in Figure 2.9 that it could be seen on the raw data. The width of these lines is given by the mass resolution, which depends only on the energy resolution as described by Equation (2.1). In [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF] Gaudefroy et al. described the impact of the energy loss correction on the mass resolution for cold ssion events. This correction notably improves the mass resolution for the heavy fragment. Then the energy loss correction done here relied on the improvement of the mass resolution for this type of events. The energy lost in the backing is expressed as:

∆E i = δE i cos θ (3.12)
where i = 1, 2 indicates the side of the chamber, δE i is the energy lost by a fragment measured in the side i of the chamber at an angle θ = 0. Energy losses through the whole backing thickness were calculated with SRIM for dierent nuclei at dierent energies. It is summarized in Table 3.1. The calculated energy loss are roughly contained in 10 to 50 keV when evolving with the mass of the fragment whereas it varies from 50 to 100 keV with the incident energy. Therefore the energy loss will be regarded as a constant with respect to the mass. Then the energy loss is parametrized as:

δE i = α i ln P i P i i = (1, 2) (3.13)
as described by the Bethe-Block formula [START_REF] Knoll | Radiation detection and measurement 2 nd edition chapter 5[END_REF]. The energy loss was calculated prior to anything else and determined in terms of channels. The method to nd the values for α 1 and α 2 is the following: for each couple of parameters the pulse heights are corrected for the energy loss, then the cold ssion events are selected through a graphical cut on the massTKE matrix. Since no neutron can be emitted it means that almost all the energy has been given through the kinetic energies of the fragments, so it can be found at high TKE. This cut is shown in light gray on Figure 3.17 for the anode facing the backing. One can clearly see well dened lines when the light fragment is detected in this side of the chamber whereas when the heavy fragment is detected it is harder to see those lines. The calculated intrinsic resolution of the FGTIC is around 200 keV while the energy loss will account for roughly 300-350 keV. Both of them are of the same magnitude so the resolution of the cold masses is expected to show little sensitivity on the energy-loss correction. A multi-step minimization was performed, starting from the calculated energy loss: α 1 was xed at 10.74 (⇔ 300 keV for typical pulse heights values) and α 2 was minimized: the value for which the average mass resolution in cold ssion is minimal. For this minimal value of α 2 , xed, α 1 is varied to nd its minimum, and so on. The nal parameters are (α 1 , α 2 ) = (12.9, 2.5) which corresponds to a total energy loss of 570 keV when the heavy fragment travels in the backing and 480 keV when it is the light one. Figure 3.18 shows the dierence between the raw data and once corrected for the energy loss. Small shifts on the mean position of the peaks can be seen, the mass resolution is similar in both cases.

Once the energy loss has been taken care of, the pulse height should be independent from the emission angle. Figure 3.19 shows the anode pulse height with the energy loss correction as a function of 1/ cos θ. One can see a clear dependence that remains. Its origin is unknown, this type of behavior looks like electron captures on impurities. The cathode and anode voltages were tuned in order to be on the pulse height plateau. It cannot be the grid ineciency (which is not corrected in the present work) because as mentioned before it is extremely low and correcting it would increase the behavior observed here. A last possibility would be the non-homogeneity of the electric eld. The suppression of the eld degrader rings between [START_REF] Gaudefroy | A twin frisch-grid ionization chamber as a selective detector for the delayed gamma-spectroscopy of ssion fragments[END_REF] and the present work might degrade the homogeneity at the edge of the fragments range. Correcting this slope (∼ 2 MeV per unit of 1/ cos θ) results in the suppression of the cold ssion lines and only deteriorates the resolution of the chamber, therefore it needs to be kept this way in order to get the best resolution. No impact was

Anode calibration

The focus will now be the two stages for the anode calibration as depicted in Figure 3.20.

From the pulse height corrected for the energy loss one needs to calibrate the energy to get the apparent one, then correct for the pulse height defect. These two stages give a rst estimate of the post-neutron kinetic energies and masses and are determined by six parameters 1 , β 1 , 2 , β 2 , γ, δ, introduced in the following. The anodes will be calibrated on the well-known mean values of the post-neutron kinetic energy for light and heavy fragment.

To do so the method depicted in Figure 3.21 will be used. One will determine the mean position of each bump, the lowest being the heavy fragment, the higher the light one. Then i , β i are determined through: The values for KE post L,H are taken from [START_REF] Henschel | Absolute measurement of velocities, masses and energies of ssion fragments from californium-252(sf )[END_REF] whereas the ones for P HD L,H are coming from [START_REF] Peck | Pulse-height defect of Ar+CF 4 mixtures as a counting gas for ssion-fragment detectors[END_REF]. Once corrected for energy loss the two sides of the chamber see the same fragments since their emission is isotropic. Therefore one can correlate 1 , β 1 , 2 , β 2 and reduce the number of free parameters to 4:

KE app i = i • P i + β i = KE post L,H -P HD L,H ⇔ i • P i + β i = KE post L,
1 • P 1 + β 1 = 2 • P 2 + β 2 (3.15)
by setting down:

2 = κ • 1 β 2 = 1 • ζ + β 1 (3.16)
One can determine κ and ζ from the data by aligning the two anode pulse heights:

1 • P 1 + β 1 = 2 • P 2 + β 2 ⇔ 1 • P 1 + β 1 = 1 (κ • P 2 ζ) + β 1 ⇔ P 1 = κ • P 2 + ζ (3.17)
Then κ and ζ are determined by:

P L,H 1 = κ • P L,H 2 + ζ (3.18)
The eect of this alignment is shown in Figure 3.22. The respective mean positions are determined through a gaussian t on each light and heavy bump. This alignment takes care of the dierence in gain chains between the two channels. The two parameters κ and ζ depend only on the energy loss. Since the latter has been previously determined, κ and ζ are xed in the following. Now that the apparent kinetic energy KE app i has been determined one can calculate the PHD, parametrized as in [START_REF] Hambsch | Is there a pulse height defect for methane?[END_REF] (it is mainly a reformulation of the Schmitt calibration [START_REF] Schmitt | Precision measurements of correlated energies and velocities of 252 Cf ssion fragments[END_REF]):

P HD i = A app i • KE app i γ + A app i δ (3.19)
The parameters γ and δ were adjusted to reproduce the data from Peck et al. [START_REF] Peck | Pulse-height defect of Ar+CF 4 mixtures as a counting gas for ssion-fragment detectors[END_REF]. The resulting PHD is displayed in Figure 3.23 together with the data from Peck et al.. The masses used here are apparent masses, namely:

A app i = 252 • KE app j KE app i + KE app j i, j = 1, 2 (3.20)
These masses do not take into account the neutron emission which of course changes the masses of the fragments but also their energies due to the recoil. Feedback The values determined here for the four free parameters are only starting points.

Including the neutron contribution, described in lengths in the following, will aect the PHD and the nal mean kinetic energies will not match the literature anymore. This analysis must reproduce the mean pre-and post-neutron kinetic energies from the literature [START_REF] Wagemans | The nuclear ssion process[END_REF][START_REF] Hambsch | Is there a pulse height defect for methane?[END_REF][START_REF] Henschel | Absolute measurement of velocities, masses and energies of ssion fragments from californium-252(sf )[END_REF][START_REF] Peck | Pulse-height defect of Ar+CF 4 mixtures as a counting gas for ssion-fragment detectors[END_REF] and have the cold lines peaked at the right masses. The rst condition ensures that the procedure gives consistent results with the existing literature. The second is trickier: having the cold ssion lines separated by one mass unit and centered on integer values is an indication of the proportionality of the measured energy with the true one, ie.

if:

KE meas = a • KE true (3.21)
then:

A meas i = 252 • KE meas j KE meas i + KE meas j i, j = L, H ⇔ A meas i = 252 • a • KE true j a • KE true i + a • KE true j i, j = L, H ⇔ A meas i = A true i (3.22)
It is a stronger constraint than just reproducing mean quantities however it does not ensure the good calibration of the FGTIC. Nonetheless, as explained in the next chapter, it will be an ingredient to re-scale the energies measured to get closer to the true ones. Then the four parameters 1 , β 1 , γ, δ will be modied to satisfy at best those conditions. This feedback is symbolized by the backward arrows in Figure 3.20. There is no pre-conception of which parameter should be changed or not, therefore in the present work the feedback was given mostly to the calibrating factors. The PHD is the least known quantity therefore the mean apparent energies used as calibration points are not well dened. Moreover changing the calibrating factors also impact the PHD parameters since they depend on the kinetic energy.

This feedback is quite independent of the neutron emission treatment, then in the following discussions one can consider that the most suited values for 1 , β 1 , γ, δ are used. This subsection will discuss the management of the neuton evaporation impact on the ssion observables, namely the kinetic energies and masses. At rst the focus will be the righthand side of Figure 3.24 which corresponds to the implemented algorithm then the formula used to estimate the number of neutrons will be discussed along its dierent inputs, which correspond to the left-hand side.

Neutron evaporation

Algorithm

Initialization: From the calibrated pulse height and the PHD correction one gets a rst estimate of pre-neutron quantities:

KE pre = KE app + P HD(A app , KE app )

A pre L,H = 252 • KE pre H,L KE pre L + KE pre H (3.23)
by assuming that no neutrons were emitted.

discontinuity and the mean value for the TKE is 183.0 ± 0.8 MeV. This value is in good agreement with the 184 ± 1.5 MeV from [START_REF] Wagemans | The nuclear ssion process[END_REF], even though it was not used as an adjustment parameter as it was previously done in various studies [START_REF] Hambsch | Is there a pulse height defect for methane?[END_REF][START_REF] Göök | Prompt neutron multiplicity in correlation with fragments from spontaneous ssion of 252 Cf[END_REF][START_REF] Hambsch | Oberstedt : Investigation of the far assymetric region in 252 Cf(sf)[END_REF][START_REF] Birgersson | Properties of the reaction 238 U(n, f ) at the vibrational resonances[END_REF]. Figure 3.25b shows the cold ssion mass distribution (selected by a preliminary graphical cut) which is obviously incorrect since these events are corrected for a neutron emission that did not happen. This has the eect of shifting the masses in an accordion eect, slowly drifting the masses away from their true value. It has been long known [START_REF] Göök | Prompt neutron multiplicity in correlation with fragments from spontaneous ssion of 252 Cf[END_REF][START_REF] Budtz-Jørgensen | Knitter : Simultaneous investigation of ssion fragments and neutrons in 252cf (sf )[END_REF]108] that the mean number of neutrons emitted displays an almost linear dependence on the TKE. Therefore taking a functional that depends both on the masses and the TKE would allow to correctly treat both cold and hot ssion.

Barreau's formula

In their study of the far-out asymmetric ssion Barreau et al. [START_REF] Barreau | Fission fragments correlation measurements for 252 Cf(sf) and structures in far-out assymetric ssion[END_REF] used Equation (3.28) to account for the TKE dependence of the neutron emission.

ν (A, T KE) = ν (A) + ν (A) ν (A) + ν (252 -A) • T KE (A) -T KE (A) B n (3.28)
This expression adds a deviation to the neutron sawtooth based on the total kinetic energy.

This deviation is related to the energy repartition between kinetic energy and excitation energy. Namely, if the kinetic energy is above the average value then the excitation energy will be reduced by the same amount, meaning that less neutrons can be emitted. On the contrary when the T KE (A) is lower than the average then more neutrons can be emitted. The ν (A) were here also taken from [START_REF] Göök | Prompt neutron multiplicity in correlation with fragments from spontaneous ssion of 252 Cf[END_REF]. For self-consistency and correct reproduction of the neutron sawtooth the T KE (A) used in Equation (3.28) has to be the one from the present work. Doing this induces another recursion as described in the upper left of Figure 3.24. The B n parameter represents the mean energy taken by the emitted neutron. This B n was taken constant at 8.6 MeV for every masses in [START_REF] Birgersson | Properties of the reaction 238 U(n, f ) at the vibrational resonances[END_REF][START_REF] Barreau | Fission fragments correlation measurements for 252 Cf(sf) and structures in far-out assymetric ssion[END_REF]. This is only an approximation since B n depends on the neutron separation energy S n which varies signicantly from one fragment to the other. This parameter will be the determining one to describe the cold ssion properly.

B n = 8.6 MeV

The use of Equation (3.28) in the literature was always done with a constant value for B n of 8.6 MeV [START_REF] Birgersson | Properties of the reaction 238 U(n, f ) at the vibrational resonances[END_REF][START_REF] Barreau | Fission fragments correlation measurements for 252 Cf(sf) and structures in far-out assymetric ssion[END_REF]. Using this method did not change the mean TKE value as shown in

B n (A)

To correct the two problems introduced by using Equation (3.28) (blank spots in the TKE-A matrix and cold ssion events not at zero neutrons emitted) the B n was made mass dependent. Its values were hand-adjusted for masses where neutronless ssion was available and for the symmetric region. It was taken constant otherwise. This constant was chosen to have an overall smooth behavior. Similarly to the sawtooth and TKE distribution, a spline was applied to the B n (A) curve to avoid articial spikes in the iterative procedure.

The nal B n (A) is displayed in Figure 3.27a. This parameter should not be interpreted as a mean energy taken away by the neutron anymore but just as a parameter to reproduce at best the TKE dependence of the neutron emission. In Figure 3.27c one can see that tuning the B n to get a good description of the cold ssion has also an eect on the whole neutron emission which is closer to experimental points. For the adjustment of the symmetric region the description is in rather good agreement with the experimental data from [START_REF] Göök | Prompt neutron multiplicity in correlation with fragments from spontaneous ssion of 252 Cf[END_REF] except for a small global shift. One can see in Figure 3.28 that the blank spots at the symmetry are greatly reduced which does not impact anymore the shape of the mean TKE distribution in Figure 3.29b that still remains higher than for ν = ν. With this parametrization the cold ssion events are correctly treated and as shown in Figure 3.29a the lines appear for close to zero neutrons emitted.

This treatment can be further improved by taking into account the non-linearity of the neutron emission with respect to the TKE which is quite important near the symmetric masses [START_REF] Göök | Prompt neutron multiplicity in correlation with fragments from spontaneous ssion of 252 Cf[END_REF]. To do so one would need to use a complete ν (A, T KE) surface to correct the neutron emission. This could not be done in the present work due to lack of time.

Absolute calibration

The calibration procedure done in the present work is only relative to the work of Henschel et al. [START_REF] Henschel | Absolute measurement of velocities, masses and energies of ssion fragments from californium-252(sf )[END_REF]. However the present work observes the cold ssion and identifying the end of cold ssion lines gives access to the point Q = T KE. In the following (see Chapter 5) the cold ssion line for the mass split 120/132 is identied and its main contributor is the fragmentation 120 Cd/ 132 Sn, moreover the 132 Sn is found in its ground state. Then the associated prompt spectrum comes only from the 120 Cd, which is the only excited nucleus, therefore the disappearance of the 2 + state will occur at The endpoint is found at 235.3 MeV for the 2 + gate and 234.6 MeV for the 4 + one. One can see that the relative position between the two endpoints is eectively equal to the γ transition of 700 keV between the 4 + and 2 + states. To re-calibrate the whole kinematics, without touching the masses, a scaling factor is applied to the TKE and the KE. This is the rst proper absolute calibration of such device.

T KE = Q -E * (2 + ).

Cold ssion limit determination

The way to previously identify cold ssion events in the present work was through graphical cuts on the TKE vs A 2D-histogram. This subsection will explain how those events can be more systematically dened.

For a given mass, let's take for example A = 132, dierent primary fragmentations (ie.

dierent charge splits) are allowed but they will have dierent Q-values. Figure 3.31 shows a simplied description of the population of the dierent charge splits in terms of TKE.

Each fragmentation will be cold for a certain energy range, until one of the two fragments exceeds its neutron separation energy. This endpoint depends on the neutron separation energy of the two fragments and on the repartition of the excitation energy between the two. When the fragmentation 120 Cd/ 132 Sn will start to emit neutrons, all the other will still be cold. The present work cannot put a veto condition on neutrons, however it can determine the start of the neutron emission in terms of TKE through the appearance of the neutron-induced γ-rays. Such selection will only give access to part of the cold ssion as it selects only events above the dashed line in Figure 3.31.

In order to properly determine the start of the neutron emission one needs to ensure that the decrease of the neutron-induced γ-rays is not just a statistical behavior. To get a more systematic determination, the TKE yield of the 203 keV and 57 keV transitions from the inelastic scattering on 127 I was looked at. In order to evaluate the end of these distributions, they were tted following the parametrization from Brosa et al. [START_REF] Brosa | Systematics of ssion-channel probabilities[END_REF] Y B (T KE):

Y B (T KE) = 200 T KE 2 • h • exp (L -l max ) 2 (L -l min ) • l d ec with L = e 0 • Z CN A CN 2 A F • (A CN -A F ) T KE (3.29)
where h, l max , l min and l dec are parameters, e 0 = 1 is the electronic charge, Z CN and A CN are the charge and mass of the ssionning nucleus, respectively and A F is the mass of the fragment. This parametrization reproduce quite well the TKE distribution gated by the 134 Te isomer as shown in Figure 3.33a. The TKE distribution gated by neutron-induced γ-rays will be truncated at high TKE since those γ-rays are not produced in cold ssion.

Then to account for this truncation the parametrization of Equation an ane function:

Y (T KE) = (-a • T KE + b) • Y B (T KE) with a, b > 0 (3.30)
An example of such adjustment is shown in Figure 3.33b for the mass A = 104. The upper limit of the distribution was taken at 2 • 10 -4 of the maximum value, it was chosen so that for the maximum yield the limit would be around one hit.

The nal endpoints for each gate are displayed in Figure 3 In terms of resolution a t with multiple gaussians, shown in Figure 3.37 gives a nal mass resolution of 0.68 a.m.u. (FWHM) for the cold ssion, to compare with the 3.9 a.m.u.

(FWHM) obtained in hot ssion by tagging on the 134 Te isomer(see Figure 3.46). The smearing in hot ssion is caused by the neutrons that are not measured. This excellent resolution will allow great selectivity in this region and it also allows an estimation of the energy resolution. From Equation (2.34) and by assuming that the energy resolution is the same for both sides of the chamber, one can express the energy resolution as:

σ KE = σ A A 1 (E L + E H ) 2 + 1 E 2 L,H + 1 (E L + E H ) 2 - 2 E L,H • (E L + E H ) 1/2 (3.31)
which gives a mean energy resolution of 570 keV (FWHM) for the kinetic energies and 800 keV for the TKE since σ T KE = √ 2σ KE .

Comparison to the literature

To validate the whole analysis performed on the FGTIC several observables are compared to the literature. Table 3.2 presents the results of this analysis on mean observables, in excellent agreement with the compiled literature.

The yields are compared to multiples data-sets from the literature [START_REF] Göök | Prompt neutron multiplicity in correlation with fragments from spontaneous ssion of 252 Cf[END_REF][START_REF] Hambsch | Oberstedt : Investigation of the far assymetric region in 252 Cf(sf)[END_REF][START_REF] Budtz-Jørgensen | Knitter : Simultaneous investigation of ssion fragments and neutrons in 252cf (sf )[END_REF][START_REF] Whetstone | Coincident time-of-ight measurements of the velocities of cf 252 ssion fragments[END_REF] in Figure 3.38. These data come from dierent methods, be it 2E with silicon detectors or FGTIC or 2V method. The present work is in excellent agreement with the previous measurements.

Similarly the evolution of the mean kinetic energy versus the pre-neutron mass is displayed in Figure 3.39a and compared with the literature. The two works of Schmitt et al. [START_REF] Schmitt | Fragment energy correlation measurements for 252 Cf spontaneous ssion and 235 U thermal-neutron ssion[END_REF] and Whetstone et al. [START_REF] Whetstone | Coincident time-of-ight measurements of the velocities of cf 252 ssion fragments[END_REF] are normalized to KE L = 104.6 MeV and KE H = 79.5 MeV because the Schmitt calibration was updated in 1981 by Henschel et al. [START_REF] Henschel | Absolute measurement of velocities, masses and energies of ssion fragments from californium-252(sf )[END_REF]. The measurements prior to 1981 were systematically overestimating the dierent energies. The present work is one of the rst to estimate the energy resolution of a FGTIC using the cold ssion lines, therefore this uncertainty is included in Figure 3 of this analysis with previous measurements from 2E method. Nonetheless a small discrepancy is observed between A=120 and A=132. This is an artifact of the neutron emission procedure where near the symmetry the ν (T KE) dependence used here possess the correct slope but is slightly shifted towards higher TKE, as can be seen in Figure 3.27c. Moreover none of the previous studies had evaluation of their uncertainties and since they do not see the cold ssion events one can assume that their error bars are at the very least of the same magnitude as the present work. Figure 3.39b shows the evolution of the standard deviation of the kinetic energy with the pre-neutron mass, compared to [START_REF] Piau | Prédiction par calcul des observables de ssion à partir d'expériences dédiées[END_REF][START_REF] Varapai | Développement d'un dispositif expérimental basé sur la digitalisation des signaux et dédié à la caractérisation des fragments de ssion et des neutrons prompte émis[END_REF]. The same tendency is observed with values 500 keV lower than [START_REF] Varapai | Développement d'un dispositif expérimental basé sur la digitalisation des signaux et dédié à la caractérisation des fragments de ssion et des neutrons prompte émis[END_REF] for the present work but on par with [START_REF] Piau | Prédiction par calcul des observables de ssion à partir d'expériences dédiées[END_REF]. Figure 3.40a displays the comparison of the mean total kinetic energy as function of the pre-neutron mass with the literature [START_REF] Göök | Prompt neutron multiplicity in correlation with fragments from spontaneous ssion of 252 Cf[END_REF][START_REF] Varapai | Développement d'un dispositif expérimental basé sur la digitalisation des signaux et dédié à la caractérisation des fragments de ssion et des neutrons prompte émis[END_REF]. All the data-sets are in agreement with each other, with larger discrepancies near the symmetry, for the same reasons as for the mean kinetic energy. If the simplest neutron correction is assumed (ν = ν, in green line) then a good agreement is found for the whole mass range. However it was stated before that going beyond this simple description is crucial for this study.

When looking at the standard deviation for the TKE distribution as function of the preneutron mass one would expect to see the same behavior than in Figure 3.39b. However Figure 3.40b shows the opposite, the TKE standard deviation is larger in this work than in the literature. This is explained by the description of the neutron emission: the data from Göök et al. [START_REF] Göök | Prompt neutron multiplicity in correlation with fragments from spontaneous ssion of 252 Cf[END_REF] are using a full ν (A, T KE) surface, so the present work overestimates the number of neutrons emitted at low TKE, increasing the width of the TKE distribution.

Isomer identication

The previous sections presented the analysis implemented to get the best resolution in mass, energy and time for the ssion fragments that are of high importance for the identication of isomers. Identifying an isomer allows the unambiguous identication of the Z and A of one fragment. When coupled to an excellent mass resolution, in the cold ssion regime for example, one can perfectly identify both fragments in mass and charge. This section will then proceed to the description of the optimization of the written data and the algorithm used to eciently identify the isomeric events.

Data optimization

Once fully processed the 4.4 TB of raw data accounts for 80 GB of ROOT les. The energy resolution of the NaI-array is not sucient to perfectly identify a nucleus by working with single gated spectra (energy condition on one γ-ray), so at least two conditions on E γ = {γ 1 , γ 2 . . . γ n } (ensemble of the γ detected in an event) will be required, to which one has to add the mass selection and time window. In the end a minimum of 4 conditions will be required to identify an isomeric state with a yield, most of the time below 1%. This means that most of the events will be rejected in the end. Therefore if the conditions on E γ can be done in a pre-selected subset one would gain a signicant amount of time. The choice was made to make a full copy of the fully processed ROOT les and dispose them as described in Figure 3.41. In multiple folders, each corresponding to a mass, lies a ROOT le possessing two TTree, one contains the delayed part (T > 10 ns) while the other contains the prompt component (|T | < 4 ns). The entries of these two trees matches each other: the prompt γ found in entry 1 of Tree_prompt are the ones associated with the delayed γ of entry 1 in Tree_delayed. Dividing the event this way reduces signicantly the ensemble E γ to consider for the selection of isomers.

Since the pre-selection is mainly on the mass, the reduction of the selection time will depend on its yield and the population of the isomer. As an example the time it takes to make dierent selections to identify the 134 Te isomer (1% of the ssion events) as well as the 95 Sr (0.3% of the ssion events) is reported in Table 3.3. One can see that the time to make these selections does not depend on the isomer of interest when looping on the whole data-set. The time reduction is on average a factor 5 for the 134 Te isomer and 30 for the 95 Sr.

37

Table 3.3: Time to make an x-fold selection for the isomer of 134 Te on the whole data les or with a pre-selection.

Example of 134 Te

The 134 Te isomer has one of the highest yield (1%) and has easily distinguishable delayed γ which makes it the perfect benchmark. Its level scheme is displayed in Figure 3.42, taken from [START_REF] Saha | Excitations of two-and three-valence-proton nuclei 134 Te and 135 I[END_REF]. The isomer of interest is the "long-lived" one ie. the 6 + at E * = 1691 keV with a half-life of 164 ns. The three delayed γ are {115, 297, 1279} keV. The 115 keV transition is highly converted and is usually not used as a condition.

Selection algorithm

In order to check if the gates used to identify an isomer are the good ones, one will need to look at γ spectra gated by one, two or more conditions. The way to ll this histogram is not so straight forward and need an explanation. The algorithm used in the present work to make selection in a set of γ is based on the work of Beausang et al. [START_REF] Beausang | Using high-fold data from the new generation of γ-ray detector arrays[END_REF]. Let is write an event of n γ as: E γ = {γ 1 , γ 2 . . . γ n }. One can consider this set to be pre-selected in mass and conditioned with a minimum delay. Let's consider that at least one γ has to satisfy a gating condition g to increment the coincident spectrum. The event is divided in singles. If the (n -1)-tuple possess the gating condition then the single is incremented. There are two possibilities:

exactly one γ satises the selection criteria: {g 1 , γ 1 . . . γ n-1 }. Then γ 1 . . . γ n-1 are incremented in the spectrum once. If now one consider that at least two γ have to satisfy two dierent gating conditions g, p respectively, then there are three possibilities:

Each selection criteria is satised exactly once:

{g 1 , p 1 , γ 1 . . . γ n-2 }. Then γ 1 . . . γ n-2
are incremented in the spectrum once.

at least two γ satisfy one criteria and the second is satised only once: {g 1 , g 2 , . . . g l , p 1 , γ 1 . . . γ n-l-1 }. Then only γ 1 . . . γ n-l-1 and g 1 . . . g l are incremented in the spectrum once.

Each selection criteria is satised at least twice: {g 1 , . . . g l , p 1 , . . . p m , γ 1 . . . γ n-l-m }. In this case any (n -1)-tuple will always possess each criteria at least once, therefore all γ are incremented once in the spectrum.

and similarly for higher number of criteria. time-of-ight, but mainly between 5 and 50 ns after the prompt cascade. Finally the isomer decay will occur with another delay, with its γ emitted at the same time (unless it decays on another isomer). Since the 134 Te isomer has a lifetime of 164 ns one expects to get 95% of the decays within 500 ns. Figure 3.44a shows the delayed spectrum pre-selected on the mass with a delay between 5 and 500 ns. The mass range was taken to be roughly ±2σ A .

Eect of the successive selections

One can see the domination of the neutron radiation since the whole neutron bump is in the time window considered, nonetheless the 3 γ of the 134 Te isomer can be seen but with an extremely poor signal over background ratio. Since the neutrons are mainly emitted within 30-40 ns from the ssion, the minimum time selection was increased to 50 ns in Figure 3.44b.

While it reduces the isomer statistics by 20% it is mandatory to get clean gates on the E γ .

The neutron contribution is signicantly reduced and dierent peaks from isomeric decays can be seen because of the mass resolution. A rst condition is set on the energies of the γ in the event. The spectrum shown in Figure 3.44c corresponds to all the γ found within 7 ns from the one satisfying E γ = 1279 ± 50 keV. This condition drastically change the spectrum where the two remaining γ of the delayed cascade from the 134 Te dominate. There are two small peaks that come from the 136 Xe isomer. Its delayed cascade is similar to the 134 Te: {197, 381, 1313} keV. Obviously the selection 1279 ± 50 partly select the 1313 keV from the 136 Xe. Luckily its lifetime is 2.92 [START_REF] Wagemans | The nuclear ssion process[END_REF] µs which explains its low intensity in Figure 3.44c.

To get rid of this pollution a second condition on the delayed γ is set. Figure 3.44d shows the spectrum in coincidence with a γ of 1279 ± 50 keV and one of 297 ± 35 keV within a time window of 7 ns. Here the spectrum contains only one γ ray, the delayed 115 keV. This selection allows a perfect identication of the isomer. From the last gating conditions one can measure the lifetime of the isomer by looking at the time distribution of such events.

The timestamp of the isomer is just the timestamp of the rst γ to satisfy one of the selection criteria. Figure 3.45a shows the multi-gated 2D-histogram of the γ energy versus the event timestamp. The red dotted lines highlight the energy selection made to obtain the spectrum of Figure 3.45b. The latter is tted with an exponential, with an excellent agreement. The half-life is determined by the slope λ of the exponential:

T 1/2 = ln 2 λ (3.32)
Then the measured half-life is 163.2 ± 2 ns, it is in excellent agreement with the reference of 164.1 ± 0.9 ns. In the present work the uncertainty mainly comes from the NaI time resolution.

(a) As discussed in the previous sections the mass spectrum gated by an isomer will give the mass resolution in the case of hot ssion. Figure 3.46 shows the post-neutron mass distribution gated by the 134 Te isomer. The sharp edges around the heavy peak come from the mass selection. The heavy peak was adjusted with a gaussian and a 1 st -order polynomial to account for the little remaining fortuitous events. This adjustment yields a mean heavy mass of 134.1 a.m.u. with a FWHM of 3.76 a.m.u.. The light fragment is found at an average mass of 114 which is in good agreement with the mean number of neutrons emitted.

Indeed the most probable pre-neutron fragmentation is 135 Te/ 117 Pd and ν(117) ∼ 3 and ν(135) ∼ 1.

The same kind of analysis was done for 28 isomers across the nuclear chart and the measured lifetimes and masses are reported in Table 3 with their reference, except for some µs isomers where the relative discrepancy is around 1µs. For 11 out of the 25 nuclei identied through their isomer(s) the measured post-neutron masses dier from more than 0.5 mass units. The neutron correction applied to the data-set is an average correction depending only on the mass of the fragment and not its charge. Therefore it is not surprising to have discrepancies when looking at specic nuclei.

Isotope E * [keV] T ref 1/2 [ns] T meas 1/2 [ns]
A Part III

Results and interpretation

Chapter 4

Isomers as a tool for multi-parameters ssion study

The previous chapters were describing all the eorts made to extract the observables from detectors signals. The following chapter will discuss the rst results of the present work with the help of isomers. At rst the prompt γ spectra will be compared to the literature to validate the work done so far. Then the structures in the spectra for masses around the double shell closure Z=50, N=82 will be investigated through isomer tagging. This approach unambiguously identies the structures as coming from the heavy fragment and that they originate from a dierence of level density between the light and heavy fragment.

Finally the combined measurements of isomers and kinetic energies represent constraining observables for the various codes that aim at describing the ssion fragments decay.

4.1 Structures in the prompt γ-spectra near the double shell closure Z=50, N=82

A way to assess the quality of the analysis is to confront the correlated observables seen in the present work with the literature. Hötzel et al. [START_REF] Hötzel | High-energy gamma-rays accompanying the spontaneous ssion of 252 Cf)[END_REF] were the rst to report the prompt γ spectrum of 252 Cf selected in masses for the full mass range. Figure 4.1a shows the evolution of the prompt spectrum with the pre-neutron mass for the present work. Each black spectrum was selected by the masses labeling them on their right. The red spectra are the spectra for the mass selection [108; 110[ used as reference to highlight the changes over the mass range. This reference, is the same as in [START_REF] Hötzel | High-energy gamma-rays accompanying the spontaneous ssion of 252 Cf)[END_REF] shown in Figure 4.1b. The present work

shows the same tendency as [START_REF] Hötzel | High-energy gamma-rays accompanying the spontaneous ssion of 252 Cf)[END_REF]: structures are seen between 3.5 and 7 MeV for masses near the symmetric region while for any other mass region the spectra show a similar behavior.

This agreement validates the correlated measurement done in the present work. and in [START_REF] Hötzel | High-energy gamma-rays accompanying the spontaneous ssion of 252 Cf)[END_REF].

for masses close to the symmetry. They divided the high energy part of the spectrum into a statistical (exponential decay tted on the energy range [1.5;3.5] MeV) and non-statistical (the enhancement) part. They compared the latter mass yield to the one for at least 2 γ of energy above 3.5 MeV. Both yields were similar and the proposed explanation was the presence of the super-long ssion mode postulated by the random-neck-rupture model [START_REF] Brosa | Multimodal ssion and neutron evaporation[END_REF].

In this mode non-statistical high energy γ-rays are expected to be emitted by strongly elongated nuclei during their contraction towards less deformed shapes. It was inuenced by the previous work of Brooks and Reines [START_REF] Brooks | Fragment-mass ratios in 252 Cf ssion versus prompt gamma-ray energy[END_REF].

Hötzel et al. [START_REF] Hötzel | High-energy gamma-rays accompanying the spontaneous ssion of 252 Cf)[END_REF]: In 1996 Hötzel et al. did the same measurement than Glässel et al. [START_REF] Glässel | 252 Cf ssion revisited new insights into the ssion process[END_REF] with the same setup. They used the doppler aberration [START_REF] Maier-Leibnitz | Average number and energy of gamma-rays emitted as a function of fragment mass in 235 U thermal-neutron-induced ssion[END_REF] to identify from which fragment the γ originates. They concluded that the structures were coming from the heavy fragment, around mass 131. It was conrmed later by Singer et al. [START_REF] Singer | High-energy γ-rays in αaccompanied spontaneous ssion of 252 Cf)[END_REF] using 252 Cf ternary ssion. Hötzel et al. used the CASCADE code [START_REF] Pühlhofer | On the interpretation of evaporation residue mass distributions in heavy-ion induced fusion reactions[END_REF] to reproduce their experimental spectra. By using the level density parameters determined by Budtz-Jorgensen et al. [START_REF] Budtz-Jørgensen | Knitter : Simultaneous investigation of ssion fragments and neutrons in 252cf (sf )[END_REF] they were able to reproduce the overall behavior, which could not be done with the previous NLD parametrization. Since this enhancement was reproduced using a statistical description it lead the authors to refute the hypothesis of Glässel et al. [START_REF] Glässel | 252 Cf ssion revisited new insights into the ssion process[END_REF].

Makii et al. [START_REF] Makii | Eects of the nuclear structure of ssion fragments on the high-energy prompt ssion γ-ray spectrum in 235 U(n t h, f )[END_REF]: In 2019, Makii et al. [START_REF] Makii | Eects of the nuclear structure of ssion fragments on the high-energy prompt ssion γ-ray spectrum in 235 U(n t h, f )[END_REF] published their results on the study of the prompt spectrum of the thermal neutron-induced ssion of 235 U. The two bumps were also observed with a poorer mass selection than before. They used the CoH3 code [START_REF] Kawano | Statistical and evaporation models for the neutron emission energy spectrum in the center-of-mass system from ssion fragments[END_REF] to reproduce their measured spectra. This code, similarly to CASCADE, possess a statistical description of the spectrum but it also describes the n-γ competition and the low-energy structure of the fragments. For them the 4 MeV bump comes from the discrete transitions in 131 Sb and 132 Sn while it is the light fragment (A L ∼ 100) that contributes to the 6 MeV bump. They explained that the 6 MeV bump for A L ∼ 100 is not seen in 252 Cf spectra because the excitation energy of the light fragment is lower in 252 Cf than in 235 U.

To summarize, the double bump structure is expected to come from the heavy fragment, centered on mass 131. Dierent origin is given to this structure: [START_REF] Hötzel | High-energy gamma-rays accompanying the spontaneous ssion of 252 Cf)[END_REF] explains it only through a statistical description, while [START_REF] Makii | Eects of the nuclear structure of ssion fragments on the high-energy prompt ssion γ-ray spectrum in 235 U(n t h, f )[END_REF] considers the 4 MeV bump as coming from the discrete transitions in the Sb and Sn isotopes. This section aims to lift the ambiguity on the origin of such enhancement by using the prompt cascade feeding isomers. As shown in Table 3.4 13 isomers have been identied near the mass 131. Figure 4.2 displays the dierent spectra selected by the isomers near A = 131.

Each prompt spectrum is the sum of the cascade feeding the isomer and the various cascades for the complementary light fragments. The spectrum for mass 108 is displayed in red as a reference to assess the evolution of the structures.

Several spectra show the enhancement while they do not possess known discrete transitions of high intensity above 3.5 MeV. Since this enhancement is seen for dierent nuclei with dierent structures it cannot be explained by discrete transitions. Moreover the width of the enhancement is too large to be compatible with an experimental resolution (see Sec. 2.4.2).

Two isomers are observed for 134 Te, with a large dierence in excitation energy: 1.691

MeV for the 6 + and 5.804 MeV for the 12 + , Figure 4.3b shows a simplied level scheme of 134 Te with the isomers reported in green and the S n in dashed red line. Figure 4.3a shows the superposition of the spectra for the two isomers, the 6 + in green and the 12 + in blue. The two peaks at 2.3 and 2.9 MeV are the transitions feeding the 6 + isomer (see the 134 Te level scheme in Figure 3.42). One can see that the structures seen in the 6 + disappear in the 12 + spectrum, which is compatible with an exponential decay (in red). If the n-γ competition is neglected, the highest energy transition landing on the 12 + isomer is 1.871 MeV while it goes up to 5.984 MeV for the 6 + isomer: the heavy cascade cannot contribute to the enhancement above 3.5 MeV. The change between the blue and green spectra in Figure 4.3a is only a change in excitation energy: according to the dierent methods to share the excitation energy, an increase of a fragment energy is always accompanied by an increase of the complementary fragment's energy. Then the light fragment's contribution at high energy is at least the same if not higher. Therefore the disappearance of the enhancement certies it comes from the heavy fragment.

(a) prompt spectrum. 4.1.3 Origin of the shape dierence in the prompt spectrum This section will try to identify the origin of the enhancement of the prompt spectrum introduced in the previous subsection. As discussed previously the prompt decay of a nucleus is usually described by a statistical part before arriving on the discrete transitions.

It was shown previously that the enhancement is coming from the statistical decay. It is governed by the probability P XL (E γ ) to emit a photon of a given type and multipolarity written as (normalization aside):

P XL (E γ ) = J,π   E 2L+1 γ f XL (E γ ) E f J+L I=J-L ρ I (E f )   (4.1)
where E γ is the energy of the transition, E f the nal excitation energy, f XL the strength function and ρ (E f ) the level density at the nal excitation energy. Figure 4.4 shows the level densities and strength functions from the dierent models in TALYS [START_REF] Koning | Talys 1.0. International Conference on Nuclear Data for Science and Technology[END_REF] for 134 Te.

The level densities shown in Figure 4.4a are quite similar, with the HFB tables predicting a small enhancement between 3 and 6 MeV in excitation energy. In terms of strength functions every model is equivalent to another, with a small overall shift between them, which does not play a role in the de-excitation process. Indeed the quantity of interest is the emission probability which is normalized to 1. Then, except for the HFB tables for the level densities, no structures are seen that could explain an enhancement in the spectrum. The dierence between a CGCM parametrization and the microscopic tables is at most a factor 5, which does not have a great impact on the γ-spectrum, as shown in Figure 4.4. In the following the Skyrme-HFB tables are taken for both the level density and strength function. In rst approximation the statistical transitions are electric dipolar (E1) and magnetic dipolar (M1) ones. Thus only the {5 -, 6 -, 7 -, 5 + , 6 + , 7 + } initial spin-parity couples will contribute to the direct decay to the 6 + isomer of 134 Te. Figure 4.5 shows the photon emission probability for these initial spins and parities at dierent initial excitation energies for both 134 Te (in red) and 114 Pd (in black). In every cases sharp peaks appear for the highest γ energies available, they are the direct feeding of discrete levels and do not depend on the level density. The curves correspond to the transitions within the continuum. Table 4.1

Level density [MeV

shows the relative intensities of the transition towards the discrete levels for both nuclei.

One can see that the 134 Te decay is fully dominated by these transitions while it is the continuum-to-continuum ones that dominate for 114 Pd. energies with an initial spin distribution J π = {5 -, 6 -, 7 -, 5 + , 6 + , 7 + }.

E * [
In P XL (E γ ) there are two terms that are clashing:

E 2L+1 γ • f XL (E γ ) ∝ Γ XL (E γ )
will favor the emission of high energy photons while the nal level density ρ (E f ) will have a preference for low energy photons as shown in Figure 4.6. The level density scales with the excitation energy so the nal level density will be higher at high excitation energy, hence the higher probabilities for low energy transitions. The radiative widths for both 114 Pd and 134 Te are similar in amplitude as shown by the red curves in Figure 4.6 and that the continuum-todiscrete transitions are of the same order of magnitude in Figure 4.6. Then the dierence in the intensity of the continuum-continuum transitions will only be due to the nal level density. One clearly sees that the 134 Te is driven by the strength function above 3 MeV while this is only the case above 5 MeV for the 114 Pd. The low level density in the 134 Te, caused by the neutron shell closure of N=82, strengthens the photon emission of high energies.

The 114 Pd is more "level density"-driven, in the sense where its level density is at most 10 3 times higher than the 134 Te density and this large increase will dominate the overall decay.

Then the enhancement in the spectrum is induced by the reduced level density of the heavy fragment that favors continuum-discrete transitions while the light one should exhibit an exponential decay in the same energy range. FIFRELIN calculations were performed to test the consistency of strength-driven or densitydriven fragment decay. The pre-neutron data used came from the VESPA [START_REF] Travar | Experimental information on mass-and tke-dependence of the prompt ssion γ-ray multiplicity[END_REF] experiment, the microscopic level density using Skyrme interaction was used, along with QRPA strength functions. Figure 4.7a shows the FIFRELIN calculation for the prompt decay on the 134 Te 6 + isomer with the complementary fragment decays. One can see that the strength-driven spectrum associated with the heavy fragment (green) show a clear slope dierence with the density-driven light contribution (red), creating an enhancement between 3.5 and 7 MeV.

In all other mass region, the ssion fragments are more deformed than 134 Te so their level density is signicantly larger, making it the main driving component of the statistical decay.

Therefore the prompt spectrum will have a smooth and close to exponential behavior at high energy for both heavy and light fragments. Figure 4.7b shows the prompt spectrum gated by 108 Tc as the light fragment using FIFRELIN. Both the heavy and light spectra show a relatively similar slope above 3 MeV, which can be understood by small variations between their level densities. They dier by at most a factor of 2 below 8 MeV. Nonetheless this explanation of strength-driven or density-driven decay is not sucient to explain the experimental spectra. If one compares the measured 134 Te prompt cascade (and complementary fragments' cascades) with the FIFRELIN simulation, as done in Figure 4.8, one can see that some structures are seen and not reproduced. Possible explanations could be that the strength functions are still lacking: there is experimental evidence for an E1 resonance in the even-even nuclei of the isotone N = 82 near 6 MeV [START_REF] Savran | Fragmentation and systematics of the pygmy dipole resonance in the stable n = 82 isotones[END_REF], that is not reproduced by the QRPA. The study of two-step cascade has proven to be sensitive to pygmy resonances in the γSF [START_REF] Denis-Petit | Isomeric ratio measurements for the radiative neutron capture 176 Lu(n,γ) at the lanl dance facility[END_REF] so looking at this type of cascade might solve the discrepancies.

Comparison with the other isomers

The previous sections explained that the enhancement seen in the spectrum gated by 134 Te is caused by a dierence in the spectrum slope between the heavy and light fragment. This subsection would like to address a curiosity observed in Figure 4.2. There, some isomer gated spectra do not show this enhancement. The cases where the bumps cannot be seen are either isomers with a high excitation energy or nuclei with low S n value, as summarized in Table 4.2. By neglecting the n-γ competition it is impossible for those nuclei to emit photons with more than 4 MeV. The 19/2 -isomer in the 133 Te and the 19/2 + isomer of 129 Sn cannot emit photons of 4 MeV or higher below S n but these two still present an enhancement above 3.5 MeV. This contribution is expected to come from the n-γ competition then the neutron emission probabilities were looked at with TALYS [START_REF] Koning | Talys 1.0. International Conference on Nuclear Data for Science and Technology[END_REF]. The γ emission is on rst approximation E1+M1 transitions, meaning that the 133 Te is fueled by {17/2, 19/2, 21/2} ± states. The neutron emission probabilities for these six spin/parity couples are displayed in Figure 4.9 for the 133 Te. The neutron emission kicks o roughly 2 MeV above S n which leads to a maximum E γ of 6 MeV. A similar trend is observed for the 129 Sn. This remaining enhancement in the spectra is then explained by the n-γ competition which is favorable to the γ emission several MeV above S n due to the high spin of the isomer.

Isotope E * iso [keV] S n [keV] E max γ = S n -E * iso [keV]

Constraints on neutron emission in ssion codes

This section will focus on the comparison with ssion codes of the KE and TKE distribution gated by isomers. The shape of the KE and TKE distributions predicted by ssion codes is closely related to the energy sharing between the fragments and the neutron emission, therefore their measurement oers a benchmark for these codes simulating the ssion observables.

4.2.1

The isomer-gated kinetic energy distribution (a) 132 Sb.

(b) 95 Sr.

(c) 154 Nd. The rst observable is the kinetic energy. When the selection of the isomer is done one can easily determine in which side of the chamber the isomer deposited its energy. It is assumed in the following discussion that the γ decay does not impact the kinematic of the fragments, therefore the experimental distribution (gated by isomers) will be directly compared with outputs from FIFRELIN and GEF gated in mass and charge. Moreover the calculated distributions are convoluted with a gaussian to account for the nite resolution of the FGTIC, determined previously (see Sec. 3.2.6). Figure 4.10 shows the comparison of the GEF and FIFRELIN calculations with the experimental data for the case of 132 Sb, 95 Sr and 154 Nd. FIFRELIN calculations for the 132 Sb are done with the NLD from BSk14, while 95 Sr and 154 Nd uses CGCM level density. Both GEF and FIFRELIN distributions are shifted to match the experimental mean kinetic energy value. This shift is expected for both: GEF is known to have a higher TKE than the measurements for the 252 Cf ssion, so it should also reect on the KE. FIFRELIN uses data-sets as inputs for the kinematics and the calculations done here were performed with the VESPA data [START_REF] Piau | Prédiction par calcul des observables de ssion à partir d'expériences dédiées[END_REF] that measured slightly dierent values for the KE and TKE than in this work. The shape of the GEF calculation is in excellent agreement with the present data for all isomers detected. The FIFRELIN calculation systematically shows a more structured distribution, it is quite pronounced for 132 Sb. The experimental resolution cannot solely explain that such structures are not seen in the experiment.

(a) 132 Sb.

(b) 95 Sr.

(c) 154 Nd.

(d) 132 Sb.

(e) 95 Sr.

(f) 154 Nd. This matter was further investigated by looking at the dierent contributions for 0, 1, 2 . . . neutrons emitted in the FIFRELIN and GEF distribution. As shown in Figure 4.11e the overlap between the dierent neutron contribution is abnormally wide when compared to the other selected nuclei. This matter is investigated in this section.

Shouldering in the TKE distribution

The TKE distribution is more sensible to the neutron emission than the KE so Figure 4.12 shows the TKE distribution for the present work gated by the 95 Sr isomer, compared with GEF calculation, divided according to the neutron emission. GEF predicts a bi-modal shape that is not compatible with the present work. The weight of a high neutron multiplicity is too big to reproduce the present work.

Role of the ssion modes

If one wants to properly understand this strong weight on high neutron multiplicities for the 95 Sr one needs to dive a bit inside GEF and introduce ssion modes and energy sorting. The following discussion is based on results provided by the GEF code. The fragmentation of Sr-Nd in GEF is at the crossing between two ssion modes (following Brosa et al. [START_REF] Brosa | Nuclear scission[END_REF]). GEF adjusts those modes to reproduce the post-neutron mass yields as shown in Figure 4.13a, 3 modes are required.

The S1 mode is usually described as a compact mode where the heavy fragment is spherical due to the proximity with 132 Sn. The S2 mode is the usual mode for asymmetric ssion while the S3 mode describes a ssion mode with higher elongation, resulting in higher deformation for the ssion fragments. Since the fragments are more deformed in S3 the TKE will be lower than for the S2 mode, leaving more room to neutron emission.

The GEF code uses an energy sorting at low excitation energy (roughly below 20 MeV) [3,[START_REF] Schmidt | Entropy driven excitation energy sorting in superuid ssion dynamics[END_REF] based on statistical mechanics arguments stating that a great part of the energy of the "hottest" fragment is transferred to the "coldest" to attain a temperature equilibrium. In this region, light nuclei are supposed to have the highest temperature as shown by the dashed This eect is not a specicity of this fragmentation since the same behavior is observed when comparing isomers seen in the present work with A L < 100 (where the S3 mode is predominant) with GEF calculations (see Figure 4.15). Since a good agreement between GEF and the present work is found for regions where only the S2 mode is present (zB. 134 Te), the S3 mode is the origin of the discrepancy between the present work and GEF. This large discrepancy on the TKE distribution questions the good agreement in the KE distribution (see Figure 4.11e). than in S2 the light fragment is getting less energy in the former. In GEF the excitation energy of the fully accelerated fragments can be approximated to:

E * L,H ∼ E intr. L,H + E def. L,H (4.2)
with E intr. L,H the intrinsic energy, distributed according to the energy sorting and E def.

L,H the deformation energy released by the fragments relaxation. Due to the energy sorting the 95 Sr will only get a small part (expected to be roughly the same in both ssion modes) of the intrinsic energy. However the deformation of 95 Sr depends on the ssion mode: β = 0.44 in S2 and β = 0.33 in S3. Then since 95 Sr is less deformed in S3 than in S2, its deformation energy is smaller, which explains the decrease of the emitted neutron number. It is the opposite for the partner: its deformation is higher in S3 (β = 0.53) than in S2 (β = 0.34) and it will receive most of the intrinsic energy from the energy sorting. This combined eect increases the neutron emission by almost a factor 2 (see Figure 4.16f ).

In order to have a better reproduction of the present work, one could play on two parameters: the intensity of this mode and the associated deformation. The goal would be to reduce the total excitation energy of the system so one can either reduce the S3 contribution regarding S2 (but it would aect the mass yield of many nuclei) or shift the S3 contribution to higher TKE, ie. less deformed scission shapes (it would mechanically impact the neutron sawtooth). Moreover the even-odd eect is not seen elsewhere, with the exception of A=140. The predominance of A=132 and A=134 in the cold ssion selection and the high Q-value of the even-even fragmentations lead to further investigations for these two cold fragmentations, starting with A=132.

5.1 Measurement of the angular momentum of 120 Cd at low excitation energy

In the following the cold mass split 120/132 is discussed. The 120 Cd is rst identied then its angular momentum is determined from the reproduction of the associated prompt spectrum with DEGA and the help of a Monte-Carlo method.

Charge identication

This subsection will explain how the 120 Cd/ 132 Sn fragmentation is identied using the TKE distribution and the measured discrete γ-rays.

The T KE pre distribution for the mass split 120/132 possess a shouldering at very high In the case of the present work, the FGTIC is smaller and operated at higher pressure than [START_REF] Knitter | Nuclear mass and charge distributions in the cold region of the spontaneous ssion of 252cf[END_REF] which induce a small range and an insucient resolution on the charges, however 5.2 and in black in Figure 5.3a, these are the transitions that should have the highest intensity after the decay of 120 Cd or 132 Sn. One can see that the peaks observed are all attributed to the low-lying levels of 120 Cd, shown in Figure 5.3b. No clear peaks are visible in Figure 5.3a that could correspond to 120 Pd, 132 Te, 120 Ag or 132 Sb. Two statistical limits can be introduced as developed in [START_REF] Gilmore | Practical gamma-ray spectrometry[END_REF] (see Appendix B), to quantify the presence or not of the γ-rays of interest: the critical limit and the upper limit. The rst one describes if a peak count is statistically signicant, the second quanties, if the count is not statistically signicant, the maximal presence of the peak. Since L U = peak net count + L C , L U can be equal to L C if the net count is negligible, which is the case here.

The critical and upper limits are listed in Table 5.2. None of the peaks corresponding to charge splits other than 48/50 are seen with sucient statistics. Their maximum presence (in the last line of Table 5.2) corresponds to the upper limit deconvoluted for the photopeak eciency and expressed as a percentage of the total number of events. Low-lying structure of 120 Cd according to [START_REF] Luo | Nuclear structures of the neutron-rich nuclei around a=120[END_REF].

For the cases of 120 Cd and 132 Sn, their rst excited states were looked at for the whole cold ssion in the spectrum shown in Figure 5.4a. Only four peaks are well dened, all below 1 MeV. Figure 5.4b shows this energy range with a smaller binning. All these peaks can be attributed to the vibrational band of 120 Cd. As can be seen in Figure 5.4a nothing statistically signicant is found around the 2 + state of 132 Sn(4.042 MeV). Using the same limits as previously, the 2 + state of 132 Sn is seen in less than 1.76% of the events (less than 4 counts in the measured spectrum). This result implies that 132 Sn is populated in its ground state and that all the transitions measured by the NaI array are coming from the 120 Cd. Since the 132 Sn is found in its ground state the excitation energy distribution of 120 Cd can EXCITATION ENERGY be extracted using: E * ( 120 Cd) = Q -T KE. This distribution is shown in Figure 5.5a, it is the rst measurement of such quantity in ssion. Cold ssion is usually described at scission as two fragments in their ground state deformation in contact with each other.

In the case of 120 Cd/ 132 Sn, both are spherical in their ground state, meaning that their deformation energy is vanishing and their excitation energy only comes from the dissipated energy before scission (see Equation (1.8)). Although this ssion without excitation in the heavy fragment might be unexpected, it is in agreement with the dierent models of energy repartition. Figure 5.5b shows the repartition done if one considers a constant temperature (red) or Fermi gas (light blue) level density compared to the present work. The lower curves are the energy given to 132 Sn, its rst excited state is symbolized by the purple dashed line.

Up to 8 MeV of TXE at most 3 MeV is given to 132 Sn, meaning that it cannot be excited. One need to be careful when looking at Figure 5.5b: the two models used are suited for averaged description but it is used here in an energy range where the levels are discrete. Then if a fragment is given an energy between two discrete levels E 1 ≤ E * < E 2 it has to stay at the lowest excitation and the remaining energy δE * = E * -E 1 is given to the other fragment.

Therefore the two models are equivalent to the green curves, representing the present work.

It is worth noticing that the energy repartition shown here is the inverse of Figure 1.4: the heavy fragment is the least excited one. This can be explained by the double magicity of 132 Sn: this double shell closure give low level density meaning that the light nucleus is the one with more states available, hence a higher excitation energy, according to the energy sorting mechanism.

(a) Excitation energy distribution for 120 Cd.

Determination of the spin distribution of 120 Cd

The reproduction of the 120 Cd prompt spectrum will put constraints on the models used in the de-excitation code. DEGA was used to simulate the cascade and some inputs are mandatory:

An initial excitation energy distribution, it was xed from Figure 5.5a. An initial spin and parity distribution, the parity distribution was taken as equiprobable and the spin distribution of the initial state was described by the usual parametrization:

P (J, σ) = 2J + 1 2σ 2 exp(- (J + 1/2) 2 2σ
2 )

(5.1)

with the spin-cuto parameter σ, the value of this parameter is determined through Markov chains (see Sec. 5.1.2.5).

A discrete level scheme, Level density and strength function models,

The last two points and the sensitivity of the corresponding calculated spectrum are the focus of the two next subsections.

Discrete level scheme

The energy range below 1 MeV corresponds to 80% of the 120 Cd prompt spectrum statistics, therefore the discrete transitions hold a signicant weight in the overall spectrum. The description of the 120 Cd structure put in DEGA will have a major role in the reproduction of the experimental spectrum. 120 Cd is 4-neutrons away from the closest stable Cd isotope and the experimental knowledge on its low-lying structure is scarce. The highest level seen in the present work is the 5 -state at 2.123 MeV so the discrete-continuum limit was put just above at 2.2 MeV. Figure 5.6a shows the calculated spectrum (with DEGA+Geant4 matrix) using only the known levels from the RIPL-3 database. One can see that the weight of the double bump between 800 keV and 1 MeV is not well reproduce.

The Cd nuclei are typical example of vibrational nuclei, the low-energy structure of the eveneven Cd isotopes are extremely similar. Therefore the 120 Cd level scheme was completed with calculated levels with systematics from the Cd isotopes and an anharmonic vibrational structure up to 2.2 MeV (discrete/continuum limit). It is shown in Figure 5.7b with the new states an transition in light blue. The spectrum in Figure 5.7a shows that the completion of the level scheme has some eects, especially in the relative feeding of the 6 + and 5 -states that are both seen in the data but was not correctly described with the 120 Cd level scheme.

The 2 + and 4 + are not really impacted by the changes. In the following the completed level scheme is used.

γ strength function

A variety of models for both γSF and NLDs are available, be it parametric or microscopic.

As discussed previously most of the statistics is found below 1 MeV, then the strength function and level density is not expected to be highly constrained by the present work.

The shape of the available γSF below 8 MeV is shown in Figure 5.9b. The three densities presented here are all adjusted (see [START_REF] Koning | Talys 1.0. International Conference on Nuclear Data for Science and Technology[END_REF] for more details)

to reproduce the discrete level density, which explain the little dierences between them.

Once again the experimental spectrum is correctly reproduce, rather independently of the NLD choice.

EXCITATION ENERGY

Initial spin distribution

It is found that the spin-cuto of the initial spin distribution is the only sensible parameter. Figure 5.10a shows the calculations from DEGA using three dierent spin-cuto parameters compared to the experimental spectrum. It shows some sensitivity on the energy range above 2 MeV even though it has low statistics. As shown in Figure 5.10b the discrete rays intensities vary signicantly with the initial spin-distribution making it a suitable parameter alongside the parameters of the constant temperature NLD model (T and E 0 ), to adjust on the experimental spectrum. The choice to include the latter two was made because the available models are re-normalized or tuned on a scarce knowledge of the level scheme. This adjustment was made with Markov Chains Monte-Carlo (MCMC). This method was used because it allows to determine the probability distribution of the parameters and not just the most probable value. This distribution can be interpreted as an uncertainty.

Normalized N γ / 50 keV (a) High energy part of the spectrum.

Markov Chains Monte-Carlo

A Markov chain is a sequence of random variables, or link, where the variable at the ith iteration depends only on the value of the previous iteration. The random variables are dened by a set of parameters q, each parameter is distributed according to a prior distribution P (q). In the present work the prior is a normal distribution whose standard deviation can be perceived as an uncertainty on the parameter. The goal is to nd the posterior P (q|E) from bayesian inference. The posterior is the probability that q describe E knowing E. From Bayes' theorem one can express the posterior as:

P (q|E) = P (E|q) • P (q) P (E) (5.2)
where:

E is the measured quantity that the parameters q should reproduce, P (E) is called the marginal likelihood and is independent of the choice of q and does not play a role in determining the posterior, P (E|q) is called the likelihood. For a given q it gives the compatibility of the evidence E with this hypothesis. For the present case the evidence is the prompt spectrum, that can be described by {x i , y i , σ i } where x i are the measured γ energies, y i their count number and σ i are the counts uncertainties. In a practical way the index i can be seen as a bin number in an histogram. Then the likelihood is dened as:

P (E|q) = i 1 √ 2πσ i exp - 1 2 α (y i -f (x i , q)) 2 σ i = e -αχ 2 (q)/2 i 1 √ 2πσ i (5.3)
where f (x i , q) associate an expected count number in the prompt spectrum for a given energy and set of parameters q. In the present work this is done through a de-excitation code. The most probable q will maximize the likelihood, ie. minimize the χ 2 . The parameter α will be discussed later.

It was mentioned before that the q n+1 depends only on q n . The next link is taken according to probability density, w(q n+1 ), depending on q n , here a normal distribution is used. The generated link is then accepted according to: a < r(q n+1 , q n ) (5.4) where:

a is a random variable following a uniform distribution between 0 and 1, r(q n+1 , q n ) = L(E|q n+1 ) • P (q n+1 ) L(E|q n ) • P (q n ) is a ratio that allows to keep values of q less probable to ensure that the whole phase space has been explore.

If a > r(q n+1 , q n ), then q n+1 is rejected, q n is registered as the new link and a new set of parameters is generated. The parameter α introduced in Equation (5.3) controls the rejection rate. Another factor to limit this rate and ensure the convergence is the standard deviation of w(q n+1 ). It is modied during the early building of the chain, typically it remains unchanged after 300 links for the present work.

The determination of the likelihood in the present work is a costly operation, a simulated spectrum needs to be determined from the new parameters q n+1 in order to compute the χ 2 . This is done through a deterministic de-excitation code providing similar results as DEGA.

For each link an emitted spectrum is computed and then convoluted by the Geant4 matrix to account for the detector response. Finally a χ 2 can be determine between the measured prompt spectrum and the calculated one.

The burn-in, shown in Figure 5.11, corresponds to the early links of the chain were the phase space of q is explored before the chain becomes stationary and converges towards the sought distribution. This nal step is called thermalisation. The burn-in is just a stage to search for the minimum of the phase space and needs to be discarded to get the posterior distribution.

In the present work 510 chains were calculated on 510 cores in parallel. The burn-in phase of each chain was excluded to determine the parameters shown in Figure 5.12. All the

.11: Evolution of the spin-cuto parameter with the number of links in a chain.

The limit between the burn-in and the thermalisation is at roughly 3000 iterations.

parameters present an almost-gaussian behavior and are well-dened. The parameters T and E 0 are highly correlated, which is expected since they are part of the same functional.

The spin-cuto is not really correlated to the temperature or E 0 . It is also expected since the initial spin distribution might only depend on the spins available at a given energy and not on the total number of levels at this energy.

The tted level density is in good agreement with the systematics, as shown in Figure 5.13.

The CGCM level density is also shown, the discrepancy below 4 MeV with the constant temperature from MCMC or Egidy et al. [START_REF] Egidy | Systematics of nuclear level density parameters[END_REF] can be understood by the adjustment made in TALYS on scarcely known levels, inducing a lower level density.

The spin-cuto found with the MCMC is σ = 3.7 ± 0.2 . Figure 5.14 shows the associated distribution. The errors are determined from the distribution associated to σ = 3.5 and σ = 3.9 .

One recalls that the total angular momentum is conserved so:

S 0 = S L + S H + L (5.5)
where S L is the spin of the light fragment, S H the spin of the heavy fragment and L the orbital momentum between the two fragments. In the present work S 0 = 0 ( 252 Cf spontaneous ssion) and the 132 Sn nucleus is identied in its ground state, so S H = 0. Then, from Equation (5.5) one concludes that:

S L = -L ⇒ S 2 L = L 2 (5.6)
which means that the 120 Cd spin distribution (Figure 5.14) determined from the prompt spectrum is also the orbital angular momentum distribution. This is the rst experimental information on this momentum.

The reproduction of the prompt spectrum of the 120 Cd was mainly sensible to the variations of the spin-cuto parameter. Markov Chains Monte-Carlo were used to determine its value and uncertainty: σ = 3.7 ± 0.2 .

Comparison with ssion codes

The present work is the rst experimental determination of the angular momentum in the cold ssion, then direct comparison can only be done with ssion codes. The comparison is done here with GEF [START_REF] Schmidt | General description of ssion observables: Gef model code[END_REF]. It uses the statistical description of Equation (5.1) as its initial spin distribution, determined for both fragments independently. The spin-cuto parameter is energy-dependent σ(E * ), with a parametrization that can be found in [START_REF] Schmidt | General description of ssion observables: Gef model code[END_REF].

Since the spin-cuto depends on the excitation energy one need to check whether the calcu- ssion through a microscopic approach have been published [START_REF] Bulgac | Fission fragment intrinsic spins and their correlations[END_REF][START_REF] Scamps | Generation, dynamics, and correlations of the ssion fragments' angular momenta[END_REF]. Work is undergoing to compare the present work with [START_REF] Scamps | Generation, dynamics, and correlations of the ssion fragments' angular momenta[END_REF].

5.2 Determination of the excitation energy repartition in 118 Pd/ 134 Te

The previous section showed that for the mass split 120/132 all the energy available could be exhausted by the TKE, which allows absolute calibration of the FGTIC. Moreover this selected cold ssion line is a special case where only one fragmentation is detected, with the heavy fragment ( Similarly to the 120 Cd/ 132 Sn case it is assumed in the following that both nuclei are created at scission in their ground state deformation, meaning that the excitation energy is only intrinsic. The splitting of the TXE is determined through a genetic algorithm.

Events/ 300 keV

Genetic algorithm

The genetic algorithm is based on the principle of natural selection and is best suited for optimizations or search problems and especially optimization with no prior knowledge on the shape of the functional to optimize. The excitation energy repartition is exactly this type of optimization problem. This type of algorithm starts with an initial population of potential solutions, each solution is dened by a set of properties (similar to chromosomes or genotypes) that will be modied through breeding and mutations. Genetic algorithms are iterative processes, at each step, or generation, the previous population will be updated with new individuals closer or not to the solution, according to a selection criterion. Throughout the iterations the population will converge towards the optimal solution. The determination of the uncertainty on the solution found by the algorithm is not an easy task and was not performed in the present work.

Genotype

In (a) The whole initial population. The population has to be sorted according to a tness criterion in order to quantify if an individual reproduces well the prompt spectrum or not. In the present work this criterion f c = 1/χ 2 is the inverse of the χ 2 between the measured spectrum and the calculated one, using the repartition determined by the genotype of the individual. To get the calculated spectrum from the genotype, spectra from a database are summed up according to the genotype. This database has been created beforehand and contains DEGA spectra for 118 Pd and 134 Te for steps in excitation energy of 20 keV, they are convoluted by the Geant4 matrix to account for the detector response. In DEGA if the excitation energy is between two discrete levels then it is decreased to the lowest one, then the TXE is not conserved.

This approximation is expected to quickly be negligible as the level spacing decreases.DEGA does not handle the timescale of a state decay so the experimental spectrum corresponds to

Evolution of the population

To create new generations the individuals will breed and create new individuals that will replace the 10% with the lowest f c . This value of 10% was determined through multiple tryouts. If the replacement rate is too high the good individuals will not have time to spread their genotype and the algorithm will not converge. On the opposite if the replacement rate is too low, the population will quickly converge towards the best individuals without exploring the full phase space, ending in a local minimum.

Breeding

There are dierent methods to breed individuals, the present work used the following: two parents are randomly selected with weight proportional to their f c , in most of the cases they are not replaced by their child. The child will inherit random parts of the genotype of its two parents. The genotypes are inherited in blocks of length randomly taken between 5 and 55, alternating between parent 1 and parent 2. The rst parent to give its genotype is randomly chosen. The child possesses in general a tness score lower than its parents, numerous iterations are required to improve the population. 118 Pd and 134 Te. The light blue dashed line marks the continuum-discrete limit for 134 Te, the one for 118 Pd is in purple. The rst thing to notice is that the 134 Te is only excited in its discrete levels. Then one can remark that the plateau in the 134 Te excitation energy corresponds to its rsts excited states. Before the 2 + , its excitation energy is almost 0, and the increase from 0 to 1279 keV is close to the fastest possible. Since discontinuities are forbidden, the excitation energy cannot jump from 0 to 1279 keV when the latter is available. During these increases the TXE is not conserved. This violation of the TXE conservation is a little as it can be using a continuous description of the excitation in the increase to the rst excited states of 134 Te and 118 Pd. Using such description is inappropriate when both fragments are excited in their discrete level scheme, still there is no modelisation, to the knowledge of this author, that can treat the TXE as a discrete quantity from the start. Nonetheless the genetic algorithm performed in the present work produces stagnation on the discrete levels of 134 Te without being given any knowledge on the level scheme and its discrete character other than the transitions intensities through the experimental spectrum.

Sensitivity to the spin-cuto

The sensitivity of the solution to the values of spin-cuto taken for 118 Pd and 134 Te is explored here. Figure 5.25 shows the evolution of the solution found with the genetic algorithm with variations of the spin-cuto parameter. Since the 134 Te is found in its discrete level scheme its decay is independent of the choice of spin-cuto. The The ranges where the TXE is not conserved are clearly the less dened ones with greater variations with the spin-cuto. Overall the solution found is weakly correlated to the spincuto, it validates the choice made to apply the spin-cuto determined for the 120 Cd directly to the 118 Pd.

Comparison with models

The rst determination of the excitation energy below S n for 118 Pd/ 134 Te done in the present work oers a common ground to compare the dierent approaches. As described in the rst chapter there are mainly two ways to share the excitation energy between the two fragments in the parametric ssion codes and the recent publications of M. Albertsson et al. [5,[START_REF] Albertsson | Correlation studies of ssion-fragment neutron multiplicities[END_REF] showed new perspectives using microscopic level densities, dependent on the pre-fragments deformation.

Parametric approaches

The rst parametric method supposes a statistical equilibrium where the energies are expressed as E * L,H = a L,H T 2 with a L,H being the Fermi-Gas level density parameter. Then the energy repartition is done through:

E * L = T XE 1 + a H a L T H T L 2 (5.7)
where the fragments are assumed spherical. This repartition needs an iterative treatment since the level density parameter a L,H depends on the excitation energy.

The second approach uses the micro-canonical description of Equation (5. The second approach assumes that the constant temperature description of the level density is valid up to a dozen MeV which simplify Equation (5.8) to:

               E * L = r + T XE 1 -exp(T XE/r) E * H = T XE • exp(T XE/r) exp(T XE/r) -1 -r, with r = T L T H T L -T H (5.9)
when the constant temperature density ρ CT = exp((E * -E 0 )/T )/T is taken. Both repartition methods depends on the temperature of the fragments. This quantity is not well dened for exotic nuclei, it is usually determined through level density adjustment, which is scarcely known for neutron-rich nuclei. It was already found that the rst method (Fermigas) needs to adjust the temperature ratio in order to reproduce ssion observables such as neutron multiplicity [4,[START_REF] Talou | Advanced monte carlo modeling of prompt ssion neutrons for thermal and fast neutron-induced ssion reactions on 239 Pu[END_REF]. The adjusted ratio deviates greatly from the systematics from [START_REF] Egidy | Systematics of nuclear level density parameters[END_REF]. The two repartitions are shown in Figure 5.26, the temperature ratio of 1.4 has been used, according to [START_REF] Talou | Advanced monte carlo modeling of prompt ssion neutrons for thermal and fast neutron-induced ssion reactions on 239 Pu[END_REF][START_REF] Piau | Prédiction par calcul des observables de ssion à partir d'expériences dédiées[END_REF], for the parametrization E * = aT 2 . The level density parameters were taken constant (a L = a L (E * ) and a H = a H (E * ) ). The temperature from [START_REF] Egidy | Systematics of nuclear level density parameters[END_REF] (T L = 0.713 and T H = 1.018 MeV) were used for the constant temperature level density. 134 Te, the full lines to 118 Pd.

The rst thing to notice is that the two approaches have dierent shapes, Equation (5.9) (constant temperature) shows a kind of stagnancy for 134 Te while Equation (5.7) displays a constant increase. Below 4 MeV in TXE both models give some excitation energy to 134 Te even if no levels are accessible, this violation of the TXE is more important when using Equation (5.9). Above TXE=5 MeV the agreement is only relative: Using E * = aT 2 gives an excitation energy systematically below the rst excited state of 134 Te for the whole TXE range considered. On the opposite the constant temperature approach will give too much excitation energy to 134 Te. Since the intensities of the discrete peaks are highly constraining, it is expected that spectra simulated using those energy repartitions do not reproduce the experimental one.

One needs to recall that both parametric approaches are approximations: the constant temperature approximation falls short to describe the level density above several MeV, and the one based on E * = aT 2 parametrizes the temperature ratio in order to reproduce the neutron sawtooth pattern. The recent publication of M. Albertsson et al. [5,[START_REF] Albertsson | Correlation studies of ssion-fragment neutron multiplicities[END_REF] introduces a method to share the intrinsic energy using microscopic level densities, which greatly reduces the number of assumptions one has to make. 5.2.3.2 Application of the micro-canonical sharing to microscopic NLD M. Albertsson et al. [5,[START_REF] Albertsson | Correlation studies of ssion-fragment neutron multiplicities[END_REF] showed that neutron emission data was greatly reproduced by sharing the intrinsic energy with respect to the number of available states in the fragments. the sharing is related to Equation (5.8) since they determine a probability to populate the heavy fragment with a certain excitation energy E * H knowing the TXE:

P (E * H |T XE) ∝ ρ H (E * H , ε H ) • ρ L (T XE -E * H , ε L ) (5.10)
where ε H and ε L are the deformation of the fragments at scission. This method allows to determine the whole probability distribution of the sharing of the intrinsic energy. The diculty of this method is to determine the deformation at scission to get the deformed level density. In the present work the fragments are populated at low excitation energy and one can assume in rst approximation that they are populated in their ground state deformation. Then the mean energy sharing using microscopic level densities are shown in 134 Te and 118 Pd using the Gogny [START_REF] Goriely | Péru : First gogny-hartree-fock-bogoliubov nuclear mass model[END_REF] or Skyrme [START_REF] Goriely | Further explorations of skyrme-hartreefock-bogoliubov mass formulas. vii. simultaneous ts to masses and ssion barriers[END_REF] interaction. the prompt spectrum by randomly generating the energy repartition according to the relevant probability distribution. This could not be done before the end of this manuscript.

The energy repartition using E * = aT 2 or the micro-canonical sharing with the constant temperature NLD rely on the nuclear temperature, that is adjusted in [4,[START_REF] Talou | Advanced monte carlo modeling of prompt ssion neutrons for thermal and fast neutron-induced ssion reactions on 239 Pu[END_REF] to reproduce the neutron sawtooth. Relying on the microscopic NLD allow to not depend on the nuclear temperature, not well known for exotic nuclei and usually parametrized. Using such NLD has already proven to improve the reproduction of photon observables [START_REF] Piau | Neutron and gamma multiplicities calculated in the consistent framework of the hauser-feshbach monte carlo code frelin[END_REF], applying them to the energy sharing could increase the consistency of the ssion codes.

The micro-canonical sharing of the excitation energy is based on statistical repartition of the energy between the available states, it allows to use microscopic NLD and therefore bypass the denition of a nuclear temperature. This approach could be used here under the assumption that the scission deformation is close to the ground state deformation. In order to apply this description to the full energy range and not just the cold ssion, the scission deformations are needed. Finally expanding the measurement of ν(A, T KE) to other ssioning systems could also help the theoretical description of the energy sharing, as shown by M. Albertsson et al. [5,[START_REF] Albertsson | Correlation studies of ssion-fragment neutron multiplicities[END_REF]. This work E * =aT 2 const. temp. Skyrme-HFB Gogny-HFB

Conclusion and Perspectives

The present work studied the radiative decay and the kinematics of the fragments created by the spontaneous ssion of 252 Cf. Such study allow to understand more precisely the ssion mechanism and creates additional constraints on the codes that aim at describing the ssion process, from the creation of the fragments to the emission of the prompt and delayed particles.

The experimental setup, composed of a twin ionization chamber and 54 Sodium-Iodide (NaI) crystals, was specically designed to measure extremely rare ssion events where no neutrons are emitted (cold ssion). In order to observe such events an ultra-thin carbon backing, ∼20 nm thick, was made, with 252 Cf deposited on it. The experiment was run for 6 months and a consequent amount of data was collected. A careful analysis was performed in order to treat correctly the cold ssion events. It lead to an excellent mass resolution for such events (0.68 a.m.u.) as well as the rst comprehensive evaluation of the uncertainties on the kinetic energies (0.57 MeV) of the fragments. From the analysis of the γ decays of the fragments 28 isomers were measured.

Previous measurements of prompt γ spectra gated on the mass of the fragments highlighted structures between 3.5 and 7 MeV for masses close to symmetry, without being very conclusive on their origin. The measurement of multiple isomers close to the symmetry range shows the statistical nature of these structures. Moreover thanks to the two isomers seen in the 134 Te with a large dierence in excitation energy it conrms, without doubts, that the structures originate from the γ cascade of the heavy fragment. By looking at the photon emission probability in both 134 Te and the Pd isotopes it was found that the cascade of 134 Te is more "strength"-driven, which will favor the emission of transitions of high energy from the continuum to the discrete levels, because of the strong shell eects that greatly reduce its level density. On the opposite, the Pd cascade is more "density"-driven, which will favor transitions of low energy within the continuum. This behavior was supported with FIFRELIN calculation showing that the enhancement is mostly due to a change of slope between the light and heavy prompt spectra. The measured and calculated spectra are in good agreement, but improvement is still possible by using a richer strength function for example. The one used does not present an E1 pygmy resonance around 6 MeV that was systematically observed in the stable isotopes of N=82, for example.

The correlated measurement of the kinematic properties of the fragments and the isomeric decay performed in the present work has proven to be a constraining observable for both FIFRELIN and GEF. The rst systematically displays more structured distribution in preneutron kinetic energy, not compatible with the excellent resolution of the present setup.

The structures are extremely marked near 132 Sn, and imputed to the 0-and 1-neutron emitted channels. While GEF displays a good agreement on the KE pre distribution, the study of the TKE distribution reveals disagreement with the present work. This disagreement is associated with the ssion mode standard III (S3), or super-asymmetric, which causes the FISSION TKE predicted by GEF to be bi-modal for the masses below A L = 98. This bi-modal shape overestimates the TKE distribution at low TKE. This overestimation was investigated with GEF, showing that the S3 mode has on average a lower TKE and a higher deformation in the heavy fragment. Because of the energy sorting a great part of the additional excitation energy will be given to the heavy and, coupled to its higher deformation, it will emit on average twice more neutrons than in the S2 mode. This is the reason behind the overestimation of the TKE distribution at low TKE in GEF. There are two possibilities to improve the GEF description, either change the intensity of the S3 mode, or reduce the deformation associated to the mode. In both cases a new t of the GEF parameters should be performed.

The study of cold ssion events was performed on two mass splits: 120/132 and 118/134.

In both cases there is a TKE range for which only one fragmentation (identied in A and Z) is possible, namely 120 Cd/ 132 Sn and 118 Pd/ 134 Te. The study of the low energy part of the prompt spectrum associated to the cold masses 120/132 allowed to clearly identify the low-lying structure of 120 Cd and evaluate the contribution of other charge splits as negligible in the cold ssion selection. Similarly the 132 Sn was not observed in an excited state and it is populated in its ground state in at least 98% of the selected events. This is a rst measurement of the excitation energy repartition in ssion, where the entirety of the excitation energy is found in 120 Cd. This result is predicted by both phenomenological approaches, either based on E * = aT 2 or a constant temperature description of the level density. It allows to measure for the rst time the excitation energy distribution of 120 Cd in the ssion, as well as the rst comprehensive absolute calibration of the twin ionization chamber. The reproduction of the prompt spectrum showed great sensitivity to the initial spin distribution that was determined through a Markov Chain Monte-Carlo method. It is well reproduced by the GEF parametrization. The next step would be to compare the determined distribution to microscopic calculations.

A similar study was performed on the mass split 118/134, where the fragmentation 118 Pd/ 134 Te is clearly identied. Since 118 Pd is two protons away from 120 Cd, it was assumed that its spin distribution is the same. 134 Te is only populated in its discrete level scheme therefore its initial spin distribution is fully determined. The excitation energy repartition was determined through a genetic algorithm. This repartition is determined for the rst time. The result showed little sensitivity to reasonable variations of the spin distribution. Both phenomenological approaches, either based on E * = aT 2 or a constant temperature description of the level density, reproduce the tendency of the determined repartition. The microscopic level densities were used for the energy sharing, assuming a statistical distribution of the intrinsic energy at scission and that the scission deformations were close to the ground state ones. Such description showed slightly better agreement to the experimental data. This type of description seems promising to get a microscopic description of the energy sharing at scission that does not rely on the concept of nuclear temperature, not well dened in exotic nuclei.

  34 MeV restants sont sous forme d'énergie d'excitation. Cette énergie d'excitation est distribuée entre les deux fragments créés et est emporté d'abord par les neutrons. Leur étude est primordiale pour les applications et de fait les propriétés des neutrons émis dans la ssion ont fait l'objet de très nombreuses mesures au cours des 80 dernières années, et encore aujourd'hui. L'énergie libérée par l'émission de neutrons représente 27 MeV soit 80 % de l'énergie d'excitation totale. De ce fait l'émission de neutron est une observable privilégiée pour comprendre la répartition de l'énergie d'excitation entre les fragments lourds et légers. La mesure la plus sensible est l'évolution du nombre de neutrons émis en fonction de l'énergie disponible.En 1986 Naqvi et al. ont mesuré le nombre moyen de neutron émis en ssion induite par neutron du 237 Npà deux énergies neutron incidentes. Augmenter l'énergie du neutron incident revient à augmenter le Q. Cette augmentation se traduit par une augmentation du nombre de neutrons émis par le fragment lourd : l'énergie supplémentaire amenée par le neutron est principalement donnée au fragment lourd sous forme d'énergie d'excitation. Ces mesures, montrant un partage de l'énergie inégal entre les deux fragments sont quasiment les seules à ce jour. Il n'existe pas de consensus sur les modèles à utiliser pour décrire cette répartition.

1 . 2 . 2 γ

 122 Introduction 1 Radiative decay of the ssion fragments 1.1 Global description of ssion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 An exothermic binary reaction . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Angular momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Excitation energy repartition . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Codes predicting ssion observables . . . . . . . . . . . . . . . . . . . 1.2 Theory of the photon emission . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Nuclear level density . . . . . . . . . . . . . . . . . . . . . . . . . . . strength function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 In-house code: DEGA . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Challenges in the study of photon emission in ssion . . . . . . . . . II Experimental setup and signal processing the study of the radiative decay of the nuclei created in ssion.

Figure 1 . 1 :

 11 Figure 1.1: Simplied description of the potential energy with respect to the nucleus elongation along a ssion path. Examples of shape for the ground state, ssion isomer, saddle and scission point are shown on top.

Figure 1 . 2 :

 12 Figure 1.2: Fission timeline. The red dots symbolize the protons while the white ones symbolize the neutrons.

Figure 1 . 3 :

 13 Figure 1.3: Rotation modes as described in [21]. Both wriggling and bending modes are degenerated.

Figure 1 . 4 :

 14 Figure 1.4: Comparison of the dierent energy repartition approaches. The red curves corresponds to

Figure 1 . 5 :

 15 Figure 1.5: Average prompt neutron multiplicity as a function of the fragment's mass for the neutron induced ssion of 237 Np at two incident neutron energies: 0.8 and 5.5 MeV.

Figure 1 . 8 :

 18 Figure 1.8: Schematical description of a cascade performed by DEGA. The red dashed line indicates the neutron separation energy, the green one the limit between a discrete description of the levels (below) and a statistical one (above). The orange arrows represent a possible cascade with transitions within the continuum, between a continuum bin and a discrete level and transitions between two discrete levels.

2. 2

 2 Setup description (a) Photo of the experimental setup. (b) Floor setup. (c) Ceiling setup. (d) the FGTIC with its plastic support.

Figure 2 . 1 :

 21 Figure 2.1: Detailed view of the structure for the ceiling, the oor and the fully connected FGTIC in the array.

  (a) Opened FGTIC. (b) Radioactive source placed in the cathode cavity. (c) Second electrode of the cathode put on top of the source.

Figure 2 . 2 :

 22 Figure 2.2: Photos of the opened FGTIC and the two electrodes of the cathode, taken at the LANSCE facility. The FGTIC was designed at CEA/DAM.

Figure 2 . 3 :

 23 Figure 2.3: Calibrated spectra from the 3α-source, on anode 2. The data is in black, the total t is in red and the individual gaussians used for the dierent α-peaks are in green ( 239 Pu), dark blue ( 241 Am) and light blue ( 244 Cm)

Figure 2 . 4 :

 24 Figure 2.4: Schematic illustration of the FGTIC (one side only) with its cathode C, grid G and anode A. One ssion fragment is emitted from the cathode with an angle θ, the other with the same angle but on the other side.

Figure 2 . 5 :

 25 Figure 2.5: Evolution of the pulse height with the anode voltage. The cathode one is xed at -1600 V.

  Figure 2.4):

Figure 2 . 6 :

 26 Figure 2.6: Energy lost in P-10 gas at 1.5 bar for several ions using SRIM.

  (a) Walk eect. (b) Jitter eect.

Figure 2 . 7 :

 27 Figure 2.7: Schematic illustration of the jitter and walk eect, from [82].

Figure 2 . 8 :

 28 Figure 2.8: Schematic view of the emission of fragments in the FGTIC.

Figure 2 . 9 :

 29 Figure 2.9: 2D-histogram of the anode pulse heights. (Left) Taken from [72], the neutronless events can be seen in the dashed ellipse. (Right) Raw data from this work, the cold ssion regime can be seen on each bump.

Figure 2 . 10 :

 210 Figure 2.10: Schematic view of the setup for thickness measurement.

  Figure 2.10 shows a schematic view of the setup: a 3α-source is placed in front of the backing behind which a silicon detector was installed. The shift of the alpha peaks measured by the silicon detector after traveling through the backing will give the energy loss hence the thickness. The energy loss in such small thickness is extremely low and hard to properly determine which explain the large uncertainty on the thickness of Formvar. The 252 Cf was placed on the backing by self transfer from a primary source in a secondary vacuum. The self transfer took place for two years, resulting in an activity of 45 ssions/s. The ultra-thin source is shown in Figure 2.11. The black/dark gray rectangle is the carbon foil, the 252 Cf was deposited on the part crossing over the hole of the aluminum plate. Using such exceptional

Figure 2 .

 2 Figure 2.11: The 252 Cf source being carefully installed inside the FGTIC.

Figure 2 . 12 :

 212 Figure 2.12: Schematic illustration of the columnar recombination. (Left) Case θ = 0°, ions and electrons are moving in opposite direction along the track, they have a high probability to interact with each other. (Right) Case θ = 90°, ions and electrons are moving in opposite directions perpendicular to the track, their interaction probability is minimized.

Figure 2 . 13 :

 213 Figure 2.13: The eect of increasing the eld on the pulse height for a 3α-source.

Figure 2 .

 2 Figure 2.13 shows the 2D-histogram of the anode signal versus the cathode one. From Equation (2.12) one can relate Q A /Q C to the cosine distribution. In Figure 2.13a one can see two eects: an overall linear increase of the anode pulse height with the cosine and a local decrease with the cosine in the vicinity of cos θ = 1. The rst eect stems fromthe electron capture by impurities in the gas while the second is an eect of the columnar recombination. When the eld is increased in Figure2.13b,the columnar recombination is suppressed. A slight decrease remains for angles close to 90°. In this case the charged particles travel a signicant distance in the backing and may also hit the cathode and lose much more energy. Therefore a decrease in the anode pulse height is systematically observed when the emission angle is close to 90°. Both eects are greatly reduced or suppressed for the columnar recombination by increasing the electric eld.

the 2 . 7

 27 MeV ray from the room radiation, but linearity was checked up to 4.4 MeV with an AmBe source (Figure2.14b). Similarly the dispersion of the calibration points around the expected values is rather small (shown in Figure2.14d) and its projection clearly exhibits a gaussian behavior centered on zero with a dispersion of 0.8%. The single hit away from this distribution is the 60 keV from the 241 Am which was not taken in the calibration range since the detector threshold is in the vicinity.

Figure 2 .

 2 Figure 2.14: (a) Calibration points (black dots) from the dierent sources for the NaI n°102. The red line is a linear t to the data. A good agreement between the linear t and the data is observed. (b) Calibrated spectrum for the AmBe source, the 4.4 MeV peak is found at 4.41 MeV which is acceptable within the deviation measured. (c) Total deviation from the expected energy for the calibration points, a gaussian behavior centered on 0 is observed. (d) Individual deviation from the calibration point, it is contained within 2% which shows a great linearity.

Figure 2 . 15 :

 215 Figure 2.15: Evolution of the NaI resolution with the photo-peak energy (data in blue crosses) and its t (purple) using Equation (2.35).

Figure 2 . 16 :

 216 Figure 2.16: Time distribution between the LaBr 3 and the NaI with a FWHM of 5.4 ns.

Figure 2 . 17 :

 217 Figure 2.17: Comparison of background-reduced experimental spectra (in blue) with the Geant4 response convoluted with the experimental resolution (in red).

Figure 2 .

 2 18c and Figure 2.18d

  Relative error between the spectrum convoluted with the weighted matrix and the Geant4 calculation. Dispersion of the relative error between the convoluted spectrum and the Geant4 calculation.

Figure 2 . 18 :

 218 Figure 2.18: Comparison of the matrices convolution and the Geant4 simulation for 10 6 events.

Figure 2 . 19 :

 219 Figure 2.19: Schematic view of the whole acquisition system. 3 NaI detectors are not represented on this 2D slice, for readability.

Figure 3 .

 3 1 for three dierent NaI crystals. The time dierence with the cathode is negative and can be understood by the dierence in the creation of the signals. The NaI crystals are coupled to photomultipliers that has fast-timing output signals of the order of a few nanoseconds. For the cathode signal while the ionization of the gas by the ssion fragment is instantaneous, the generation of a signal on the cathode will be longer. This generation time depends on the electron drift time which is of several µs -1 in the present work. One can see that this time dierence is constant "by blocks", it is entirely due to the various reboot of the acquisition. Since FASTER works with baskets composed of one motherboard and several daughterboards the triggering system requires synchronized clocks between each component. When the acquisition starts the clocks are synchronized between the motherboard and the multiples daughterboards.Obviously when the acquisition is restarted the clocks are once again synchronized. The native period of the clocks is 2 ns which explains that the jumps are only multiples of 2 ns. Due to the modularity of FASTER one can, if needed, reboot a single daughterboard which will be re-synchronize with the others. This explains that sometimes in Figure3.1 the three times are changed (e.g.: for run number 153), and sometimes not all of them (e.g.: run number 41). For each run le and each crystal the time is set to zero by subtracting the measured time dierence.

Figure 3 . 1 :

 31 Figure 3.1: Evolution of the mean position of the NaI time with respect to the time of the experiment, expressed in run number.

aFigure 3 . 2 .

 32 Figure 3.2.In order to write those events on disk the lossless trigger mode of FASTER was used. Moreover the neutron inelastic scattering on the iodine create a 203 keV γ-ray with high intensity. With these three γ-rays the calibration factors could be properly monitored.Such monitoring was done oine and also used to align the dierent detectors in order to sum their spectra. The correcting factors (calibration and alignment) were recalculated every two hours.

Figure 3 .

 3 Figure 3.3 shows the evolution of the 40 K peak position with respect to the acquisition time

Figure 3 . 2 :

 32 Figure 3.2: Room's radiation background.

Figure 3 . 3 :

 33 Figure 3.3: Evolution of the relative gain for two NaI channels of the same daughterboard.

Figure 3 .

 3 Figure 3.4 shows the evolution of all the gains throughout the acquisition time. In Figure 3.4a one can see the gain drift from the initial value for each channel. Most of the

  Variations relative to the gain value at the start of the experiment. Variations relative to the initial gain value of the reference channel (1).

Figure 3 . 4 :

 34 Figure 3.4: Gain variations through time.

Figure 3 .

 3 6 corresponds to the interactions of the ssion neutrons in the detector volume. The delay is explained by the neutron time-of-ight: the NaI are placed between 16 to 20 cm away from the source so the neutron (E n ∼ 0.9 MeV) interaction will occur on average with a delay of 15 to 17 ns depending on the crystal position. The γ spectrum gated on this delayed bump (T ∈ [6; 30] ns) is displayed in Figure3.7. The identication of the reactions in action is done by matching the γ detected Neutron delayed radiation spectrum (single NaI).

Figure 3 . 5 :

 35 Figure 3.5: Eect of the gain matching.

Figure 3 . 6 :

 36 Figure 3.6: 2D histogram of the γ energy versus its time from the ssion.

Figure 3 . 7 :

 37 Figure 3.7: γ spectrum gated on the second bump.

  E γ ∈ [0; 500] keV. E γ ∈ [500; 1000] keV. E γ ∈ [1500; 2000] keV.

Figure 3 . 8 :

 38 Figure 3.8: NaI time distributions.

  (a) Neutron mixing.

  Prompt γ outside the time selection.

Figure 3 . 9 :

 39 Figure 3.9: Evolution of the γ-n mixing with respect to the γ energy.

Figure 3 . 10 :

 310 Figure 3.10: Diagram representation of the analysis procedure.

Figure 3 .

 3 Figure 3.10 is a schematic description of the whole analysis procedure. The rst step is the calibration of the measured anode pulse heights, in orange in Figure 3.10. The literature only gives post-neutron quantities, corrected for PHD and energy loss. Then one needs to rst estimate each contribution to subtract them from the literature values in order to calibrate the data and determine afterwards the PHD. The choice made here is to correct the pulse heights for energy loss (P corr i

Figure 3 .Figure 3 . 11 :

 3311 Figure 3.11: Schematic description of the angle reconstruction

  ∆T distribution for a given pulse height.

Figure 3 . 13 :

 313 Figure 3.13: Determination of R/v e and T 0 from the anode pulse height vs ∆T 2D-histogram.

Figure 3 .

 3 [START_REF]Strutinsky : shells in deformed nuclei[END_REF] shows the evolution of the ∆T (θ = θ max ) and R/v e parameter with the anode pulse height for one of the two anode.One can see a slope break above a pulse height of 120 ADC in Figure3.14a: it comes from the time dependence of the pulse height, it is not taken into account to determine ∆T (θ = θ max ). As expected ∆T (θ = θ max ) possess a linear dependence with the anode pulse height because it still depends on the range of the fragment. Then extrapolating this tendency to ADC=0 gives the T 0 value. Such extrapolation was done and is represented by the blue line in Figure3.14a. Once the T 0 = D/v e value is determined for each side of the chamber the pulse height dependence of R/v e can be straight-forwardly extracted from ∆T (θ = 0) and is represented in Figure3.14b.

  (a) ∆T (θ = θ max ).

  [ADC] R/v [ns] (b) R/v e .

Figure 3 . 14 :

 314 Figure 3.14: Pulse height dependence of R/v e and T 0 .

T 0 -

 0 ΔT [ns] Anode pulse height [ADC](a) selection in pulse height (red dahsed lines). (b) Evolution of the mean Cathode-Anode time with the experiment time (run number).

Figure 3 . 15 :

 315 Figure 3.15: Dependence of the cathode-anode time with the gas properties.

  (a) Cosine distribution. (b) Distribution of ∆ cos. Δ (c) Cosine selection on the anode.

Figure

  Figure 3.16: Cosine distributions extracted from the electron drift time method.

Figure 3 . 17 :

 317 Figure 3.17: Selection in pulse height. The light gray line is the graphical cut used to select the cold ssion events. The TKE values are obtained with a rough estimate of the calibration, similarly the masses are estimated from the pulse heights

Figure 3 . 18 :

 318 Figure 3.18: Cold ssion masses detected on the backing side for the raw data (red) and with energy loss correction (α 1 , α 2 ) = (12.9, 2.5) (blue).

Figure 3 . 19 :

 319 Figure 3.19: Angular dependence of the pulse height for both sides of the chamber

Figure 3 . 20 :

 320 Figure 3.20: Diagram representation of the analysis procedure. Focus on the calibration.

Figure 3 . 21 :

 321 Figure 3.21: Calibration method for the anodes.

Figure 3 . 22 :

 322 Figure 3.22: Alignment of the energy loss corrected pulse heights from each side of the chamber. It is done through Equation (3.17).

Figure 3 . 23 :

 323 Figure 3.23: Adjusted PHD from Equation (3.19) compared to the data from Peck et al. [101].

Figure 3 . 24 :

 324 Figure 3.24: Diagram representation of the recursive neutron evaporation algorithm.

  (a) TKE vs A pre . (b) Cold ssion distribution.

Figure 3 . 25 :

 325 Figure 3.25: TKE vs pre-neutron mass and cold ssion mass distribution for the neutron evaporation using ν (A) = ν (A). A clear drift of the peaks position is seen in (b).

Figure 3 .

 3 Figure 3.26a, except for the symmetric region. This increase in the mean TKE for symmetric fragmentation and the spike at A=126 is a consequence of the "hole" that can be seen in the 2D-histogram of TKE vs pre-neutron mass in Figure 3.26b. The origin of this hole is probably a limitation of Equation (3.28). The ν is not perfectly linear with the TKE and the slope depends on the mass of the fragment [103, 107]. Therefore, as shown in Figure 3.26c where Equation (3.28) with B n = 8.6 MeV is compared to the data from Göök et al. [103] for A pre = 124, using a constant slope for every mass can induce an overestimation of the mean neutron number for low TKE, here for TKE∼ 150 MeV the data from Göök et al. are almost 2 neutrons below the estimation of Equation (3.28). Moreover the cold ssion lines are at least found about 0.2 neutrons emitted as shown in Figure 3.26d.

  B n =8.6 MeV (c) ν vs T KE pre .

  Cold ssion lines not at 0 neutron emitted.

Figure 3 . 26 :

 326 Figure 3.26: Impact of Barreau's formula with B n = 8.6 MeV on the TKE and neutron emission.

Figure 3 . 27 :

 327 Figure 3.27: Eect of the B n (A) on the mean neutron emission. (a) shows the B n (A) curve adjusted on the cold ssion. The constant B n and B n (A) parametrization are compared to Göök et al. [103] for A pre = 108 in (b) and A pre = 124 in (c).

Figure 3 . 28 :

 328 Figure 3.28: TKE vs A distribution.

  T KE vs A pre .

Figure 3 . 29 :

 329 Figure 3.29: Neutron and TKE distributions for the hand-adjusted B n distribution.

  Figure 3.30.

Figure 3 . 30 :

 330 Figure 3.30: TKE distribution for the cold ssion line A H = 132 and gated by the 2 + and 4 + transitions of 120 Cd.

Figure 3 .Figure 3 . 31 :

 3331 Figure 3.31: Schematic view of the population of cold fragmentations for A = 132. The endpoints of the cold ssion are calculated using an energy repartition following the constant temperature description.

Figure 3 . 32 :

 332 Figure 3.32: Evolution of the neutron delayed radiation with the lower limit in TKE for A=134.

  .34a for the light masses. Since the 57 keV and 203 keV are the rst and second decay to the ground state of127 I the endpoints determined from both should dier from about 150 keV. The hierarchy is globally conserved except for masses 94 -96. Moreover the spacing is too great for masses109 -111. Let us dene δ lim as the endpoint of the 57 keV minus the endpoint of the 203 keV, its distribution is shown in Figure3.34b. It was tted with a gaussian (in red) on the interval delimited by the dashed lines. The mean value is 0.16 MeV with a standard deviation of 0.8 MeV, it is in excellent agreement with the theoretical value and the deviation is compatible with the TKE energy resolution determined in the following.The two mass regions were δ lim > 1 MeV can be explained by the presence of short-lived isomers with γ of energies close to 57 and 203 keV in the neighborhood of the cold fragmentations. Then the delayed spectra were investigated for the high-end of the TKE distribution and are shown in Figures 3.35a and 3.35b. For the case of masses 94 -96, the 95 Sr is one of the most populated nuclei near cold fragmentations[START_REF] Knitter | Nuclear mass and charge distributions in the cold region of the spontaneous ssion of 252cf[END_REF], it possesses two transitions of 204 and 352 keV respectively. The rst one will be mixed with the 203 keV used to determine the cold ssion limit, which explains the hierarchy inversion for these masses. Similarly the masses 109 -111 are polluted with several isomers in 109 Mo [112], 109 Ru [113], and 111 Ru [114] that will articially increase the limit determined through the 57 keV gate.neutrons (a) Delayed spectrum for A = 95 ± 0.5 and T KE > 193 MeV. Delayed spectrum for A = 109 ± 0.5 and T KE > 208 MeV.

Figure 3 . 35 :

 335 Figure 3.35: Determination of the cold ssion limit.

  Focus on the light masses.

Figure 3 . 36 :

 336 Figure 3.36: Mass distribution for cold ssion using the previously determined selection.

Figure 3 . 37 :

 337 Figure 3.37: Cold ssion masses (blue) tted with multiple gaussians sharing the same standard deviation (red).

Figure 3 . 38 :

 338 Figure 3.38: Pre-neutron yields.

  σ KE vs A pre .

Figure 3 . 39 :

 339 Figure 3.39: Comparison of pre-neutron kinetic energies and deviation with the literature.

  (a) T KE vs A pre . σ T KE vs A pre .

Figure 3 . 40 :Figure 3 . 41 :

 340341 Figure 3.40: Comparison of pre-neutron total kinetic energy and deviation with the literature.

Figure 3 . 42 :

 342 Figure 3.42: Level scheme of the 134 Te [119]. The pink rectangle highlights the delayed

Figure 3 .

 3 Figure 3.43 shows a simplied version of the timeline of detected γ-rays: the ssion prompt cascade is instantaneous, then the neutrons will interact in the NaI with a delay, due to their

Figure 3 . 43 :Figure 3 . 44 :

 343344 Figure 3.43: Schematic view of the timeline of the γ-rays.

  (b) Time distribution for the 115 keV.

Figure 3 . 45 :

 345 Figure 3.45: Determination of the half-life of the 134 Te isomer.

. 4 .Figure 3 . 46 :

 4346 Figure 3.46: Post-neutron mass distribution for 134 Te.

4. 1 . 1

 11 Bumps between 3.5 and 7 MeV: state of the art These structures between 3.5 and 7 MeV were measured in dierent studies and various setups, leading to dierent and contradictory interpretations concerning their origin. This subsection will present the main articles of the literature on this subject.Glässel et al.[START_REF] Glässel | 252 Cf ssion revisited new insights into the ssion process[END_REF]: In their study of 1984 Glässel et al. measured the prompt γ spectra of the 252 Cf with respect to the fragment masses with Crystal Ball[START_REF] Metag | The darmstadt-heidelberg-crystal-ball[END_REF] and a FGTIC. It was the rst observation of an enhancement of the high energy component of the spectra (a) Prompt spectra gated on the masses.(b) From[START_REF] Hötzel | High-energy gamma-rays accompanying the spontaneous ssion of 252 Cf)[END_REF].

Figure 4 . 1 :

 41 Figure 4.1: Comparison of the mass selected prompt γ spectra observed in the present work

Figure 4 . 2 :

 42 Figure 4.2: Prompt spectra selected by isomers in blue, the red one corresponds to the reference of A = 108. The green labels identify the dierent isomers seen in a nucleus.

  Simplied level scheme of134 Te.

Figure 4 . 3 :

 43 Figure 4.3: (a) Comparison of the prompt spectrum feeding the 6 + (green) or 12 + (blue) isomer in the 134 Te. (b) Level scheme of 134 Te, the isomers are in green and the S n is reported in red dashed line.

- 1 ]

 1 (a) Level density.

  γ strength function.

Figure 4 . 4 :

 44 Figure 4.4: Comparison of the level densities and strength functions (E1+M1) for 134 Te.

  E * = 3.66 MeV.

Figure 4 . 5 :

 45 Figure 4.5: Photon emission probability for the 134 Te and 114 Pd for dierent excitation

Figure 4 . 6 :

 46 Figure 4.6: Comparison of the density-driven (black) and strength-driven (red) term for 134 Te (in full lines) and 114 Pd (in dashed lines) with initial states at 7.66 MeV for J π = {5, 6, 7} ± . The 134 Te curves are normalized to one while the 114 Pd ones are normalized by the same factors to conserve the relative variations.

Figure 4 . 7 :

 47 Figure 4.7: FIFRELIN spectra gated by the isomer of 134 Te (a) and gated by 108 Tc (b) in

Figure 4 . 8 :

 48 Figure 4.8: Comparison of the calculated prompt cascade feeding the 6 + isomer of 134 Te in FIFRELIN with the present work.

Figure 4 . 9 :

 49 Figure 4.9:Probability to emit a neutron from133 Te for spins and parity of {17/2, 19/2, 21/2} ± .

Figure 4 . 10 :

 410 Figure 4.10: Comparison of the KE distributions gated in (Z post , A post ) by the isomers with

Figure 4 . 11 :

 411 Figure 4.11: Comparison of the dierent contributions due to neutron emission in the FIFRELIN (a-c) and GEF (d-f ) calculations.

Figure 4 .

 4 11a-c (d-f) shows the KE distribution gated by a post-neutron ssion fragment in (Z,A) in FIFRELIN (GEF).One can see that the structures near the double shell closure of132 Sn are generally caused by the 0-and 1-neutron channels (see Appendix A). It is extreme in the case of132 Sb because of the almost non-existent overlap between the two. The predominance of these two channels for the mass region around the double shell closure Z=50, N=82 is a consequence of the low ν in this mass region, however the non-overlapping contributions are not understood.GEF shows a relatively good agreement with the experimental data and displays stronger overlaps between the dierent neutron channels.The cases of95 Sr and 154 Nd (Figures 4.11b

  and 4.11c) are in better agreement with the present work as they are both less structured in FIFRELIN. The GEF calculations for these two nuclei (in Figures 4.11e

  and 4.11f) are both in good agreement with the present work, however this agreement is strange in regards of the next discussion. The weight attributed to a high number of emitted neutrons (>3) in 154 Nd is higher in GEF than in FIFRELIN. Also the contributions for the95 Sr are extremely broad and overlapping almost on the full range of the distribution.

4. 2 . 2

 22 Investigation of the fragmentation Sr-Nd in GEF

Figure 4 . 12 :

 412 Figure 4.12: T KE pre distribution selected by95 Sr as the post-neutron light fragment. The present work is compared with GEF calculations and the latter is decomposed following the total number of emitted neutrons.

Figure 4 .

 4 Figure 4.13: (a) Adjustment of the ssion modes to reproduce the post-neutron mass yield for 252 Cf. The ssion modes are labeled only for the light fragment, the region around A = 95 is highlighted by the red dashed circle. Taken from [7]. (b) Systematics on the temperature dependence with the nucleus mass. It is obtained by adjusting the known level densities at low energy with a constant temperature description. Taken from [134].

Figure 4 .

 4 Figure 4.14: T KE pre distribution selected by 95 Sr as the post-neutron light fragment. The present work is compared with GEF calculations and the latter is decomposed following the ssion modes.

Figure 4 .

 4 Figure 4.14 shows the GEF calculation compared with the present work for the 95 Sr with a decomposition in ssion modes. One can see that the shouldering at low TKE is due to the S3 mode (black) whose contribution seems to be overestimated compared to the present work. Nonetheless the ssion mode S2 (green) cannot solely describe the measured distribution.

Figure 4 . 15 :

 415 Figure 4.15: Comparison of the TKE distribution for the present work with GEF calculations for dierent mode mixing: (a) S2-S3 ∼ 10%-90%, (b) S2-S3 ∼ 60%-40%, (c) S2-S3 ∼ 100%-0%.

Figure 4 .

 4 Figure 4.16a-d shows the breakdown of the KE distribution with the ssion mode. One clearly sees that the bi-modal shape comes from the two contributions of S2 and S3 mode. Moreover the neutron emission of the light fragment (see Figure 4.16e) is less spread and slightly shifted in the S3 mode compared to the S2. Even if more energy is available in S3

Figure 4 .

 4 Figure 4.16: (a)-(d) KE distributions for the 95 Sr selected by the number of neutrons emitted by the light fragment in GEF. The total distribution and the S2 and S3 contributions are shown. (e) Comparison of the neutron distribution between S2 and S3 for the light fragment. (f ) Comparison of the neutron distribution between S2 and S3 for the heavy fragment.

Figure 5 . 1 :

 51 Figure 5.1: Focus on cold ssion (Same as Figure 3.28).In black squares the maximum Q-value for the masses, the cold ssion limit is reported in white line.

Figure 5 . 2 :

 52 Figure 5.2: T KE pre distribution for A pre = 132 (in blue) compared to A pre = 133 (in red).

  the coupling with the NaI array can allow the charge identication through the discrete transitions of the prompt spectrum. The prompt spectrum for T KE ∈ [229.4; 231.5] MeV, where mixing between the 120 Cd/ 132 Sn cascade and other fragmentations is possible, is displayed in Figure 5.3a. For each nucleus other than 120 Cd and 132 Sn the rst transition above a threshold of E γ > 100 keV is reported in Table

N γ / 10

 10 keV (a) Prompt spectrum.(b)120 Cd low lying levels.

Figure 5 . 3 :

 53 Figure 5.3: Identication of the discrete levels in cold ssion. (a) The prompt spectrum is selected by A pre H = 132 and T KE ∈ [228.7; 231.5] MeV, the identied levels are in red. (b)

N γ / 30

 30 keV (a) Full spectrum with a 30 keV binning.

N γ / 10

 10 keV (b) Low energy part.

Figure 5 . 4 :

 54 Figure 5.4: Prompt spectrum for the cold ssion line of A pre H = 132.

  TXE sharing between the two fragments.

Figure 5 . 5 :

 55 Figure 5.5: (a) Excitation energy for the 120 Cd. (b) Excitation energy repartition between 120 Cd and 132 Sn below 8 MeV of TXE. The present work (green) is compared to the two parametrizations used, based either on a constant temperature (red) or Fermi gas (light blue) NLD. The purple dashed line represents the rst excited state of 132 Sn.

Figure 5 .

 5 8a along an example of calculated spectra for two dierent γSF with the same level density in Figure 5.8b. One should remember that the relative scaling of the dierent models used is not relevant since EXCITATION ENERGY Normalized N γ / 20 keV (a) Low energy part of the prompt spectrum.(b)120 Cd level scheme.

Figure 5 . 6 :

 56 Figure 5.6: Reproduction of the low-lying transitions using the known 120 Cd level scheme

Figure 5 . 7 :Figure 5 .

 575 Figure 5.7: Reproduction of the low-lying transitions using a completed level scheme in DEGA. The light blue levels and transitions are the added levels and transitions.

Figure 5 . 8 : 1 ]

 581 Figure 5.8: Impact of the strength function used in DEGA on the prompt spectrum. (a) Comparison of the dierent γSF models. (b) Calculated spectrum using the same level density (CGCM) and two dierent γSF compared to the measured one.

Figure 5 . 9 :

 59 Figure 5.9: Impact of the level density used in DEGA on the prompt spectrum. (a) Comparison of the dierent NLD models. (b) Calculated spectrum using the same γSF (D1M-QRPA) and two dierent NLD compared to the measured one.

  Normalized N γ / 20 keV (b) Low energy part of the spectrum.

Figure 5 . 10 :

 510 Figure 5.10: Impact of the spin-cuto parameter used in DEGA on the prompt spectrum.

FISSION

  Correlation between the spin-cuto and T.

Figure 5 . 12 :

 512 Figure 5.12: Distribution and correlations of the parameters from the MCMC algorithm.

lated excitation energy of the 120 1 ]Figure 5 . 13 :

 1201513 Figure 5.13: Comparison of the level density from MCMC, the systematics from Egidy et al.[START_REF] Egidy | Systematics of nuclear level density parameters[END_REF] and the CGCM from TALYS.

Figure 5 . 14 :

 514 Figure 5.14: Angular momentum distribution for the 120 Cd determined from the Markov

Figure 5 . 16 :

 516 Figure 5.16: Low-energy part of the prompt spectrum for the cold mass split 118/134.

Figure 5 . 17 :

 517 Figure 5.17: Total excitation energy distribution for the fragmentation 118 Pd/ 134 Te.

  the present work, the genotype represent the partitioning of the TXE between the two fragments. The TXE that spans for roughly 8 MeV is divided in 405 bins of 20 keV. Then the genotype of an individual is a binary sequence of length 405, stored in an array. The binary value b i of a cell corresponds to the repartition of the additional 20 keV of TXE: if b i = 0 the 20 keV are given to the heavy fragment, if b i = 1 they are given to the light one. An example is shown in Figure 5.18, the genotype binary sequence is shown at the bottom and the graph represents the light fragment excitation energy as a function of the TXE. Increases (b i = 1) are in red while stagnation (b i = 0) are in blue.A population of 2000 individuals is randomly generated. The average slope of the initial individuals is controlled in order to explore the whole phase space. Figure5.19a shows the randomly generated population in colors, the full phase space is covered. The thick dark line represent the solution found by the algorithm, it is presented and discussed later.

Figure 5 .Figure 5 . 18 :

 5518 Figure 5.19b shows an example of the light fragment excitation energy as a function of

  Example of some generated individuals.

Figure 5 . 19 :

 519 Figure 5.19: Initial population. (a) the whole population is shown, covering the whole phase space. The thick black line is the best solution found. (b) Example of several individuals of the initial population.

123 CHAPTER 5 .

 1235 ANGULAR MOMENTUM AND ENERGY REPARTITION THE COLD FISSION a time selection of T ∈ [-4 : 500] ns to get the counts associated to the delayed decay of the 6 + isomer of 134 Te.

Figure 5 .Figure 5 . 20 :

 5520 Figure 5.20: Breeding of two individuals.

Figure 5 . 23 :

 523 Figure 5.23: Comparison of the energy repartition and the calculated spectrum at dierent generations. The fragment taking most of the energy is the 118 Pd.

Figure 5 .

 5 Figure 5.24 shows the best solution found by the genetic algorithm. One can see in Figure 5.24a that the measured spectrum is extremely well reproduced by this energy sharing.

Figure 5 .

 5 Figure 5.24b shows the sharing of the TXE between

Figure 5 . 24 :

 524 Figure 5.24: Comparison of the energy repartition and the calculated spectrum at dierent generations. The fragment taking most of the energy is the 118 Pd.

Figure 5 . 25 :

 525 Figure 5.25: Evolution of the energy repartition with the spin-cuto parameter.

Figure 5 . 26 :

 526 Figure 5.26: Usual parametrization of the energy sharing according to Equation (5.9) and Equation (5.7) compared to the energy repartition determined in the present work. The dashed lines corresponds to

Figure 5

 5 Figure 5.27.

Figure 5 . 27 :

 527 Figure 5.27: Comparison of the excitation energy repartition using the microscopic level densities. The one from the Skyrme interaction [57] are shown in light orange and the one from Gogny interaction [58] are in purple. The full lines are the share of the light fragment while the dashed lines correspond to the share of the heavy fragment.

Figure 5 . 28 :

 528 Figure 5.28: Microscopic level densities for

Figure 5 . 29 :

 529 Figure 5.29: Comparison of the excitation energy repartition using the parametric or microscopic level densities. The full lines are the share of the light fragment while the dashed lines correspond to the share of the heavy fragment.

  Comparison of the presented γSF models for the case of134 Te. code for the radiative decay of nuclei populated below S n . It simulates γ cascades from an initial state s i = {J i , π i , E i } to the ground state. The initial state is dened by the user. The nucleus is described by a discrete region below a threshold energy E cut , where the discrete levels from TALYS

	10 -5
		SLO
	10 -6	EGLO Skyrme D1M
	10 -8 10 -7 E1 (E γ ) [MeV -3 ]
	f
	10 -9
	10 -10
		2 4 6 8 10 12 14 16 18 20
		E γ [MeV]
	Figure 1.7:

Table 2 .

 2

	Gases	First ionization potential (eV)	W-value (eV/ion pair) for α-particles
	Ar	15.7	26.3
	CH 4	14.5	29.1
	P-10	-	26.6

4 and P-10 are tabulated in Table 2.1. 1: W-values for gases used in this study.

Table 2 .

 2 .6. The results are summarized in Table2.2. An average ratio X/R of 0.348 was found.

	Ions	charge barycentre X [mm] Range [mm] X/R
	86 Se	7.071	19	0.372
	96 Sr	6.357	17	0.374
	103 Nb	6.407	18	0.356
	110 Ru	5.962	17	0.351
	118 Ag	5.351	16	0.334
	129 Sn	5.484	16	0.343
	134 Te	5.162	15	0.344
	144 Ba	4.79	14	0.342
	151 Pr	4.47	13	0.344
	158 Sm	4.163	12	0.347
	Mean	5.522	15.7	0.348

2: SRIM calculation for energy loss in P-10 gas at 1.5 bar for typical ssion fragments.

From the results in Table

2

.2 and Equation (2.25) one can estimate the mean correction from the grid ineciency:

  〈A post 〉 L,H & 〈A pre 〉 L,H

								Validation
								requirements
	Litterature					Cold masses
								without drift
				Peck	et al
	Henschel 〈KE post 〉 L,H et al	Peck 〈PHD〉 L,H et al PHD(A post )	NO |A pre	i-1 -A pre	i |<ε YES	A post & A pre KE post & KE pre Agreement? Exp-Litt
	correction Energy loss	P corr	calibration Pulse height	A app KE app	of the PHD determination	A 0 pre KE 0 pre	Neutron ν=f(A pre ,TKE pre ) emission
			hand-	adjust.			hand-	adjust.	Neutron evaporation
	Measurement of P 1 & P 2

NO YES

〈KE post 〉 L,H & 〈KE pre 〉 L,H

Target observables

Table 3 .

 3 3.16: Cosine distributions extracted from the electron drift time method. E inc [MeV] δE 95 Sr δE 108 Mo δE 115 Pd δE 134 Te δE 144 Ba δE 156 Nd

	60	283	285	297	299	293	293
	70	297	302	312	317	315	315
	80	308	317	325	333	332	333
	90	316	329	340	346	347	351
	100	323	338	353	358	362	366
	110	329	346	363	370	374	379
	120	333	354	371	382	386	392

1: Energy loss (keV) for several nuclei in 5 µg • cm -2 of carbon foil with 10 nm of Formvar.

Table 3 .

 3 .39a. One can see that the strip representing this work contains all the previous experiments. This shows the consistency 2: Experimental pre-neutron results compared to the literature.

		Present work	Literature
	KE L	104.5 ± 0.57	104.64 ± 0.8
	σ E L	5.78	6.41
	KE H	78.97 ± 0.57	79.47 ± 0.6
	σ E H	8.52	8.76
	A L	108.2	108
	σ A L	6.95	7.08
	A H	143.8	144
	σ A H	6.95	7.08
	T KE [MeV] 183.5 ± 0.8	184.1 ± 1.5
	σ T KE [MeV]	11.21	12.14

  {A, T, E γ 1 , E γ 2 } {A, T, E γ 1 , E γ 2 , E γ 3 }

		134 Te
		w/o pre-selection [min]	w/ pre-selection [min]
	3-fold: {A, T, E γ 1 }	20.8	3.1
	4-fold: 20.8	3.2
	5-fold: 23.8	4.1
		95 Sr

w/o pre-selection [min] w/ pre-selection [min] 3-fold: {A, T, E γ 1 } 19.7

40

4-fold: {A, T, E γ 1 , E γ 2 }

  Time distribution of the spectrum in Figure 3.44d.

	Counts/ ns							/ ndf Constant 2 χ Slope -0.004247 6.147 438.9 / 434 0.007 ± 0.000032 ± / ndf 2 χ 438.9 / 434 Constant 0.007 ± 6.147 Slope 0.000032 ± 0.004247 -
	2 10
	10
	50	100	150	200	250	300	350	400	450	500
									Time [ns]

Table 3 .

 3 post [a.m.u.] δA post [a.m.u.] 91 Rb 4: Comparison of the measured half-life and masses for the isomers with the reference values from NUDAT 3.0, unless specied.

		1134	18	19.7	92.1	+1.1
	92 Rb	284	54	57.9	92.5	+0.5
	94 Rb	1485.2	18			94.2	+0.2
	95 Rb	835	113	104.7	94.4	-0.6
	95 Sr	556	23	22.3	95.3	+0.3
	97 Sr 97 Sr	308 831	169 395	167.8 444.3	96.6	-0.4
	97 Zr	1264	103	104.5	98.5	+1.5
	98 Rb	178	358	344.8	98.4	+0.4
	98 Y	1181.5	780	782.7	97.9	-0.1
	99 Zr	252	293	296.2	99.3	+0.3
	Tc 330.6 + x 94 [121]	110.2	107.6	-0.4
	Sn	2084.8	49	46.5	130.3	+0.3
	Sn	4605 + x	300	300	132	+1
	Sb	254	102	103.9	132.2	+0.2
	Sn	4715.9	20.1			131.9	-0.1
	132 Te	1774.8	149	145.9	133	+1
	133 Te	1610.4	100	105	133.6	+0.6
	134 Te	1691.3	164	163.2	134.1	+0.1
	135 Te	1554.9	511	514	134.7	-0.3
			T ref 1/2 [µs]	T meas 1/2	[µs]
	94 Y	1202.3	1.35	1.24	95.9	+1.9
	98 Y	496.1	6.9			97.9	-0.1
	Sn	1761.6	3.4	4.2	130.2	+1.2
	Sb	2165.6	1.1	0.95	132.2	+1.2
	Sn	4848.5	2.08	2.08	131.8	-0.2
	Sb	4560	16.6	15.4	133
	Xe	1891	2.95	2.89	137.1	+1.1
	Nd	1298	3.2 [122]	2.2	154

Table 4 .

 4 1: Intensities of the transition to the discrete levels relative to the total probability for134 Te and 114 Pd.

	MeV]	7.66	5.66	3.66
	134 Te	71.5 %	94.9 %	99.6 %
	114 Pd	0.5 %	2.6 %	20.7 %

Table 4 .

 4 2: Compilation of the maximum energy available for γ emission to the isomer below S n .

	129 Sn	1761.6	5316	3554
	130 Sn	2084.8	7597	5512
	132 Sn	4848.5	7353	2505
	131 Sb	2165.6	7767	5601
	132 Sb	254	5725	5471
	133 Sb	4560	7358	2798
	132 Te	1774.8	8048	6273
	133 Te	1610.4	5815	4205
	134 Te	1691.3	7675	5984
	135 Te	1554.9	3263	1708
	136 Xe	1891	8087	6196

Table 5 .

 5 1 for the dierent charge splits one can see that there is a 5 MeV dierence between the fragmentation 120 Cd/ 132 Sn and the next energetically allowed ones. Such fragmentations are associated to a cold ssion line going at higher TKE than the neighboring masses. It is not the case for the majority of the cold ssion. Sn is responsible for this gap. It means that for 5 MeV below the Q-value the only possible nuclei detected are 120 Cd and 132 Sn. In their work Gönnenwein et al. had access to the charges of the fragments, from this they deduced that the 120 Cd/ 132 Sn was still dominating until 225 MeV in TKE. However this conclusion is in disagreement with the work of Knitter et al. [111]. In their work Knitter et al. also used a twin ionization chamber and they identied the charges of the fragments through the analysis of the range of the fragments in the gas. For them the total contribution of the 120 Cd/ 132 Sn fragmentation in the energy range Q max -T KE ∈ [0; 10] MeV is only 52%.

			EXCITATION ENERGY
			A=132
		Z H Q-value [MeV]
		49	224.177
		50	236.538
		51	231.322
		52	231.503
		53	220.305
	Table 5.1: Q-value for mass 132 as a function of the heavy fragment charge. The maximum
	value is in bold.
	The double shell closure of	132

120

  Pd 132 Te 120 Ag 132 Sb

	E γ [keV]	438	974.1	158.1	162.8
	L C (95% CL) [counts] 2.99	1.89	0.36	0.36
	L U (95% CL) [counts] 2.99	1.89	0.36	0.36
	Presence [counts]	<8	<6.5	<0.7	<0.7

Table 5 .

 5 2: 1 st transition above a threshold of 100 keV, critical (L C ) and upper (L U ) limits for the four potential contaminating nuclei.

132

  Sn) populated in its ground state. This observation of a repartition of the TXE being 100%0% is in agreement with the two main energy repartition models: the and 229.608 MeV. Unlike the120 Cd/ 132 Sn case, the low energy part of the spectrum is dominated by transitions from134 Te and 118 Pd as shown in Figure5.16, moreover the rst measurable transitions of134 Sn,118 Cd,134 Sb and 118 Ag are too close to observed transitions coming from118 Pd or134 Te, considering the energy resolution. Then it is not possible to use statistical arguments to exclude a potential contamination. By considering the work of Knitter et al.[START_REF] Knitter | Nuclear mass and charge distributions in the cold region of the spontaneous ssion of 252cf[END_REF], they give the contributions of the dierent fragmentations for each cold ssion line, determined through analysis of the fragments' range in a FGTIC. The present work selects the cold ssion line roughly at Q max -T KE = 8 MeV, Knitter et al.[START_REF] Knitter | Nuclear mass and charge distributions in the cold region of the spontaneous ssion of 252cf[END_REF] determined the weight of 118 Pd/134 Te to be 92.5 ± 10.4% and 94.6 ± 5.7% for similar selections (Q max -T KE = 7 and Q max -T KE = 9 MeV respectively). Therefore the contamination was considered to be negligible for the present work. This assumption is supported a posteriori by the excellent agreement between the calculated and measured spectra.

	N γ / 10 keV	Te 4 + →2 +	134 Te 118 Pd
		134
		→0 +
		134 Te 2 +

-10 3 -10 2 -

5 -10 4 -10 3 -10 2 -

Remerciements

Recursive loop:

1 st step: From the pre-neutron masses one can estimate the number of neutrons emitted by each fragment using dierent methods (detailed later), be it empirical parametrizations or experimental data. This number of neutrons gives the postneutron masses.

pre , T KE (i-1) pre )

pre -ν (i)

2 nd step: Using these post-neutron masses a new PHD correction is computed, giving access to more accurate post-neutron kinetic energies.

3 rd step: From these energies one can compute the pre-neutron kinetic energies through the momentum conservation. Then the new pre-neutron masses can be determined with Equation (3.3).

4 th step: For consistency the post-neutron observables are computed once again.

5 th step: If these new pre-neutron masses dier by less than 1 from the previous iteration, the procedure ends, otherwise start again at step 1.

This algorithm converges within 3 to 4 iterations. The most sensible point is the function used to evaluate the number of neutrons emitted. In the following subsections the dierent functions used in the literature will be discussed along with a new parametrization more suited for this present work.

Toy model: ν (A) = ν (A)

The most forward way to get an estimate of the neutrons emitted is to use the well known ν data as done in [START_REF] Hambsch | Is there a pulse height defect for methane?[END_REF]. Even if the number of emitted neutrons is xed for a given mass, it still needs to be incorporated in the iterative procedure since the starting point is not the true post-neutron mass. The ν (A) data from Göök et al. [START_REF] Göök | Prompt neutron multiplicity in correlation with fragments from spontaneous ssion of 252 Cf[END_REF] was taken for the present work. Splines [START_REF] De Boor | Spline Basics[END_REF] were used to interpolate the data points to have a doubly continuous estimation and avoid discontinuities that could make the procedure diverge. Figure 3.25

shows the results on the total kinetic energy and pre-neutron mass distribution once the algorithm previously described converged. The TKE vs A pre in Figure 3.25a shows no Therefore the nal cold ssion cut will be made of the limit from the 57 keV gate except for the masses 109 -111 where the point from the 203 keV gate will be used instead. Each point is shifted by 57 or 203 keV, respectively.

Then the mass distribution associated with this selection is shown in Figure 3.36a. The rst thing to notice is that the masses are placed on the right masses without any drift, as shown in Figure 3.36b. It validates the whole procedure except for the energy calibration, which is correctly calibrated in the following chapters. Even-odd eects are quite marked, especially for masses 115 -120 as shown in Figure 3.36b. The highest yields happens for masses where an even-even fragmentation possess a Q-value signicantly higher than the pared to the present work (black dots). One can notice the excellent agreement between the two. Then the angular momentum determined in GEF can be directly compared to the present work. Figure 5.15b shows the angular momentum determined in the present work and compared to the one calculated in GEF, in red. The GEF distribution is selected by asking the cold fragmentation 120 Cd/ 132 Sn and an excitation energy in 120 Cd below 8 MeV.

The agreement between the two is quite good, with an average value slightly lower for GEF.

Following Wilson et al. energy sorting based on the constant temperature [3,[START_REF] Schmidt | Entropy driven excitation energy sorting in superuid ssion dynamics[END_REF] and the parametrization:

However looking at other cold fragmentations can yield better discrimination between the two. The mass split 118/134 is the next cold ssion line where an even-even fragmentation is favored by the selection. The distancing of the heavy fragment from 132 Sn should induce a non-zero excitation in the heavy fragment. The genetic algorithm is a powerful tool for optimization when the shape of the target functional is unknown. It requires little prior knowledge and only for the computation of the criterion, all the other steps are random.

Fragmentation identication

Convergence

The energy repartition converges towards a solution in a few hundreds of generations, increasing the number of generations is still useful to further rene the result and make sure, through the mutations, that the solution found is not local. Litaize.

Appendix B

Critical and upper limit

B.1 Critical limit

This limit L C will quantify the statistical signicance of a number of counts in a histogram with respect to the background. Let's consider one measures a total number of counts G over n channels in a peak region. this total number is the sum of counts coming from the background B and true peak counts A:

The true peak area A will be considered signicant if it strictly exceeds the limit L C , it is dened as:

where σ 2 0 is the variance of A when A = 0 and k α is a factor that will x the level of condence for the conclusion: if one wants a 95% CL (condence level) then k α = k 0.05 = 1.645. The variance of A is simply: var (A) = var (G) + var (B)

The background is estimated from m-channels outside the peak area (if possible m/2 channels before the peak region and m/2 after) and extrapolated to the peak region. If all the channels used for background estimation are denoted Ω then:

where C i is the count if the i-th channel. Then its variance is :

B.2 Upper limit

If the net count is not statitically signicant, one can still determine a upper limit of presence, for a certain CL. It is simply dened as:

For each γ-ray the background was determined as much as possible with two intervals after and before the peak region, where the histogram was tted with an exponential. Then the net count was obtained by tting the peak region with a gaussian of xed mean value and standard deviation and the background exponential.