Manuel Caamaño

Fanny Rejmund
email: frejmund@ganil.fr

Karl-Heinz Schmidt

Evidence for the predominant influence of the asymmetry degree of freedom on the even-odd structure in fission-fragment yields

Keywords: numbers: 24.75.+i, 25.70.-z, 25.85.-w, 25.85.Ec, 25.85.Jg

come

Evidence for the predominant influence of the asymmetry degree of freedom on the evenodd structure in fission-fragment yields

Introduction

Even-odd staggering in proton (Z) and neutron (N) numbers is a well-known characteristic of low-energy fission-fragment yields [1]. The large amplitude of this staggering, which may reach 40% in the case of the element distribution of fission fragments of thorium [2], has always been fascinating to nuclear physicists. The experimental access to the exact number of neutrons of the fission fragments at scission is difficult to obtain because the number of neutrons is modified by evaporation processes. In contrast, evaporation of protons from the neutron-rich fission fragments is negligible. ‡ Present address: Universidade de Santiago de Compostela, E-15706 Santiago de Compostela, Spain Therefore, if measured prior to their beta-decay, the element yields, and the associated even-odd staggering, reveal the properties of the fissioning system at scission. During the fission process, the total energy of the system is subject to substantial reorganization. At the fission barrier, the part of the initial excitation energy which corresponds to the height of the barrier is bound in potential energy and the intrinsic excitation energy is accordingly reduced. On the further path to scission where the two fragments separate, the potential energy decreases again. This energy release drives the nascent fragments apart and feeds the pre-scission kinetic energy.

The observation of odd-Z fragments from an even-Z fissioning nucleus testifies to the breaking of proton pairs during the re-organisation of the intrinsic structure of the fissioning nucleus on its path towards scission. Indeed, in thermal-neutron-induced fission of even-Z actinides, the intrinsic energy available above the fission barrier is lower than the pairing gap, and thus, the system crosses the fission barrier in a fully paired configuration. When odd-Z fragments are observed, an ensemble of fully paired protons undergoes deformation down to scission, where at least one proton pair is broken and both unpaired protons end up in different fission fragments, producing odd-Z species. The breaking of pairs consumes part of the energy stored in the system in the form of collective kinetic energy [3]. This coupling between collective and individual degrees of freedom is the consequence of the viscosity of the nuclear matter, and is defined as a dissipation process. The amplitude of the even-odd staggering is therefore linked to dissipation during the deformation in the fission process. It has always been a challenge to understand the mechanism of dissipation and the relation between pairing effects and the dissipated energy. The present work focuses on isotopes for which nuclear-charge yields are accessible. The data emerge from experiments performed at ILL for fissile actinides and at GSI for long chains of neutron-deficient actinium, thorium, protactinium, and uranium isotopes. This ensemble of data allows accessing an unprecedented systematic on pairing effects in fission-fragment yields. They show new general properties that cannot be explained with the conventional interpretations.

Global even-odd staggering and dissipated energy

A simple method to quantify the even-odd structure in the fragment production is to define the global even-odd effect δ as the average difference between even-and odd-Z total yields over the full available distribution [2]:

δ = Z even Y (Z) - Z odd Y (Z) Z Y (Z) (1)
Several models have attempted to quantitatively relate the global even-odd staggering to the dissipated energy. They are all based on the idea that the evenodd effect in element yields is determined by the probability that the protons remain in fully paired all the way up to the scission configuration.

The model proposed by Nifenecker et al. [4] is certainly the most widely used as it correlates δ and the dissipated energy E diss with a very simple expression. This model calculates the maximum number of broken pairs at scission as the ratio between the dissipated energy and the amount of energy necessary to break a pair (the pairing gap). The nucleus at scission is then considered to consist of a fully paired core and an ensemble of broken pairs. The probability to break a proton versus a neutron pair, the probability to break one or more pairs if the necessary amount of energy is available, and the probability that the nucleons of the broken pairs end up in two different fragments, are determined by a combinatorial analysis. This model estimates a dissipated energy of about 4 MeV for 230 Th to 12 MeV for 250 Cf.

An alternative approach by Bouzid et al. [5] is based on a dynamical description of the fission process. In this model, the descent from saddle to scission is considered to be adiabatic, and the violent neck rupture leading to the formation of the two separated fragments causes the pair breaking. The probability to break a pair is correlated with the velocity of the neck rupture, which is shown to increase with the Coulomb repulsion at the scission point. The Coulomb repulsion is linked to the Coulomb parameter

Z c = Z 2 f /A 1/3
f , where Z f and A f are the nuclear charge and mass of the fissioning nucleus, respectively. The probability that the broken pairs end up in different fragments is a parameter fitted to reproduce the data. In particular, this model considers the difference in the proton-and neutron-number staggering as a consequence of the less violent neck rupture for protons, since they are less likely to be present in the neck due to the Coulomb repulsion.

A rigorous formulation of the even-odd staggering has been derived by Rejmund et al. [6] within the framework of the statistical model. It is based on a realistic description of the number of quasi-particle excitations of the proton and neutron ensembles as a function of the excitation energy at scission. The pairing-gap parameter depends on excitation energy, deformation, and the number of quasi-particle excitations. The probability to break proton pairs as a function of the excitation energy is derived accurately as the ratio of the proton excited states over all available single-particle states. This is in contrast to the model of Nifenecker et al., where the even-odd effect is deduced from a combinatorial analysis, based on the ensemble of possibly broken pairs, using fitted parameters.

Recently, new ideas about the division of the intrinsic excitation energy between the two nascent fragments [7] lead to an extension of the model of Rejmund et al. [6] to asymmetric splits. The development of this new model [8] was guided by the analysis of the empirical data performed in the present work. The central idea is that the magnitude of the even-odd effect is not governed by the total intrinsic energy available in the fissioning system but by the nascent fragment which carries the lowest intrinsic excitation energy at scission.

The evolution of the global even-odd staggering from measurements of fragment yields of fissile actinides at ILL is displayed as a function both of the fissility and the Coulomb parameter in figure 1, left and right panels, respectively. A clear decrease is observed as a function of both parameters. The correlation of the even-odd staggering with the fissility [START_REF] Gönnenwein | The Nuclear Fission Process[END_REF] suggested that more energy is dissipated in nuclei with higher fissility, since the amplitude of the global even-odd effect was already associated with the dissipated energy gained by the nucleus. The fissility parameter x = Z 2 f /A f reflects the stability against fission, but its connection with the dissipated energy is not evident. On the other hand, the total energy released from saddle to scission has been shown to be essentially determined by the Coulomb parameter [5]. Therefore, the evolution of the even-odd staggering with the fissioning nucleus is usually investigated as a function of the Coulomb parameter [6,[START_REF] Bocquet | [END_REF]11].

Evolution of the fragment distribution with the fissioning nucleus and its influence on the even-odd staggering

In low-energy fission of most actinides, shell effects induce an asymmetry in the mass and charge distributions of fragments, which show two groups [START_REF] Unik | Proc. Symp. Phys. Chem. Fission[END_REF]. The group of heavy fragments is distributed around an average value of A∼140, independent of the mass of the fissioning system. In order to conserve the total mass of the fissioning nucleus, the group of the light fragments increases towards heavier masses for heavier fissioning nuclei, gradually approaching symmetry. The equivalent behaviour is observed in charge distributions. However, for the latter, until an experiment exploiting inverse kinematics [START_REF] Schmidt | [END_REF], only the light part of the distribution was experimentally accessible. Element-yield distributions reported in figure 2 have been obtained at the Lohengrin spectrometer [2,14,3,15,16,17,18,19,20]. For this particular experimental procedure, only the light fragment distributions were measured. In addition, the present analysis uses solely those element yields for which the complete isotopic distribution is available. This restriction is necessary to avoid incorrect element yields [21]. The data show an average light charge centred on values varying from Z = 36 to 44, for fissioning nuclei from Th to Cf, as indicated by arrows in figure 4. This coincides with a heavy charge distribution centred on a constant value Z=54, independent of the fissioning nucleus, as reported already in [22]. To explore the fission asymmetry, it is convenient to define the asymmetry parameter: a = (Z H -Z L )/Z f , where Z H and Z L are the charge of heavy and light fragment, respectively. In figure 2, the element yields are displayed as a function of this parameter, which results in a common scale for the asymmetry of the distribution for all considered systems. As it was previously mentioned, and in order to conserve the total nuclear charge, the average asymmetry < a > of the nuclear-charge distributions of the light fission-fragments shifts from 0.28 to 0.13 when considering fissioning systems from 230 Th to 250 Cf. In figure 3, the corresponding global even-odd effect is displayed as a function of the average asymmetry of the light fragment distribution. A clear relationship is observed; when the average asymmetry decreases, the global even-odd effect decreases.

As there exists a clear decrease of the even-odd effect with increasing excitation energy at saddle [23,24] and a prediction for an increasing energy release between saddle and scission with the Coulomb parameter [5,[START_REF] Bocquet | [END_REF], it is conventionally assumed that the decrease in even-odd effect with the fissility or with the Coulomb parameter is due to the increase in dissipated energy from saddle to scission. However, figures 1 and 3 show that the global even-odd effect is correlated also with other parameters which are not directly connected to the energy dissipated between saddle and scission; the fissility x and the average asymmetry < a > of the fragment distribution. The clear correlation between the global even-odd effect and the mean asymmetry opens the question on the potential influence of the asymmetry degree of freedom on the even-odd effect.

Local even-odd staggering and influence of the asymmetry

In order to obtain more detailed information on the influence of the asymmetry degree of freedom on the amplitude of the even-odd effect, the local even-odd staggering δ(Z) can be investigated. Its magnitude is a measure of the deviation of the nuclear-charge distribution from a smooth behaviour, and is usually studied following the prescription of Tracy et al. [25]. For different fissioning systems [2,14,3,15,16,17,18,19,20], the local even-odd staggering has been shown to be larger for large asymmetry. This experimental observation is presented in figure 4 for a number of nuclei. The rate of increase is largest for the lightest system, 230 Th, and decreases for the heavier systems. The values of the local even-odd effect for the different nuclei approach each other at symmetry, but due to missing experimental information at symmetry and due to the scattering of the data points one can only say that they converge to a rather narrow range between 5 and 20 percent. For several systems, the data points that are closest to symmetry present an appreciably higher local even-odd effect than expected from the global trend. This effect may be associated with the influence of the Z=50 shell in the complementary fragment, which is known to enhance the yield of tin isotopes and, thus, leads to a local increase of the deduced even-odd effect. The local even-odd effect, namely the increase towards asymmetry has led to the notion of cold asymmetric fission, for which an extreme deformation takes most of the available excitation energy, and consequently the intrinsic excitation energy would remain low [15]. However, no elaborate model existed to quantitatively describe the even-odd effect based on these assumptions. Moreover, it will be shown in the following that, even in the case of scission configurations with invariably at least one unpaired proton, a large even-odd effect can be observed at large asymmetry. Therefore, the excitation energy and the consequent number of broken pairs cannot be considered as being uniquely accountable for the amplitude of the even-odd effect.

Local even-odd staggering in odd-Z fissioning systems

In the late 90´s the general appearance of a large even-odd effect in the Z distributions of odd-Z fissioning nuclei has been reported [28]. In these odd-Z systems, the probability to reach the scission configuration at least unpaired proton is always one. Assuming that any unpaired proton ends up in one or the other fragment with equal probability, it was expected that the even-odd effect would be zero over the full element distribution. With experimental techniques based on inverse kinematics, the evenodd staggering has been systematically measured for a large number of actinium and protactinium isotopes, over the complete fragment distribution. Its value was found to be zero close to symmetry and systematically increasing for large asymmetry, up to amplitudes as large as 40 %. A similar observation of a large even-odd effect has been reported in neutron-induced fission of 238 Np [26], and 242m Am [27], as shown in figure 4. The even-odd effect of the odd-Z fissioning systems at large asymmetry follows the general behaviour of the even-Z fissioning systems. Their values are very close to those of the neighbouring even-Z systems, as was reported already in [26]. In the inversekinematics data, where the heavier part of the fragment distribution has been measured, the even-odd staggering was found to be negative for heavy fragments, revealing a higher probability for the unpaired proton to end up in the heavy fragment. In these odd-Z fissioning systems, an even-odd effect may only be generated by a mechanism which is related to some difference in the properties of the fragments in asymmetric splits. The similarity of the local even-odd effect values of close-by even-Z and odd-Z systems suggests that a similar mechanism is responsible for the increase of the even-odd effect in even-Z fissioning systems. These experimental observations lead to the interpretation that the conventionally assumed relation between pair breaking and even-odd effect in the fission yields is valid only close to symmetry, as it was previously discussed in [28,6]. In addition, the variation of the even-odd effect close to symmetry is limited to a value below 20%, which does not vary much as the fissility (or Coulomb parameter) of the fissioning system varies. Most of the amplitude of the even-odd effect is then linked to the asymmetry of the fragment distribution, and is common for odd-Z and even-Z fissioning systems.

The observation of an even-odd staggering for odd-Z fissioning nuclei and the interpretation presented reveal that the relation between the amplitude of the even-odd staggering in fission-fragment charge yields and the intrinsic excitation energy at scission is not as direct as suggested by the established models discussed in section 2. Indeed, neither the statistical description of Nifenecker et al. nor the dynamical description of Bouzid et al. can explain the appearance of any global or local even-odd structure for odd-Z fissioning nuclei since in these models, the probability of unpaired nucleons to end up in one or the other fragment does not depend on the size of the fragments. The statistical model of Rejmund et al. [6] considers the local effect of dissipated energy for symmetric scission, separately of the influence of asymmetry in the fission-fragment yields. In references [26,27], the phenomenon is qualitatively discussed in of energy because the pairing gap is decreasing with the fragment mass, the light fragments are more likely to remain fully paired. However, only the binding energies of cold systems are considered. A statistical description of the local even-odd staggering as function of the asymmetry based on the level density of the fission fragments formed at scission [28] reproduces the higher probability for the unpaired nucleons to end up in the heavy fragment. This model gives a quantitative prediction of the general increase of the local even-odd staggering with the asymmetry, for odd-Z fissioning nuclei as well as for even-Z fissioning nuclei. Recently, the large local even-odd effect in asymmetric splits has been explained as the result of the energy-sorting mechanism in superfluid nuclear dynamics [8]. This model is the first one that reproduces all experimental data on the local even-odd effect for different fissioning systems and its variation with asymmetry rather well.

Local even-odd staggering at symmetry

The general trend of the even-odd effect towards symmetry is to decrease and to remain restricted to the range between 5 and 20%, as depicted in figure 4. However, due to the lack of data close to symmetry, it is difficult to draw further conclusions. The experimental technique based on inverse kinematics [START_REF] Schmidt | [END_REF] allows to access the element yields over the complete element distribution, with high resolution and for a wide systematic investigation of neutron-deficient fissioning systems. In addition, fission is induced via electromagnetic interaction, and occurs therefore at excitation energies which are, on the average, a few MeV higher than in fission induced by thermal neutrons. This results in higher yields for symmetric splits. As a consequence, this technique provides unique and high-quality data on element yields at symmetry. In figure 5, the local even-odd effect measured for similar fissioning systems using both techniques (thermal-neutron-induced fission in direct kinematics and electromagneticinduced fission in inverse kinematics) is displayed in the left panel. The inversekinematics data cover the full element distribution; due to the higher excitation energy the measured even-odd staggering has a lower value, but similar characteristic patterns are observed with both experimental approaches. This is demonstrated in the right panel of figure 5, where the ratio between the amplitude of the even-odd staggering for both experimental methods is displayed. The result is a constant ratio around 60% on the full range of asymmetry. From this value, it is possible to extrapolate that for both 230 Th and 234 U, the even-odd effect in low-energy fission at symmetry is of the order of few percents, below 10%. It is important to note, that this small but non-zero value of the even-odd staggering at symmetry has two major consequences:

Firstly, the parameterization used for the evaluation of fission-fragment yields [29],

which is based on former radio-chemical data, considers no even-odd effect at symmetry, in contradiction to the present experimental observation. The parameterization should be reformulated appropriately. Secondly, the major contribution to the global even-odd effect (40% for 230 Th, 23 % for 234 U, see figure 1) emanates from the asymmetry of the fragment distribution, which is not directly related to the probability to break pairs in the descent from saddle to scission, because it is also present in odd-Z fissioning systems. As a consequence, previous estimates on the dissipated energy derived from the amplitude of the global even-odd staggering [4,5] are not justified. In addition, the estimated value for the evenodd effect at symmetry for 230 Th and 234 U is very close to the value measured close to symmetry for heavier systems such as 246 Cm and 250 Cf. Both 246 Cm and 250 Cf have a relatively smooth behaviour when approaching symmetry, suggesting values around few percents (see figure 4). Within the experimental uncertainty, the variation of the amplitude of the even-odd effect at symmetry with the fissility of the fissioning nucleus seems to be weak. The standard interpretation of the global even-odd effect attributes a strong variation of the dissipated energy with the fissility of the fissioning system, based on the evolution of the global even-odd effect with the fissility (figure 1). The present investigation shows the fact that the global even-odd effect is strongly modified by the influence of the asymmetry of the fission process. The even-odd staggering at symmetry remains in a range of small values, and shows at most a weak variation within the experimental error bars. However, the conclusions on the variation of the even-odd effect at symmetry in nuclei studied with neutron-induced fission suffer from the lack of data and large error bars. New data sets and improved measurements would be needed to further precise these observations.

Dependence on asymmetry and fissioning system

The data analysed in the present work suggest that the local even-odd effect depends on both the fissioning system and the asymmetry the split. This two-parameter dependence figure 6, where the even-odd effect is displayed as a function of the fissility (left panels) and the Coulomb parameter (right panels) of the fissioning nucleus, for different values of the asymmetry (open symbols) and compared to the values closest to or at symmetry (full symbols). The latter are repeated in each figure as reference for better comparison. For symmetric splits measured in electromagneticinduced fission, the local even-odd staggering shows a small but definitively non-zero amplitude, remarkably independent of the fissioning nucleus. The data presented in figure 6 confirm the conclusions drawn from figure 5 for a wider range of nuclei. The data from neutron-induced fission do not provide direct information on this issue, as symmetric splits cannot be reached due to technical limitations already mentioned above. The full squares in figure 6 correspond to yields from the most symmetric splits measured. Due to the properties of the fragment distributions and the technical limitations, discussed in section 3, the access to the most symmetric splits is correlated with the fissioning system, making it easier to experimentally approach the symmetry for larger systems, and decreasing from a = 0.15 to 0.02 when considering fissioning systems from 230 Th to 250 Cf. This correlation produces a steadily decreasing amplitude of the even-odd effect at the most symmetric yield as a function of fissility or Coulomb parameter.

For large asymmetry (upper panels of figure 6), although fission is induced with moderately higher excitation energy in the inverse-kinematics technique, electromagnetic-and thermal-neutron-induced fission data show the same trend. The amplitude of the even-odd staggering at a given asymmetry is decreasing with fissility or Coulomb parameter. For lower values of the asymmetry (shown in the middle and lower panels of figure 6), the slope and amplitude of the local even-odd effect reduces and gradually approaches the value of the even-odd staggering at symmetry.

Ordering parameter

The dependence of the local even-odd effect with the fissioning system is usually reduced to an ordering parameter defining the fissioning nuclei. An optimum ordering parameter shows the same behavior of the even-odd effect for nuclei with the same parameter. Figure 1 shows that there exists a relation between the global even-odd effect and both the fissility and the Coulomb parameter. The validity of these quantities as ordering parameters for the local even-odd effect is investigated in detail in this section.

Left and right panels of figure 6 show the evolution of the even-odd effect of the same data set with respect to the fissility and the Coulomb parameter of the fissioning nucleus, respectively. Conventionally [6,11,[START_REF] Bocquet | [END_REF], the Coulomb parameter is considered to be the most appropriate ordering parameter, since it is associated with the available energy gain on the path from saddle to scission [5]. However, this conclusion has been drawn on the basis of the limited range of accessible nuclei in direct kinematics, while ignoring the correlation between the Coulomb parameter and the average asymmetry of the fragment distribution. Figure 6 displays data for fixed values of the asymmetry distribution, thus eliminating the role of the asymmetry parameter. The panels on the right-hand side show that the data of the long isotopic chains of thorium obtained in electromagnetic-induced fission shrink to a narrow range when plotted as a function of the Coulomb parameter. The systematic decrease of the local even-odd effect with increasing mass number (established in figure 4) produces a steep slope in the even-odd effect of each fissioning element when represented as a function of the Coulomb parameter. An extrapolation of the slope in the chain towards higher Z c suggests a zero value the local even-odd staggering at Z c ∼ 1400 in the three right panels of figure 6. However, considerable even-odd effects have been observed for heavier systems (see figure 1). Thus, there are severe problems in considering the Coulomb parameter as the ordering parameter for the local even-odd effect, since the behavior of the effect is different when considering different species with the same Z c . This could not be observed earlier, because the number of investigated nuclei was too limited (in general only one isotope per fissioning element, as shown by the black squares), and restricted to nuclei close to the stability line. The other possible ordering parameter, the fissility, is investigated in the left panels of figure 6. This parameter allows for a coherent description of the even-odd effect throughout the whole ensemble of collected data, originating from electromagnetic-or thermal-neutron-induced fission. The systematic decrease of the even-odd effect at fixed asymmetry suggests that the even-odd effect would disappear at x ∼ 39, which is compatible with the available data on even-odd effect in fission, since all systems investigated have smaller values of fissility.

Influence of the excitation energy

Figure 5 suggests that an increase in excitation energy influences the even-odd staggering in element yields of the even-Z 234 U and 229 Th systems with a constant reduction factor over the complete fragment distribution. The number of initially broken pairs has an impact on the amplitude of the even-odd effect. There exist no experimental data on the evolution of the even-odd effect in element distributions of odd-Z fissioning systems with the excitation energy. However, it is possible to compare neighbouring odd-Z and even-Z systems investigated in electromagnetic-induced fission, where the compound nucleus is created with a few MeV excitation energy above the fission barrier [START_REF] Schmidt | [END_REF], which allows for the breaking of several nucleon pairs. Interestingly enough, figure 7 shows that, in contrast to the low-energy fission case (figure 4), at several MeV of excitation energy, the amplitudes of the even-odd staggering in odd-Z fissioning systems are systematically lower than their neighbouring even-Z systems. In low-energy fission, the pairing correlations in even-Z and odd-Z fissioning systems are very different; one is totally paired (the excitation energy at saddle is below the pairing gap) while the second has an ensemble of totally paired protons plus one unpaired proton; this additional proton is expected to weaken strongly the pairing correlations of the nucleus by blocking effects, while figure 4 shows that the pairing effects in close-by even-and odd-Z fissioning systems have similar amplitudes. At higher excitation energy, the protonproton correlations in both systems are expected to be more similar, as the possible broken pairs in the even-and odd-Z systems equally weaken the pairing correlations of the remaining pairs. This would imply a smaller but similar even-odd effect in the fission of even and odd-Z nuclei at larger excitation energies. This is in contradiction with the data presented in figure 7, which exhibit a systematically lower amplitude of Local even-odd staggering in neighbouring even-Z and odd-Z actinides measured in electromagnetic-induced fission [START_REF] Schmidt | [END_REF] the even-odd effect in odd-Z fissioning nuclei, and thus a larger influence of the unpaired proton on the magnitude of the even-odd effect at higher energies.

Conclusion

A systematic investigation on even-odd staggering in fission-fragment yields based on thermal-neutron-induced fission of actinides and electromagnetic-induced fission of neutron-deficient actinides is reported. This comprehensive data base allowed for the study of properties of the even-odd effect that were not accessible previously on the basis of thermal-neutron-induced fission alone due to the limited variety of fissioning nuclei investigated. The global even-odd effect is shown to vary with properties of the fissioning system, which do not have an evident connection with the available energy available on the deformation path from saddle to scission and the possible quasi-particle excitations. For all considered systems, the amplitude of the local even-odd effect at symmetry is shown to be small compared to the value at large asymmetries, while the latter is varying strongly with the fissioning system. The evolution of the global evenodd effect with the fissioning system is thus shown to be essentially due to the evolution of the fragment-distribution asymmetry, and its influence on the local even-odd effect. Consequently, the global even-odd effect cannot be considered to derive conclusions on dissipation, as it includes a strong contribution of the asymmetry of the fission-fragment distribution, which is unrelated with energy dissipation. The Coulomb parameter of the fissioning system, which is the conventional ordering parameter to investigate the evolution of the even-odd effect with the fissioning nucleus, is shown to be problematic. Despite its correlation to the available energy in the path down to scission, it is unable to describe the evolution of the even-odd effect over the ensemble of the investigated fissioning systems, which confirms that the even-odd effect is not only connected to the dissipated energy.

The results of the present analysis refute great part of the traditional theoretical models and ideas, which were developed to explain the even-odd effect in fission-fragment distributions. The new findings should be a guidance for a better understanding of this beautiful signature of the influence of nuclear structure on nuclear dynamics.

Figure 1 .

 1 Figure 1. Global even-odd effect as a function of the fissility parameter (left) or the Coulomb parameter (right). Data are from thermal-neutron-induced fission of 229 Th [2], 233 U [14], 235 U [3, 15], 239 Pu [16], 245 Cm [17, 18] and 249 Cf [19, 20].

Figure 2 .

 2 Figure 2. Element distributions displayed as a function of the asymmetry parameter of the distribution, for thermal-neutron-induced fission of 230 Th, 236 U, 234 U, 240 Pu, 246 Cm and 250 Cf, from top to bottom.

Figure 3 .

 3 Figure 3. Global even-odd effect as a function of the average asymmetry of the fragment distribution.

Figure 4 .

 4 Figure 4. Local even-odd effect for the series of element distributions of even-[2,14,3,15,16,17,18,19,20] and odd-Z[26,27] nuclei studied with neutron-induced fission. The arrows indicate the value of the average asymmetry of the fragment distributions.

Figure 5 .

 5 Figure 5. Left panel: Local even-odd staggering measured in similar fissioning systems using thermal-neutron-(full symbols) and electromagnetic-induced-(open symbols) fission. Right panel: Ratio between the data obtained with the two different techniques for the two fissioning systems considered.

Figure 6 .

 6 Figure 6. The local even-odd effect is displayed as a function of the fissility x (left panels) and Coulomb parameter Z c (right panels). Upper panels show the effect for an asymmetry of 0.27 (open symbols), and compared to the local even-odd effect measured at symmetry (full symbols). Data of electromagnetic-induced fission of neutron-defficient Th and U isotopes are shown as blue circles and red diamonds, respectively. Data from thermal-neutron-induced fission are shown as black squares. Middle and bottom panels: same as above with an asymmetry of 0.21 and 0.19, respectively. Data at symmetry are shown in all panels for reference.

Figure 7 .

 7 Figure 7. Local even-odd staggering in neighbouring even-Z and odd-Z actinides measured in electromagnetic-induced fission[START_REF] Schmidt | [END_REF]

Acknowledgments

This work has been supported by the Région Basse Normandie with a Chair of Excellence position in GANIL, as well as by the EURATOM programme under the contract number 44816.


T Lönnroth

K.-M Källman

M Guttormsen

A C Larsen

P Manngård

Study of the high-lying, high-spin α+ 28 Si resonance structure in 32 S

The structure of highly excited elastic α-scattering resonances in 32 S was studied with the reaction 28 Si(α, α 0 ) 28 Si at beam energies between 22 and 30 MeV. The data were collected with a thick-target method giving continuous energies. The properties of 24 resonances in the spin range = 9 -12 h, and up to 32 MeV excitation in 32 S, were determined. The strong drop-off in elastic cross section at about 27.5 MeV laboratory energy was studied, and a similar but less drastic effect is observed at 21.5 MeV. Some possible explanation for these behaviours are discussed. The present results complement previous high-resolution data at lower energies, and favours the interpretation of the resonances as α-cluster states. The implications on potential models from resonances with angular momenta as high as 12h are discussed.

Introduction

During the last decade there has been a renewed interest in cluster states, called molecular states for heavier components. This has been spurred by the finding that high-lying states, that are still narrow, persist in light nuclei where a continuum has earlier been presumed [1]. In very light nuclei, with A∼8-16, α-cluster structures are the most conspicuous, see e.g. [2]. In heavier nuclei, also other cluster combinations like 12 C and 16 O have been observed. Indeed, these kinds of structures, both α-clusters and molecular clusters of heavier specimen, were discussed to some detail almost three decades ago [3]. Further, see reference [START_REF] Greiner | Nuclear Molecules[END_REF] for a comprehensive presentation of nuclear molecules.

The appearance of α-cluster structures in medium-light nuclei, with A ∼ 20-44, is not properly understood. Such structures have been studied in 20,22 Ne [START_REF] Rogatchev | [END_REF]6] (band structures), in 36 Ar [7] (low-spin states) and in 40 Ca and 44 Ti (α-clusters) [8]. One of the most detailed studies of α-cluster structures in medium-light nuclei was reported in [9]. In that work the elastic α+ 28 Si channel in the energy range E Lab = 6.0 -19.6 MeV was studied. More than 80 α-cluster states were identified, having unambiguous angular momentum values in the excitation energy range 12 -23 MeV, out of about 200 resonances totally observed. That study was preceded by another one [10] at low energies with E Lab = 4 -7 MeV. It has also been followed by a complete study 28 Si scattering over a large energy range. From the present work and [9,10]. The inset is a magnification of the uppermost part at E Lab ∼ 23 -31 MeV. of the region [11]. There also exists an old work of α+ 28 Si scattering [12], albeit with low energy resolution.

All the above-mentioned studies (except [12]) rely on the so-called thick-target method, which allows continuous energy registration [13]. The present work aims at verifying the structures observed in the preliminary studies up to E Lab ∼ 31 MeV. Further, angular-momentum measurements give the spin values of these relatively narrow resonances.

Experimental procedure and excitation function

The α+ 28 Si elastic-scattering experiment was performed at the K=36 cyclotron of the Department of Physics of Oslo University (OCL), using a compact scattering chamber of 47 cm inner diameter. The OCL cyclotron is equipped with a 90 • , 1 m radius analyzing magnet, and the overall accuracy of the energy determination has been measured to be some few tens of keV [14]. The excitation function was followed continuously from 19 MeV up to 31 MeV. The thick-target method of [13] was used for this purpose, since it allows recording the large energy range of about 12 MeV beam energy in a relatively short time, in steps of ∼ 400 keV. Here, a very highresolution experiment is not needed since the resonance witdhs are larger than about 60 keV.

The angular distributions were measured in nine angles between θ lab = 173 • and 133 • for the energy interval E Lab = 26-30 MeV. The detectors were 1.5-5 mm thick and had resolutions between 17 and 25 keV. The large-angle detectors were shifted in steps of 3 • since large angular-momentum values of = 10 -12 were anticipated. A detector at a fixed angle, θ norm = -160 • , was used for normalization. At the highest energies, where the elastic cross section is very low, one can separate out the inelastic contributions from both the 2 + 1 state at 1.78 MeV, and the 4 + 1 state at 4.62 MeV. This is done over an energy range of ∼ 2.5 MeV. These excitation curves are in very good agreement with the previouly measured data in references [12] and [15]- [18]. The total excitation function of the elastic α+ 28 Si reaction, including the present data, i.e. for an energy span of E Lab = 4 -31 MeV, is shown in Figure 1. In this figure one should especially note the enlarged high-energy part of the excitation function (inset panel). There are two noticeable features. First, there is a bump in the excitation function at E Lab ∼ 24.5 -27.5 MeV, and within this bump one can clearly distinguish a rich resonance structure at these high energies, E x ≥ 29.5 MeV. Secondly, there is a strong drop-off at E Lab ∼ 27.5 MeV above the ∼ 3 MeV wide bump. The intensity reduction is about a factor of 10 in comparison with energies around 26 MeV, and the cross section stays low at still higher energies. In this region the resonances seem almost to disappear. This behaviour seems suspicious, however, a similar drop-off has been observed in several investigations before, see [12,15,16,17,18]. But the feature has gone unnoticed, and has not been discussed to any detail. One should also notice a similar behaviour of the cross section at and above 21 MeV of beam energy, see Figure 1. These two bumps will be one of the main issues of the present study, and they will be discussed later. The present investigation continues the study of the α-cluster states above about 20 MeV of excitation energy, and especially up to and beyond the drop-off at about E Lab = 27.5 MeV, corresponding to an excitation energy of 33.4 MeV in 32 S. It may also be noted that the drop-off occurs over an energy span of only about 500 keV. This question will be addressed in subsection 4.2.

Data analysis and results

The excitation functions were analyzed in the framework of the R-matrix approach [20]. The method was developed in [21] and previously applied e.g. in [22]. Following the procedure outlined in [23], the method was used with success by the Wisconsin group, see e.g. [24,25] and references therein. The scattering amplitude, f (θ), is separated into a nonresonant term and a sum of resonant partial waves. For spinless 1.

E Lab =23.2 MeV, l=9 E Lab =26.2 MeV, l=10 E Lab =27.0 MeV, l=11 E Lab =27.7 MeV, l=12 a) b) c) d)
particles the total scattering amplitude can be written as

f (θ) = ρ(θ)× exp(iχ) - - i 2k m (2l m + 1) Γ lm Γ [ exp(2iβ lm ) -1] exp(2iφ lm )P lm (cos θ), (1)
where ρ and χ are the background amplitude and the phase shift, θ is the center-ofmass angle, k is the wave number, β is a resonant phase shift, and φ is a relative background phase shift. The resonant phase shift is given by

β lm = arctan Γ 2(E res -E Lab ) , (2)
where E res and E Lab are the resonance and particle energies, respectively. The relation between the excitation energy E x and the laboratory energy E Lab is

E x = 0.875 E Lab + Q, ( 3
)
where Q is the reaction Q-value, equal to 6.95 MeV for the present reaction. The background amplitude ρ was assumed to be a function that is smoothly depending on energy, and was interpolated by lines connecting five points for the 5 MeV energy interval. The phase shifts φ lm are fixed for each resonance and are not varied with energy and angle. With the above premises the cross section is given by the standard expression

dσ dΩ =| f (θ) | 2 . ( 4
)
The result of the R-matrix fit to the data of the present experiment is shown in Figure 2. The structure of the data confirms the previous findings in refs. [12,15,16,17,18]. The present data reaches beyond the intensity drop by more than 3 MeV. The fit is very good, and thereby unambiguous resonance quantum characteristics, i.e 1.

One should here note the fact that all the structure revealed in Figure 2 can be attributed to resonances, and that the continuous background contribution is insignificant. Indeed, the cross section for Rutherford scattering at 173 • is only ∼ 1 mb at these energies. Further, the cross section goes to almost zero at about 27.5 MeV, but there still remain some scattered elastic resonances at higher energies, even up to an excitation of almost 34 MeV. The angular momenta at these excitation energies are surprisingly high, up to ∼ 12 h, which will be discussed in section 4.

The general reduction in cross section of more than an order of magnitude above E x ∼ 31 MeV is still better demonstrated in Figure 4, showing the total excitation function from ∼ 10 MeV up to ∼ 34 MeV excitation. The continuous line is the result of smoothing the experimental data with a Gaussian of width 1.0 MeV FWHM. What especially should be noted is, that the reduction in fact is preceded by a bump with a centroid at E x ∼ 30 MeV and a width Γ 30 ∼ 2 MeV. But more than that, there is clearly another similar bump at E Lab ∼ 25 MeV, having an apparent width of Γ 25 ∼ 1.5 MeV. The smoothed data clearly illustrate these gross features, which will be discussed in the next section.

Discussion

The discussion is divided into three subsections addressing the structure and properties of the elastic α-particle resonances, the reduction of the elastic α-scattering cross section at high energy, and the implications of the existence of states with ∼ 12 h on an α+ 28 Si potential model.

Elastic resonances

The elastic resonances as observed in [9,10] and this work are collected in Figure 5. The excitation energies of the resonances are plotted as a function of ( + 1). (In the lower left corner there would be other spectroscopic states with known spin and parity J π , see [26]; they are omitted here.) The band-like structure starting at E x ∼ 12 MeV consists of the previously studied resonances at low energy [10], at intermediate energies [9], and of states up to the right established in the present study. The band closely follows the expression

E = h2 2J [ ( + 1)], (5)
and therefore it is quite suggestive that the set of states with natural spin and parity, i.e. 1 --9 -and 0 + -10 + , group according to increasing energies as expected from a rotational behavior. This structure was thus interpreted as a rotating 32 S nucleus described by an α+ 28 Si nuclear molecule configuration, and studied using the procedure of [27]. The moment of inertia for the two constituents at touching distance (using r 0 = 1.3 fm) is J mol = 7.6 h2 /MeV, whereas for a spherical mass with A = 32 it is J spher = 2.6 h2 /MeV. The experimental value, extracted from the ( + 1) behavior of the weighted averages of the individual states with spin , is J exp ∼ 4.0 h2 /MeV for the data reported in [9,11]. This effective moment of inertia corresponds to an elongated object, but is less than that of two osculating spheres, in accordance with the intuitive picture of an α-particle located at or in the nuclear surface.

---- -- - -- ------ ---- ------------ --- -- - ---- ---- -------- --- -- --- ------- - --- ------------ ---- --------- ---- --- --- - - - - ----- - --- ---- -- - -- - - 0
However, one notices a peculiar effect when the data from the present work, shown topmost in Figure 5, is compared to the previously observed band-like structure. The states with J π = 8 + -12 + seem to follow another trajectory on this plot than do the lower-lying 1 --9 -and 0 + -10 + states of the band described above. The slope represents a larger effective moment of inertia, close to that of two osculating spheres, J mol ∼ 8 h2 /MeV. The band seems to intercept the axis at about E x ∼ 22 MeV, as compared to ∼12.2 MeV for the band reported in [9].

We further note that the analysis of [9] showed that the energy span of a certainvalue only was about 3-5 MeV, see also [11], as indicated in the lower band members, with = 1-7 h, of Figure 5. When states of the next -value begin to occur, only few further members of the previous spin occurred. That is, there is only little overlap between the different -groups. Thus, if e.g. all the J π = 9 -states displayed in Figure 5 belonged to one and the same -group, the energy span of the resonances with this particular -value would be more than 10 MeV, which is not compatible with the statement above. Consequently, it would be a natural interpretation that the upper states with = 8 -12 h belong to a band with the α-particle excited to one higher oscillator quantum number N , cf. [19].

Further, it is of interest to study the systematic properties of the resonances, i.e. their spin-parities and their widths, as function of excitation energy. The previously observed resonances have widths ranging from 10-30 keV in the low-energy region, E x ∼ 12 -15 MeV in [10], and the widths increase to ∼50-150 keV in the intermediate-energy region E x ∼ 15 -25 MeV [9,11]. The resonances observed in this work follow this pattern and have widths increasing from ∼50 to ≥200 keV, cf. Table 1.

Finally we compare the mean lifetimes of these levels with the α-particle transit times at the corresponding energies. A width of Γ α = 40 keV corresponds to a lifetime of about τ = 1.6 • 10 -20 s, and an α-particle energy of 15 MeV gives a transit time of t tr ∼ 2.9 • 10 -22 s, whereas Γ α = 150 keV represents τ = 4.4 • 10 -21 s and 30 MeV gives t tr ∼ 2.1 • 10 -22 s. Thus these lifetimes are longer than the transit times by factors ∼ 20 -60, and these estimates show that even at these excitation energies the system is somehow quasi-bound. Or, as it is often expressed, that the doorway states are coupled to more complicated structures.

Reduction of cross section at high energies

It is difficult to understand the rapid decrease of the elastic cross section above E x ∼ 30 MeV, see Figures 2 and4. There are two physically feasible possibilities:

1. Two strong resonances interfere destructively at large angles. This would explain the strong reduction of cross section in backward angles.

2. The potential cannot sustain the increasing -values, and the cross section is dispersed over other reaction channels.

Regarding the first point we note that if there is destructive interference in backward angles, then in the angle plane there must also be positions, at specific angles, where there are constructive interference, and also intermediate situations, as required by the conservation of current density. In our angular distributions we find no trace of intensity anywhere, and therefore we must conclude that a two-resonance destructive interference cannot be the explanation.

With respect to the question of reaction channels we notice that the cross sections of fusion-like reactions, like (α,n), (α,p), (α,pn/d), (α, 2α), etc., are smooth, and the change in the (α, α) channel would not be drastic. The threshold values for the mentioned reactions 9.25, 2.19, 16.26/13.72 and 11.41 MeV. As a consequence a smooth decrease starting above 10 MeV is therefore expected. Indeed, this is observed in the elastic cross section starting from about 10 MeV beam energy, as is clearly seen in Figures 1 and4.

The energies for the break-up of 32 S into various multiple-fragment configurations are presented in Table 2. These configurations can be compared to configurations reported in the classical Ikeda diagrams, see e.g. ref. [28,29]. The cluster-break-up Q-value for 32 S → 16 O + 4 • α is 30.96 MeV, and this is almost exactly where the cross-section drop at the higher energy is situated, see Figure 4. The possibility of this break-up was first noticed in ref. [30]. Also another break-up, namely 32 S → Table 2: Threshold energies for all possible break-ups of 32 S into configurations X(+Y)+n • α, that is, one or two heavy multiple-alpha fragments X(+Y), e.g. 12 The physics behind break-up phenomena has been suggested to be that the αparticles form a kind of Bose gas on the nuclear surface of 16 O, that is, a kind of α-particle matter on a core nucleus, as discussed in [31]. However, the α-particles must carry away about 12h of angular momentum, so there remains (at least) the problem of an angular-momentum barrier. The possibility of this kind of structures was in fact discussed already long ago, see [START_REF] Brink | Proc. Int. School "Enrico Fermi[END_REF][START_REF] Clark | [END_REF], but not further elucidated, probably because of a total lack of experimental data at that time.

No quantitative calculations of α-particle bosonization on the nuclear surface have been performed. There exist, though, calculations for a phase transition to a Bose condensate of α-particles for light nuclei. This feature is discussed for mainly 12 C and 16 O. The first work of this kind is in [34], where differences in the groundstate and the threshold-state properties were discussed, in low-density nuclear matter. In [35] explicit α-cluster wave functions were constructed, based on the interactions derived in [36]. Threshold states for 2α -5α nuclei were discussed in [37,38]. But, as pointed out above, this concerned the bosonization of the nucleus as a whole. Further, a recent work dicusses multiple α-particles on a 40 Ca core, [39]. For a very recent discussion of these effects, see [START_REF] Funaki | Cluster Structure of Atomic Nuclei[END_REF] and other articles therein.

Finally, we shall shortly comment on the results from the inelastic α-particle scattering. Our data, as well as the previous results from the same region, [12,15,16,17,18], show no trace of a change in cross section as the Q-value for the 4α-emisson is reached or surpassed. Therefore it seems unlikely that at a specific energy, just above the corresponding Q-value, all the elastic cross section would concentrate in a single reaction channel. A natural choise would be to leave the core in an excited state, irrespective of the opening of this exotic emission channel. This is indeed what the inelastic data show. There is presently no final answer on this question, and, in fact, this last objection is also in contradiction to the bosonization picture above.

A potential model for the α+ 28 Si elastic cross section

The interaction between a (composite) particle and a nucleus is usually described by a local central complex optical potential U (r). The potential is often parametrized with a squared Woods-Saxon form factor for both the real and the imaginary parts.

In the present work the potential is parametrized according to the prescription of [START_REF] Michel | [END_REF]42], where a universal potential was obtained by fitting to data of α+ 16 O and α+ 40 Ca. The present potential,

U (r) = -V f(r, R V , a V ) -i W f(r, R W , a W ), (6)
has form factors given by f (r, R i , a i ) = 1/[1 + exp(r -R i /a i )] 2 , where the indices are i = V, W for the real and imaginary parts, respectively. The two best parameter values for the present elastic α+ 28 Si data, obtained from fits to angular distributions, were determined to be:

Set 1 V = 189.4(1 -0.00173E Lab ), W = -3.00(1 -0.15E Lab ), R V = 1.30, R W = 1.95, a V = 1.3 and a W = 1.0, Set 2 V = 192.4(1 -0.00173E Lab ), W = -3.35(1 -0.20E Lab ), R V = 1.45, R W = 1.65, a V = 1.
2 and a W = 1.0, in units of MeV and fm. Note the energy dependences of the potential depths.

Figure 6 shows the excitation functions calculated with the above potentials in the backward angle 173 • , superimposed on the measured data. As can be seen, there is generally good agreement for both potentials for the overall behavior. Further, one should notice the parameters in the expression above: the diffuseness parameters have the value a V = 1.2/1.3 and a W = 1.0, and these values are relatively large in comparison with standard values. In order to globally fit the present elastic cross section the corresponding potential has an extended surface. It is not clear whether this feature may be related to the proposed break-up of the 32 S intermediate nucleus.

There is one fairly clear difference between the two sets. For laboratory energies of 8 -20 MeV the fits are quite comparable, although Set 2 underestimates for energies below 8 MeV. However, Set 2 (dashed in Figure 6) fits the region around 20 MeV partly better, but has an overshoot around 20-24 MeV. On the other hand, Set 1 (full line) fits the region where the cross section disappear much better, when Set 2 has an overshoot of almost an order of magnitude. This is also the case for energies below 10 MeV. The potential of Set 1 is the more diffuse one of the two. However, it turns out that the potential is unable to sustain angular momentum values in excess of about 8h. Thus the experimental values up to 12h are in disagreemnet with the potential picture. This observation is presently not understood.

Summary and conclusions

The results from the present work confirm the existence of narrow resonances, Γ α ∼ 50 -200 keV, in the elastic α-particle scattering channel. These structures persist even to excitation energies in excess of 30 MeV, see figure 5. The resonances group into a band-like structure with an effective moment of inertia corresponding to an α+ 28 Si configuration of a touching molecular shape, and with a band-head energy of ∼ 12 MeV. The topmost resonances may form a second band with a higher bandhead energy and a larger moment of inertia.

The intensities of the resonance structures in the elastic-scattering cross section, slowly decrease up to about 25 MeV excitation, where rapid decreases in strength occur at excitation energies close to the Q-values of the 32 S → 20 Ne + 3 • α, 32 S → 16 O + 4 • α and/or 32 S → 12 C + 12 C + 2 • α break-ups in the elastic channels. The effect is not observed in the inelastic channel. Whether it is a collective multiple-α break-up effect cannot be decided by the data of the present study.

The highest-lying resonances have spin values of = 12 h, and this is difficult to reconciliate with a standard potential. However, in order to reproduce the experimental cross section, the diffuseness parameters of the potential have to be chosen substantially larger than the standard values. This corresponds to an extended surface diffuseness.

1 Confidential

 1 [mb/sr]

Figure 1 :

 1 Figure 1: Excitation function of the elastic α+ 28 Si scattering over a large energy range. From the present work and [9, 10]. The inset is a magnification of the uppermost part at E Lab ∼ 23 -31 MeV.

Figure 2 :

 2 Figure 2: (color online) R-matrix fit (solid black line) to the elastic excitation function of α+ 28 Si (red) over the excitation energy range 27 -32.5 MeV.

  [arb.unit]

Figure 3 :

 3 Figure 3: Experimental angular distributions (circles) for some strong resonances in the energy range 23.2 -27.7 MeV and curves of P 2 (cos θ). The superposition clearly gives the angular-momentum values from = 9 to = 12, cf. Table1.

Figure 4 :

 4 Figure4: The α+28 Si excitation function for E Lab ∼ 3 -31 MeV. The low-energy data are from[10], the intermediate data up to 19.6 MeV from[9], and the highest from the present work. Note especially the bumps at E x ∼ 25 and ∼ 30 MeV.

Figure 5 :

 5 Figure5: The topmost α-cluster levels in 32 S are from the present work. The levels in the middle, forming a band-like structure, are taken from[9,10].

Figure 6 :

 6 Figure 6: Calculated cross section as compared to the experimental data. The description and the parameter values of the two sets are given in the text.

Table 1 :

 1 Properties of strong resonances in 32 S from the elastic scattering α+ 28 Si.

	Alpha energy Excitation energy Spin	Width Γ CM
	E Lab [MeV]	E x [MeV]	[h]	[MeV]
	19.33	23.86	7	∼0.1
	20.55	24.93	8	∼0.1
	22.80	26.90	11	∼0.2
	23.20	27.25	9	0.08
	23.38	27.44	8	0.04
	23.65	27.69	9	0.15
	23.84	27.82	9	0.11
	24.08	28.04	10	0.04
	24.28	28.17	10	0.07
	24.40	28.30	8	0.08
	24.64	28.48	10	0.17
	24.85	28.67	10	0.22
	25.15	28.97	10	0.19
	25.50	29.25	9	0.13
	25.95	29.66	10	0.16
	26.12	29.88	10	0.20
	26.24	29.91	10	0.16
	26.64	30.26	9	0.17
	26.76	30.37	10	0.13
	27.03	30.61	11	0.25
	27.39	30.89	12	0.14
	27.72	31.19	12	0.20
	28.30	31.71	9	0.22
	28.60	31.98	12	0.22
	29.43	32.7	-	∼0.3
	30.34	33.5	-	∼0.2
	excitation energy E

x , angular momentum -value and α-width Γ α , can be extracted for all resonances. Examples of angular distributions are shown in Figure

3

, together with best-fitting squared Legendre polynomials P 2 (cos θ), and they indeed indicate unambiguous angular momentum values. The values determined are collected in Table

  C,16 O, ..., and n additional α-particles. C + 12 C + 2 • α, would be possible. The second bump at E x ∼ 25 MeV is also followed by a strong reduction of the elastis cross section. Turning to Table2one sees that the cluster-break-up Q-value for 32 S → 20 Ne + 3 • α is 25.93 MeV. It is therefore tempting to describe this feature as the same kind of collective effect as for the 32 S → 16 O + 4 • α break-up.

	Fragments	n • α Threshold energy
	X(+Y)		[MeV]
	4 He	7	45.41
	12 C	5	38.14
	16 O	4	30.96
	20 Ne	3	25.93
	24 Mg	2	16.92
	28 Si	1	6.95
	12 C + 12 C	2	30.86
	12 C + 16 O	1	23.70
	16 O + 16 O	0	16.54
	20 Ne + 12 C	0	18.97

12

Acknowledgement

T.L. and K.-M.K gratefully acknowledge the financial support from the foundation Magnus Ehrnrooths Fond in Helsinki. We are also grateful for the magnificent support from Eivind-Atle Olsen in running the OCL cyclotron. M.G and A.C.L gratefully acknowledge financial support from the Norwegian Research Council.


Dr Nuwan Niyadurupola

Dr Peter Sidaway

Andrew Osborne

David C Broadway

Dr Julie Sanderson
email: j.sanderson@uea.ac.uk

Mr David

C Broadway

The Development of Human Organotypic Retinal Cultures (HORCs) to study Retinal Neurodegeneration

Keywords: Retina, human, glaucoma, model, explant, neurodegeneration, neuroprotection

come   L'archive ouverte pluridisciplinaire

Introduction

Organotypic explant cultures allow controlled experimentation of retinal tissue and have the advantage over dissociated cultures by retaining regional morphology.

Animal organotypic retinal cultures (ORCs) have been developed to investigate retinal physiology [START_REF] Feigenspan | Modulation of GABAC receptors in rat retinal bipolar cells by protein kinase C[END_REF][START_REF] Pérez-León | Spontaneous synaptic activity in an organotypic culture of the mouse retina[END_REF][START_REF] Koizumi | Organotypic culture of physiologically functional adult mammalian retinas[END_REF]. Adult rabbit ORCs retained morphology and electrophysiological function for ≤6 days, suggesting intact neural circuitry [START_REF] Koizumi | Organotypic culture of physiologically functional adult mammalian retinas[END_REF]. Furthermore, viability in rat ORCs has been demonstrated for ≥17 days [START_REF] Johnson | Development and characterization of an adult retinal explant organotypic tissue culture system as an in vitro intraocular stem cell transplantation model[END_REF] making them useful for neuroprotection studies. For example, rat [START_REF] Manabe | Quantification of axotomized ganglion cell death by explant culture of the rat retina[END_REF] and mouse [START_REF] Mckernan | Age-dependent susceptibility of the retinal ganglion cell layer to cell death[END_REF] ORCs have been used to investigate axotomy-induced RGC death and the neuroprotective effect of caspase inhibitors. Glutamate and N-methyl-D-aspartate (NMDA) excitotoxicity of RGC layer cells and the neuroprotective effect of NMDA antagonists have also been studied in both rat [START_REF] Ruscher | Neuroprotective effects of the β-carboline abecarnil studied in cultured cortical neurons and organotypic retinal cultures[END_REF] and rabbit [START_REF] Haberecht | N-methyl-D-aspartatemediated glutamate toxicity in the developing rabbit retina[END_REF] ORCs.

We aimed to develop human organotypic retinal cultures (HORCs) to investigate loss of RGCs induced by either excitotoxicity or ischaemia, insults known to cause RGC death in in vivo and in vitro models of glaucoma [START_REF] Kitano | Hypoxic and excitotoxic damage to cultured rat retinal ganglion cells[END_REF][START_REF] Nash | Assessment of Thy-1 mRNA levels as an index of retinal ganglion cell damage[END_REF].

Materials and Methods

Human Organotypic Retinal Cultures (HORCs)

Donor human eyes were obtained within 24hr post mortem (PM) from the East Anglian Eye Bank with full ethical approval, under the tenets of the Declaration of Helsinki. Eyes with known pathology were excluded. Under sterile conditions, the neural retina was detached from the retinal pigment epithelium and choroid, dissected at the optic nerve and transferred RGC-side up into CO 2 -independent medium (Gibco Invitrogen, UK). The retinal edges were cut, allowing the retina to lie flat. 4mm diameter micro-dissecting trephine (Biomedical Research Instruments, USA) punch retinal explants were placed into serum-free Dulbecco's Modified Eagle Medium (DMEM)/HamF12 (Gibco Invitrogen, UK) in 35mm dishes (Corning, USA), or onto Millicell inserts (12mm diameter; 0.4μm pore) (Millipore, UK) RGC-side up in Neurobasal A, supplemented with B27/N2 (Gibco Invitrogen, UK) in a 12-well plate (NUNC, Denmark). Both media contained 50μg/ml gentamicin (Sigma-Aldrich, UK). Each HORC was placed into a separate culture dish or well. HORCs were incubated at 37°C in a humidified atmosphere of 95%O 2 /5% CO 2 . The medium was unchanged during the course of experiments unless necessitated by protocol (see oxygen/glucose deprivation below).

Neurotoxic insults

N-methyl-D-aspartate excitotoxicity

N-methyl-D-aspartate (10μM) (Tocris Bioscience, UK) was added to the HORCs in serum-free DMEM/HamF12 .

Oxygen/glucose deprivation (OGD) (simulated ischaemia)

HORCs were placed in serum-free DMEM without glucose and pyruvate (Gibco Invitrogen, UK), previously warmed and bubbled with 95%N 2 /5%CO 2 for 10min to remove oxygen. HORCs were placed in a modular incubator container (Billups-Rothenburg, USA) and gassed (10min) with humidified 95%N 2 /5% CO 2 before sealing the chamber. HORCs were incubated for a further 50min, then switched to serum-free DMEM/HamF12 and incubated for 24hr. Control HORCs were placed into DMEM with glucose (Gibco Invitrogen, UK) for the initial 60min incubation period.

THY-1 mRNA expression by Quantitative Real-Time Polymerase Chain Reaction (QRT-PCR)

Total RNA was extracted from HORCs using the RNeasy Mini Kit column-based method (Qiagen, UK). The concentration of total RNA was measured using a NanoDrop ND-1000 spectrophotometer (NanoDrop Technologies, USA). Total RNA was reverse transcribed to synthesise cDNA using a Peltier Thermal Cycler DNA engine (PTC-200, MJ Research, USA). The ABI Prism 7700 Sequence Detection System (Applied Biosystems, UK) was used for QRT-PCR. cDNA was mixed with Human THY-1 probe (Hs00174816_m1, Applied Biosystems, UK) and TaqMan® PCR Master Mix (Applied Biosystems, UK).

The geNorm programme (http://medgen.ugent.be/~jvdesomp/genorm) identified the most stable house-keeping genes for HORCs as cytochrome c-1 (CYC1), topoisomerase DNA I (TOP1) and ATP synthase H + transporting mitochondrial F1 complex β subunit (ATP5B). The geometric mean of C T values of either CYC1 and TOP1 or TOP1 and ATP5B were used as described previously [START_REF] Vandesompele | Accurate normalization of real-time quantitative RT-PCR data by geometric averaging of multiple internal control genes[END_REF] to normalise the data for THY-1 mRNA.

Immunohistochemisry

HORCs were fixed in 4% paraformaldehyde for 24hr and cryopreserved in 30% sucrose in phosphate buffered saline (PBS) (Oxoid, UK) for a further 24hr, before being placed into cryostat block moulds filled with optimal cutting temperature medium (Sakura Finetek, Netherlands) and frozen on dry ice. Retinal slices (13μm) were cut using a Hacker Bright OTF 5040 cryostat (Bright Instruments, UK) and collected on 3'aminopropyl-triethoxyl silane (TESPA)-coated glass slides.

Retinal slices were blocked in 5% normal goat serum (Sigma-Aldrich, UK) with 0.2% Triton X-100 (Sigma-Aldrich, UK) in PBS for 90min (room temperature) before incubating with primary antibody (1:200) for mouse neuronal nuclei (NeuN) (Millipore, UK) at 4°C overnight. Secondary antibody (goat anti-mouse AlexaFluor 488; Invitrogen, UK) was used at 1:1000 and incubated for 2hr (room temperature).

The nuclei were counterstained with 4',6-diamidino-2-phenyindole dilactate (DAPI) (1:100) for 10min (room temperature). Slides were mounted in immunofluorescence mounting medium (National Diagnostics, UK). A wide-field Zeiss Axiovert 200M fluorescent microscope (Zeiss, UK) was used with Zeiss Axiovision 4.7 software.

NeuN is a well-characterised RGC marker [START_REF] Wolf | NeuN: a useful neuronal marker for diagnostic histopathology[END_REF][START_REF] Buckingham | Progressive ganglion cell degeneration precedes neuronal loss in a mouse model of glaucoma[END_REF] and NeuN-labelling in HORCs was co-localised with nuclei in the RGC layer (Supplementary Figure 1). The number of NeuN-labelled RGC layer cells was used to determine RGC number and inversely as an index of RGC death. Six non-consecutive immunohistochemical slices were prepared for each HORC and NeuN-stained RGC layer cells counted (masked) in three 200μm sections. The mean for 6 slices was taken as one biological replicate.

TUNEL Assay

Apoptosis in the HORCs was detected by TUNEL assay (Promega Life Sciences, UK). TUNEL staining was carried out in conjunction with NeuN immunohistochemisty. Following incubation with primary antibody, slides were incubated with TUNEL reagent for 1hr at 37˚C. The reaction was stopped using standard citrate solution prior to addition of secondary antibody. Slides were then processed and analysed as described above.

Statistical Analysis

Significance was analysed with a non-paired Student's t-test. A probability lower than 5% was considered statistically significant.

Results

Human retinal THY-1 mRNA distribution reflected expected RGC distribution

Explants were taken from macular, para-macular and peripheral retinal regions at the time of dissection (Figure 1A) and assessed for THY-1 mRNA. Macular THY-1 mRNA was highest, at greater than twice the level for the para-macular region, the latter having approximately twice the level compared with peripheral regions (n=4 donor eyes; Figure 1B), reflecting the expected retinal distribution of RGCs.

Labelling of RGCs using NeuN immunohistochemistry also followed the same distribution (Figure 1C-E). There was no significant difference between the amount of THY-1 mRNA in retinal explants from the 5 para-macular regions (n=6 donor eyes; Figure 2A) and numbers of NeuN-labelled RGC layer neurones were found to be similar in each (n= 4 donor eyes; Figure 2B). Due to the similar levels of THY-1 mRNA and NeuN-stained RGC layer neurones, the 5 para-macular regions from each eye were used for development of HORCs to study RGC death. Retinas were not used beyond 24hr PM, since THY-1 mRNA levels tended to be low thereafter. Within 24hr, no correlation between THY-1 mRNA levels in the para-macular regions and PM time was identified.

Optimal culture medium for HORCs

Previous studies have used a variety of media and culture conditions for ORCs [START_REF] Koizumi | Organotypic culture of physiologically functional adult mammalian retinas[END_REF][START_REF] Johnson | Development and characterization of an adult retinal explant organotypic tissue culture system as an in vitro intraocular stem cell transplantation model[END_REF][START_REF] Zhang | Murine cytomegalovirus infection and apoptosis in organotypic retinal cultures[END_REF][START_REF] Hernández-Sánchez | Autocrine/paracrine role of insulin-related growth factors in neurogenesis: local expression and effects on cell proliferation and differentiation in retina[END_REF][START_REF] Koriyama | Upregulation of IGF-I in the goldfish retinal ganglion cells during the early stage of optic nerve regeneration[END_REF]. In the present study, the viability of HORCs was compared under two culture systems: placing the HORCs directly into serum-free DMEM/HamF12 and culture on inserts (RGC-side up) in Neurobasal A medium plus B27/N2 supplements.

Over 96hr no difference in gross appearance (architecture, opacity and colour) of HORCs was identified between culture conditions. There was a similar reduction in THY-1 mRNA levels in both conditions, with an approximate 50% decrease at 24hr and a further 25% decrease at 48hr, reaching basal levels after 72hr (n=4 donor eyes; Figure 3A). Subsequent experiments were performed in serum-free DMEM/HamF12 since medium composition was known. Over the 96hr period, gross appearance remained unchanged (Figure 3B). Retinal architecture remained intact over the culture period with no notable decrease in thickness/density of the nuclear layers (Figure 3C-G). NeuN-labelled cell number remained stable over the first 48hrs, but decreased at the 72 and 96hr time points (Figure 3C-H). The numbers of TUNELpositive apoptotic nuclei were also assessed (Figure 3C-G). In freshly dissected retina no TUNEL-positive nuclei were observed (Figure 3C). At 24 and 48hrs apoptotic cells were observed mainly in the inner nuclear layer (Figure 3D&E). By 96hrs some TUNEL-positive cells were apparent in all nuclear layers, including co-localisation between NeuN-and TUNEL-staining (Figure 3G arrows).

N-methyl-D-aspartate excitotoxicity in HORCs

N-methyl-D-aspartate (10μM) caused a significant reduction (19±8%) in THY-1 mRNA expression in HORCs compared to controls at 24hr (p<0.05, n=4 donor eyes; Figure 4A). At the equivalent time point, there was no difference in number of NeuNlabelled RGC layer cells between control (mean 8±3 NeuN-labelled neurones/200μm) and NMDA-treated HORCs (mean 7±1 NeuN-labelled neurones/200μm) (n=4 donor eyes; Figure 4B, E &F). However, by the 48hr time point a significant reduction of 50±6% was observed (p<0.05, n=4 donor eyes; Figure 4C, G &H).

Oxygen/glucose deprivation (OGD) (simulated ischaemia) in HORCs

Oxygen/glucose deprivation for 60min caused a significant reduction (44±13%) in THY-1 mRNA expression at 24hr compared to controls (p<0.05, n=4 donor eyes; Figure 5A). OGD (60 min) also caused a significant reduction (40±8%) in NeuNlabelled RGC layer neurones at 24hr compared to controls (p<0.05, n=5 donor eyes; Figure 5B-E).

Discussion

We have developed a simple system for culture of human retinal explants to investigate RGC death. Our specific interest in RGC cells led us to investigate the distribution of RGC markers in the human retina for the purpose of selecting comparable regions for subsequent use in HORC-based studies. THY-1 mRNA distribution reflected the known retinal RGC density distribution and was at a similar level in 5 para-macular regions. Thy-1 is almost uniquely expressed by RGCs [START_REF] Barnstable | Thy-1 antigen: a ganglion cell specific marker in rodent retina[END_REF] and has been used as an index of RGC death in ischaemic and excitotoxic retinal injury [START_REF] Nash | Assessment of Thy-1 mRNA levels as an index of retinal ganglion cell damage[END_REF]. NeuN is another marker of RGCs, giving extensive labelling in the RGC layer, whilst labelling only a minority of inner nuclear layer cells and none of the photoreceptor layer [START_REF] Wolf | NeuN: a useful neuronal marker for diagnostic histopathology[END_REF] -this was consistent with our findings. For experimentation, the 5 para-macular regions from each donor retina were selected for HORCs since they contained similar numbers of NeuN-stained RGC layer neurones and useful amounts of THY-1 mRNA. Most eyes were dissected and cultured within 12hr PM, although human retinas were still useful within 24hr.

A number of studies have developed animal ORCs in DMEM/HamF12 culture medium with the addition of various supplements including serum [START_REF] Haberecht | N-methyl-D-aspartatemediated glutamate toxicity in the developing rabbit retina[END_REF][START_REF] Zhang | Murine cytomegalovirus infection and apoptosis in organotypic retinal cultures[END_REF][START_REF] Homma | Early downregulation of IGF-I decides the fate of rat retinal ganglion cells after optic nerve injury[END_REF][START_REF] Mayer | Neural progenitor cells from postmortem adult human retina[END_REF].

Others have found that Neurobasal culture medium with supplements optimised ORC viability [START_REF] Johnson | Development and characterization of an adult retinal explant organotypic tissue culture system as an in vitro intraocular stem cell transplantation model[END_REF][START_REF] Manabe | Quantification of axotomized ganglion cell death by explant culture of the rat retina[END_REF][START_REF] Leaver | Adult olfactory ensheathing glia promote the long-distance growth of adult retinal ganglion cell neurites in vitro[END_REF][START_REF] Xin | A novel organotypic culture model of the postnatal mouse retina allows the study of glutamate-mediated excitotoxicity[END_REF]. The simplest method of culturing ORCs involved placing the explants directly into medium, which maintained the ORCs for at least 5 days [START_REF] Hernández-Sánchez | Autocrine/paracrine role of insulin-related growth factors in neurogenesis: local expression and effects on cell proliferation and differentiation in retina[END_REF][START_REF] Koriyama | Upregulation of IGF-I in the goldfish retinal ganglion cells during the early stage of optic nerve regeneration[END_REF][START_REF] Chen | Inhibition of caspase-3-like activity reduces glutamate induced cell death in adult rat retina[END_REF]. The optimal medium for rat ORCs was determined to be serum-free Neurobasal A medium supplemented with B27/N2, with explants supported on cell culture inserts, RGC-side up [START_REF] Johnson | Development and characterization of an adult retinal explant organotypic tissue culture system as an in vitro intraocular stem cell transplantation model[END_REF]. These conditions maintained explant viability for ≥17 days compared to explants in media containing normal horse serum that started to degenerate at 10 days in vitro [START_REF] Johnson | Development and characterization of an adult retinal explant organotypic tissue culture system as an in vitro intraocular stem cell transplantation model[END_REF]. In order to determine suitable culturing conditions for HORCs, this method was compared to the simplest method of placing the HORCs directly into serum-free DMEM/HamF12. Experiments indicated that the viability of HORCs in serum-free DMEM/HamF12 and serum-free/nutrient-supplemented Neurobasal A medium was equal, hence DMEM/HamF12 medium was selected since the exact medium composition was known. Excessive manipulation of HORCs was found to be detrimental and because placing the HORCs directly into medium was less traumatic than manipulating the tissue onto culture inserts, the former method was utilised. The surface tension of the medium helped flatten the HORCs avoiding the need for further 'trauma'. The HORCs floated just below the surface of the medium, which may have allowed advantageous gaseous exchange.

Freshly dissected human retina showed robust THY-1 mRNA expression, NeuNlabelling and, importantly, no evidence of apoptosis. Consistent with data from explants derived from adult rat [START_REF] Mckernan | Age-dependent susceptibility of the retinal ganglion cell layer to cell death[END_REF], this indicated a lack of significant apoptotic events during the PM period. With culture duration, there was a reduction in THY-1 mRNA and the number of NeuN-labelled RGC layer neurones in the HORCs. The rate of loss of THY-1 mRNA was greater than that for NeuN-labelling; at the 48hr time point basal THY-1 expression had been reached, but there was no significant loss of NeuNlabelling and no increase in TUNEL-labelling in the RGC layer. This indicates that the level of THY-1 mRNA was a more sensitive index of RGC health. Timedependent loss of cultured RGCs has not previously been determined using HORCs, but has been shown to occur in animal ORC models, although at a slower rate [START_REF] Manabe | Quantification of axotomized ganglion cell death by explant culture of the rat retina[END_REF][START_REF] Mckernan | Age-dependent susceptibility of the retinal ganglion cell layer to cell death[END_REF][START_REF] Katsuki | Neuronal nitric oxide synthase is crucial for ganglion cell death in rat retinal explant cultures[END_REF]. By using our HORC methodology there were still useful amounts of THY-1 mRNA for ≤36hr in culture and useful numbers of NeuN-labelled RGC layer neurones for ≤48hr. The best time-point to assess THY-1 mRNA in HORCs subjected to neurotoxic insults was 24hr, when there was a significant reduction in THY-1 mRNA following exposure to 10μM NMDA and 60min simulated ischaemia. The reduction in THY-1 mRNA preceded loss of NeuN-stained neurones from the RGC layer following NMDA excitotoxicity. At 24hr, there was no difference between NeuN-labelled RGC layer neuronal cell counts in control and NMDA-treated HORCs, although at 48hr there was a 50% reduction. The reduction of THY-1 mRNA prior to the loss of RGCs has been reported previously in rodent eyes subjected to optic nerve crush, intravitreal NMDA injection or elevated intraocular pressure [START_REF] Schlamp | Changes in Thy1 gene expression associated with damaged retinal ganglion cells[END_REF]. Consistent with the time course data discussed above, this suggests that the reduction in THY-1 mRNA appears to be a marker of RGC stress before cell death. Using HORCs, we have shown that NMDA excitotoxicity and simulated ischaemia caused a reduction of RGC markers in the human retina. HORCs, therefore, provide a useful model to study RGC insult by neurodegenerative mechanisms that may lead to glaucoma.

In vivo models are 'ideal' for studying glaucomatous processes; however, they lack in vitro model versatility that allows changing experimental conditions. Primate models are more relevant to human glaucoma than rat and mouse models [START_REF] Weinreb | The importance of models in glaucoma research[END_REF]. However, the lack of experimental primate availability and high costs limit their use for investigating glaucoma. HORCs provide a model for investigating the processes involved in RGC death and human retinal neuroprotection, with greater relevance to the clinician. In addition, retinal explant models are valuable for investigating the processes involved in RGC axonal regeneration [START_REF] Siddiqui | The glia-derived extracellular matrix glycoprotein tenascin-C promotes embryonic and postnatal retina axon outgrowth via the alternatively spliced fibronectin type III domain TNfnD[END_REF][START_REF] Bates | Differential effect of serum on laminin-dependent outgrowth of embryonic and adult mouse optic axons in vitro[END_REF][START_REF] Wizenmann | Growth preferences of adult rat retinal ganglion cell axons in retinotectal cocultures[END_REF][START_REF] Takano | Brainderived neurotrophic factor enhances neurite regeneration from retinal ganglion cells in aged human retina in vitro[END_REF]. By using different substrates HORCs may also be useful to study axon regrowth; this certainly warrants further investigation.

There are some limitations with ORCs. Unlike hippocampal slices that can be maintained for weeks, retinal neurones in explant cultures can be difficult to maintain for long periods, perhaps due to the high energy requirements of the retina [START_REF] Ames | Energy metabolism of rabbit retina as related to function: high cost of Na + transport[END_REF]. The development of ORCs involves transection of the optic nerve and retrograde RGC degeneration. Recognising that there is a loss of RGCs with time in these cultures is important when interpreting results and thus adequately time-controlled experiments are essential. In the present study, the use of similar para-macular regions from each donor made the use of HORCs ideal for controlled experimentation.

The main problem with HORCs is that completely fresh human tissue cannot be obtained (cf animal tissue). The relatively long PM interval means that processes involved in cell death are likely to be already activated. However, it should be noted that in the freshly processed samples TUNEL-labelling was not observed. An additional reason for the relatively poor survival of cultured human retina could relate to differences in vascular anatomy between animals and humans. Specifically, the relative avascularity of the rabbit retina may explain the success of detecting RGC electrophysiological recordings from rabbit retinas for ≤6 days in culture [START_REF] Koizumi | Organotypic culture of physiologically functional adult mammalian retinas[END_REF], since rabbit retina may extract nutrients from medium in a similar way to that from the choroid in vivo. In the human retina, branches of the central retinal vessels, supply the inner two-thirds of the tissue with only the outer third relying on choroidal nourishment. It is possible that the human retina may be unable to achieve the same supply of nutrients from culture medium as rabbit retina.

In summary we have developed a human retinal explant culture model that can be used to investigate RGC death from neurotoxic insults such as NMDA excitotoxicity or ischaemia. HORCs are useful for studying the effects of neurotoxic insults for ≤48hr. HORCs may represent a good model to investigate the processes that lead to RGC death and neuroprotection in human glaucoma.

Figure legends Supplementary Figure 1 .

 1 Figure legends

Figure 1 .

 1 Figure 1. (A) Freshly dissected human retina within 24hr post mortem showing

Figure 2 .

 2 Figure 2.(A) Normalised THY-1 mRNA level (mean ± S.E.M.) in the 5 para-

Figure 3 .

 3 Figure 3. (A) Normalised THY-1 mRNA (mean ± S.E.M.) from HORCs in

Figure 4 .

 4 Figure 4. (A) Normalised THY-1 mRNA (mean ± S.E.M.) of control and 10μM

Figure 5 .

 5 Figure 5.(A) Normalised THY-1 mRNA (mean ± S.E.M.) of control and 60min