R L Canavan

M Rudigier

P H Regan

M Lebois

J N Wilson

N Jovancevic

P.-A Söderström

S M Collins

D Thisse

J Benito

S Bottoni

M Brunet

N Cieplicka-Oryńczak

S Courtin

D T Doherty

L M Fraile

K Hadyńska-Kl Ęk

G Häfner

M Heine

Ł W Iskra

V Karayonchev

A Kennington

P Koseoglou

G Lotay

G Lorusso

M Nakhostin

C R Niţȃ

S Oberstedt

Zs Podolyák

L Qi

J.-M Régis

V Sánchez-Tembleque

R Shearman

V Vedia

W Witt

Half-life measurements in 164,166 Dy using γ-γ fast-timing spectroscopy with the ν-Ball spectrometer

We report on the measurement of lifetimes of excited states in the near-mid-shell nuclei 164,166 Dy using the gamma-ray coincidence fast-timing method. The nuclei of interest were populated using reactions between an 18 O beam and a gold-backed isotopically enriched 164 Dy target of thickness 6.3 mg/cm 2 at primary beam energies of 71, 76, and 80 MeV from the IPN-Orsay laboratory, France. Excited states were populated in 164 Dy, 166 Dy, and 178,179 W following Coulomb excitation, inelastic nuclear scattering, two-neutron transfer, and fusionevaporation reaction channels respectively. Gamma rays from excited states were measured using the ν-Ball high-purity germanium (HPGe)-LaBr 3 hybrid γ -ray spectrometer with the excited state lifetimes extracted using the fast-timing coincidence method using HPGe-gated LaBr 3 -LaBr 3 triple coincident events. The lifetime of the first I π = 2 + excited state in 166 Dy was used to determine the transition quadrupole deformation of this neutron-rich nucleus for the first time. The experimental methodology was validated by showing consistency with previously determined excited state lifetimes in 164 Dy. The half-lives of the yrast 2 + states in 164 Dy and 166 Dy were 2.35(6) and 2.3(2) ns, respectively, corresponding to transition quadrupole moment values of Q 0 = 7.58(9) and 7.5(4) eb, respectively. The lifetime of the yrast 2 + state in 166 Dy is consistent with a quenching of nuclear quadrupole deformation at β ≈ 0.35 as the N = 104 mid-shell is approached.

I. INTRODUCTION

The study of nuclear structure in deformed nuclei away from sphericity is important in achieving a complete understanding of the nuclear many-body problem. It is well established that nuclear quadrupole collectivity increases with the valence-proton (N π ), valence-neutron (N ν ) product [1]. However, for rare-earth nuclei near N = 102-106, micro-* Corresponding author: r.canavan@surrey.ac.uk scopic effects cause a saturation of the B(E 2) values a few nucleons below the mid-shell at N = 104 [2,3]. The current work aims to establish the lifetime of the first 2 + excited state in 166 Dy to track the evolution of the quadrupole deformation across the Dy isotopic chain, towards the 170 Dy 104 mid-shell. 170 Dy is a double mid-shell nucleus with the largest number of valence nucleons below the doubly magic 208 82 Pb 126 [4]. However, the consideration of only the number of valence nucleons cannot explain the energy systematics in the vicinity of 170 Dy, possibly due to the presence of deformed and spherical subshell closures, similar to those suggested for the Sm and Gd nuclei along the N = 100 isotonic chain [5,6]. Microscopic theoretical studies predict that along the isotope chain the maximum quadrupole deformation occurs below the N = 104 mid-shell [7,8].

To date, there are no experimental measurements of the yrast 2 + lifetimes in any of the neutron-rich even-even Dy isotopes with A > 164, the last stable isotope of this element. Existing studies for the neutron-rich nuclei report only on the energies of excited states and ground-state decay lifetimes within the nuclei [9][10][11][12][13][14][15]. The focus of the current work is to measure the lifetime of the first 2 + state in 166 Dy and to determine the B(E 2) ↓= B(E 2 : 2 + 1 → 0 + g.s. ) reduced transition strength for 166 Dy and the corresponding β 2 deformation parameter, for the first time in a neutron-rich Dy isotope. The production of the 166 Dy nucleus is also of interest due to its use as an in vivo generator for the radiopharmaceutical 166 Ho, which is used for radiotherapy [16,17], with the 166 Dy mother produced via sequential two-neutron capture on 164 Dy.

II. EXPERIMENTAL DETAILS AND REACTION CHANNEL SELECTION

The states of interest in 166 Dy were populated at an experiment carried out using the accelerator at the ALTO facility at the IPN Orsay. A pulsed 18 O beam was provided at three separate primary energies of 71, 76, and 80 MeV, each with a pulse duration of 2 ns and a period of 400 ns, and an average current of 35 enA charge state Q = 6 + . A 164 Dy target of 6.3 mg/cm 2 and 95% isotopic enrichment was used with 1 mg/cm 2 Au backing. The nominal fusion-Coulomb barrier for this reaction, in the laboratory frame, is approximately 71 MeV. The desired reaction was via 164 Dy( 18 O, 16 O) 166 Dy. The production of this channel was significantly suppressed relative to the main reaction channels (with cross sections approximately 10 3 times stronger than the 2n transfer) from the Coulomb excitation by inelastic scattering on the 164 Dy target nucleus, and the 164 Dy( 18 O, 4n) 178 W fusion evaporation reaction (a more detailed study of 178 W from this experiment can be found in [18]).

To detect the γ rays produced, the ν-Ball hybrid γ -ray detector array containing 24 high-purity germanium (HPGe) clover detectors, 10 coaxial HPGe detectors, and 20 LaBr 3 detectors was used [19][20][21]. All of the HPGe detectors were shielded against Compton scattering using bismuth germanate (BGO) scintillators. The HPGe detectors and BGO shields were were able to see radiation coming from the target position and could be used for calorimetry purposes. The timing signals from the array were obtained using digitizers and the software of the FASTER system, developed by LPC Caen, France [19,21]. For the LaBr 3 scintillators a digital CFD (constant-fraction discriminator) algorithm, which evaluates a second order polynomial to interpolate the zero crossing of the discriminator signal, was used by the QDC-TDC (chargeto-digital converter and time-to-digital converter) module to achieve subnanosecond time precision, with the capability of 7.8 ps LSB (least significant bit) accuracy [19,21]. The data were acquired with a trigger in place, so events were accepted when at least one LaBr 3 and one HPGe, or, two LaBr 3 detectors, were hit within 2 μs.

Figure 1 shows the total energy spectra for events which contain at least one clean HPGe γ ray (not vetoed by Compton suppression), from the three beam energies. The experiment was run at 71, 76, and 80 MeV for ≈22, ≈60, and ≈48 hours, respectively.

The event total energy and multiplicity (number of detectors fired) were exploited to improve the reaction channel selection in the current work. The three main reactions produced 164 Dy, 166 Dy, and 178 W via different reaction mechanisms, each of which has its own distribution of total event energy (E ) and total event multiplicity (N). These quantities are defined as follows: E = E (HPGe) + E (LaBr 3 ) + E (BGO) and N = nHPGe + nLaBr 3 + nBGO, where nHPGe is the HPGe detector multiplicity after add-back and Compton suppression, nLaBr 3 is the LaBr 3 detector multiplicity, and nBGO is the BGO multiplicity in events which were not Compton vetoed. The γ rays, which contribute to the event energy and multiplicity, are those that have not been Compton vetoed, and which are detected within the 2 μs coincidence window of each event.

Figure 2 shows the effectiveness of N and E gates to select a particular reaction channel. HPGe γ -γ matrices were created with the constraint that at least two HPGe detectors fired ±50 ns of the beam pulse, within the 2 μs event window. Additional constraints were placed on some of the matrices to preferentially select either fusion evaporation or Coulomb excitation events. Plot (a) gives the projection of the prompt HPGe-HPGe matrix, with no additional constraints, at 76 MeV beam energy. Plot (b) has N 4 and E > 2 MeV constraints to select transitions originating from 178 W. Plot (c) has 2 N 3 and E < 2 MeV constraints to pick out transitions originating from 164 Dy.

Figure 3 demonstrates the ability to separate the 164 Dy and 166 Dy nuclei using background-subtracted HPGe energy gates; in addition it justifies the level scheme of 166 Dy discussed in the next section. The plots are created from a prompt HPGe-HPGe coincidence matrix using the data taken at 76 MeV beam energy, where at least two HPGe detectors fired ±50 ns of the beam pulse and the 2 μs event window contained N 4. Plot (a) shows the HPGe spectrum after gating on the yrast 4 + → 2 + transition at 169 keV in 164 Dy and applying a background subtraction. Plot (b) shows the HPGe spectrum after gating on the yrast 4 + → 2 + transition at 177 keV in 166 Dy and applying a background subtraction. Plot (c) shows the HPGe spectrum after gating on the (2 +

2 ) → 0 + g.s. transition at 857 keV in 166 Dy and applying a background subtraction. Plot (d) shows the HPGe spectrum after gating on the (4 -) → (3 + ) transition at 252 keV in 166 Dy and applying a background subtraction. All background subtractions were performed by subtracting a background-gated HPGe projection from the peak-gated HPGe projection. The normalization factor used for the background subtraction was determined using the relative intensity of the 237 keV peak, which corresponds to the yrast 4 + → 2 + transition in 178 W. The difference in production cross section between the Coulomb excitation and 2n transfer reactions is clear from the reduction in γ -ray intensity originating from 166 Dy.

III. LEVEL SCHEME FOR 166 Dy OBSERVED IN THE CURRENT WORK

Observed transitions between the excited states populated in 166 Dy via the 164 Dy( 18 O, 16 O) 166 Dy reaction are shown in the partial level scheme in Fig. 4. The data from a 76 MeV beam was sorted into a prompt HPGe-HPGe coincidence matrix, with a coincidence time window of 100 ns. Backgroundsubtracted HPGe gates were set on various transitions within 166 Dy to complete the level scheme with the excited states I. The relative intensities were calculated by measuring the integrals of the γ rays in coincidence with the 177 keV yrast 4 + → 2 + transition and assuming 100% intensity for the 273 keV yrast 6 + → 4 + transition. In the current work, the yrast states up to the previously identified 10 + state at 1341 keV (which depopulates via the 449 keV transition) [9] are observed [see Fig. 3(b)]. Higher-spin states such as the yrast I π = 12 + at 1868 keV or the 14 + at 2467 keV, reported by Wu et al. [9], which depopulate via the 527 and 599 keV transitions respectively were not observed. This suggests an angular momentum population limit in the ( 18 O, 16 O) reaction mechanism. 166 Dy in the current work. Gamma ray energies, and spins and parities, where assigned, are taken from Ref. [22]. The total internal coefficients α T are obtained from BRICC [23], for α T > 0.02. The relative intensities, I γ (Rel.), are calculated for the data taken at a beam energy of 76 MeV, looking at the γ rays coincident with a 177 keV HPGe gate and assuming 100% intensity for the 273 keV transition. The total intensity, I Tot. , is calculated as I γ (1 + α T ). The uncertainty on the γ -ray energies is 0.1 keV unless stated otherwise. Excited states in 166 Dy have been reported previously, following population via 166 Tb β -decay [11], the 164 Dy(t, p) reaction [10], and successive thermal neutron capture on 165 Dy [22,24]. The current work clearly identifies coincident γ rays at energies of 675, 770, and 888 keV; see Figs. 4 and 3(b). These correspond to de-excitations from previously identified states [25] in the nominal K = 2 γ band with spinparity values (3 + ), (4 + ), and (5 + ), and excitation energies of 929, 1023, and 1141 keV respectively. The coincident 252 keV transition has also been reported previously as depopulating the I π = 4 -, K π = 2 -two-quasi-particle state with excitation energy 1181 keV [25]; this is clearly observed in the current work [see Figs. 4 and3(d)]. No evidence was observed in the current work for any delayed, out of beam component for the 252 keV 4 -→ 3 + E 1 transition in 166 Dy, consistent with a small change in K value.

Transition E γ I γ (Rel.) I Tot. J π i J π f α ICC E i → E f 76.6 34 (

IV. LIFETIME MEASUREMENT TECHNIQUES

To measure the excited state lifetimes in Dy isotopes the fast timing technique [26,27] was implemented. This γ -ray coincidence method takes advantage of the excellent timing resolution available in the LaBr 3 scintillators. A time difference distribution is obtained by sampling the time difference between the detection of the γ rays populating (feeding) and depopulating (decaying) the excited state. From the analyses, a HPGe-gated E -E -T cube is produced, enabling LaBr 3 energy gates to be set on the decay E d and feeder E f transitions to create the T distribution. The T distribution, produced by N 0 pairs of γ rays feeding and decaying from an excited state, can be described by a convolution of the prompt response function (PRF) and an exponential decay due to the mean lifetime, τ , of the state, such as in Refs. [26,28]:

D(t ) = 1 τ N 0 t -inf PRF(t )e t-t τ dt . ( 1
)
For cases where τ FWHM, the mean lifetime can be obtained by fitting the slope of the exponential decay in the time distribution [21]. If τ < FWHM, the lifetime can be measured using the generalized centroid difference (or centroid shift) method [28][29][30]. To use this method, the prompt response curve (PRC), which describes the energy-dependent time walk of the setup, must be obtained [31]. The PRC calibration was performed using a 152 Eu source and taking the 344 keV 2 + → 0 + transition of 152 Gd as the reference energy; the obtained PRC is shown in Fig. 5. The shift of the centroid of the time difference distribution C(D(t )) of the measured feeder and decay transitions can then be compared with the PRC to obtain the lifetime of the state:

C = C(E d , E f ) = PRC(E d , E f ) + τ, ( 2
)
where C(E d , E f ) is the centroid of the time difference distribution T = T (E decay ) -T (E feeder ), and

PRC(E d , E f ) = PRC(E f ) -PRC(E d ).
When using the centroid shift method, corrections for the background present in the LaBr 3 energy gates have to be applied, using the correction method described in Ref. [32], where,

C t PP = n PP C PP -n PB C PB -n BP C BP + n BB C BB n PP -n PB -n BP + n BB , ( 3
)
where C t PP is the true position of the centroid, after correcting the measured centroid C PP for the centroids of the background time distributions: C PB , C BP , and C BB . The corrections were weighted according to the integrals of these background time distributions: n PB , n BP , and n BB respectively. In this notation PP refers to T (peak, peak) and PB refers to T (peak, background), to indicate whether the LaBr 3 energy gate was set on the feeder/decay peak or on a neighboring background region.

V. LIFETIME ANALYSES

To maximize the available statistics and reduce uncertainties on the obtained lifetimes, the data acquired at all three beam energies was summed together for the lifetime analyses. First, the results for the 164 Dy lifetime measurements will be presented, followed by the half-life measurement for the first 2 + excited state in the 166 Dy nucleus.

A. 164 Dy

The channel selection of 164 Dy and lifetime measurements in this nucleus form a proof-of-principle analysis which verify the quality of the dataset. Triple coincident HPGe-LaBr 3 -LaBr 3 events were selected, where the HPGe γ ray was prompt (±50 ns of the beam pulse) and the LaBr 3 γ rays were both prompt (±17 ns of the beam pulse). Coincident events in the LaBr 3 detectors were vetoed if a nearest-neighbor detector fired within the coincidence time window, which was in essence an active Compton suppression condition. A HPGe gate was set on a discrete γ ray from within the yrast band, and two LaBr 3 energy gates were set subsequently on the transitions required to obtain the time difference distribution to establish the excited state lifetime. The purity of the LaBr 3 gates was verified by HPGe-HPGe and HPGe-LaBr 3 -HPGe gates on the data.

A HPGe gate was set on the 6 + → 4 + transition of 164 Dy at 259 keV, to enable a clean LaBr 3 -LaBr 3 time difference to be obtained between the 169 keV 4 + → 2 + and 73 keV 2 + → 0 + transitions. Figure 6 The resulting T (73, 169) time distribution is shown in Fig. 7; an exponential decay and constant background are fitted simultaneously. The half-life obtained is 2.35 (6) ns, in good agreement with the literature value of 2.393( 29) ns [33,34].

The lifetime of the first 4 + excited state was measured using the centroid shift technique. A HPGe gate was set on the 8 + → 6 + transition of 164 Dy at 342 keV [see Figs. 6(d)-6(f)]. Two-dimensional (2D) background/random gates were set at energies above and below the 169 and 259 keV transitions, as shown in Fig. 8(a). The values for the centroids and integrals were calculated as an average of the two distributions created using the background above and below the peak.

The T (169, 259) time distribution is shown in Fig. 8(b) with the three background time distributions which were used for the correction. For simplicity, only the time spectra corresponding to regions P|B 1 , B|P 1 , and B|B 1 are plotted. Using Eq. ( 3) the background-corrected value for the centroid was calculated as 0.243 (7) ns. This centroid was then corrected for the LaBr 3 time walk using the PRC shown in Fig. 5 to obtain the lifetime of the yrast 4 + state in 164 Dy of τ ( 164 Dy, 4 + 1 ) = 0.273( 10) ns [T 1/2 = 0.189( 7) ns], which compares with the literature value of T 1/2 = 0.201( 8) ns [33,35].

For the 6 + yrast state in 164 Dy, the E -E -T cube was constructed with a HPGe gate on the 4 + → 2 + transition at 169 keV. Figure 8(c) shows where the 2D LaBr 3 gates were set to produce the four time distributions. Again, the centroids and integrals of three background time distributions were calculated as averages from the gates above and below the 259 and 342 keV transitions. The T (259, 342) distribution is shown in Fig. 8(d), with the three background component time distributions when using the background gates below the peaks. The background-corrected value for the centroid was 0.019(4) ns. The additional correction for the PRC then gave τ ( 164 Dy, 6 + 1 ) = 0.031(8) ns, corresponding to T 1/2 = 22(6) ps, consistent with the literature value of 27.2(8) ps [33,35].

B. 166 Dy

For the optimal selection of the 166 Dy nucleus, for timing gates, it was useful to use a combination of HPGe gating with a total event multiplicity constraint. Gated E -E -T cubes were produced with a HPGe gate on either the yrast 6 + → 4 + or the 4 + → 2 + transition in 166 Dy, and only the events with a total multiplicity of N 4 were used. Figures 9(a The similarities of low-lying levels in 164 Dy and 166 Dy, and the fact that T 1/2 ( 164 Dy, 4 + 1 ) T 1/2 ( 164 Dy, 2 + 1 ), suggests that the exponential decay of the 4 + 1 in 166 Dy is short FIG. 6. Gamma-ray coincidence spectra for transitions in 164 Dy. (a)-(c) HPGe-gated, LaBr 3 projected γ -ray spectra to demonstrate the selectivity of the LaBr 3 gates used for T (73, 169). (d)-(f) HPGe-gated, LaBr 3 projected γ -ray spectra used for T (169, 259). Arrows indicate the energies where gates were set. Note that there are still peaks present at 169 and 73 keV even when this is the gate energy due to Compton coincidences. These plots were produced using combined data from all three beam energies. enough to not significantly affect the decay curve of the 2 + 1 state. The time differences T (77, 177) and T (77, 273) are summed and fitted with an exponential decay plus a constant background, as shown in Fig. 10. The obtained half-life value is 2.3(2) ns. FIG. 7. Time distribution for the yrast 2 + state in 164 Dy, obtained using gates on the decay energy E d = 73 keV and feeding energy E f = 169 keV. The deduced half-life is given in the legend.

VI. RESULTS AND DISCUSSIONS

The reduced transition probability B(E 2) ↓ is related to the lifetime of the excited state by [36] 2 , where τ is the neutral atom mean lifetime in seconds, E γ is the stretched E 2 transition energy in MeV, and α T is the total internal conversion coefficient. The relationship between the intrinsic quadrupole moment Q 0 and the reduced transition probability is given by [36]

B(E 2) ↓= 1 τ (1 + α T ) × 1.225 × 10 13 × E 5 γ (4) to give B(E 2) ↓ in e 2 b
B(E 2) ↓= 5 16π Q 2 0 | IK20|(I -2)K | 2 (5)
where IK20|I -2K is the Clebsch-Gordan coefficient for an initial nuclear spin of I, a nuclear spin of I -2 following the decay, and a projection of the intrinsic angular momentum on the symmetry axis of K. Equation ( 5) applies for E 2 transitions within a rotational band and gives Q 0 in eb. If the nucleus is an even-even nucleus then it is assumed that K = 0 [37]. Finally, the β 2 deformation parameter can be calculated using the expression [38] where Ze is the nuclear charge and R 0 = 1.2A 1/3 fm is the nuclear radius. Uncertainties on B(E 2) ↓, Q 0 and β 2 are calculated by propagating through the uncertainty on the measured mean lifetime τ .

Q 0 = 16π 5 3 4π Ze R 2 0 β 2 , (6)
For the 164 Dy nucleus, Table II gives the lifetime results and corresponding B(E 2) ↓ and Q 0 values calculated in this work.

For the 166 Dy nucleus, the lifetime for the 2 + 1 state obtained in the current work and its corresponding B(E 2) ↓ and β 2 values are given in Table III. The values are compared with [33]. The values for the total internal conversion coefficient α T were obtained from BRICC [23]. Nuclear data for the 160 Dy and 162 Dy nuclei are taken from Refs. [40] and [41] FIG. 9. Gamma-ray coincidence spectra for transitions in 166 Dy. (a)-(c) HPGe-gated, LaBr 3 projected γ -ray spectra demonstrating the selectivity of the LaBr 3 energy gates used for T (77, 177). (d)-(f) HPGe-gated, LaBr 3 projected γ -ray spectra used for T (77, 273). The peak labeled "c" corresponds to a weak contamination from the 237 keV yrast 4 + → 2 + transition in 178 W, which is the strongest line in the total projection. These plots were produced using combined data from all three beam energies.

The value for B(E 2) ↓ in 164 Dy obtained in the current work is clearly compatible with the value calculated from [33].

Relativistic mean-field calculations by Lalazissis et al. [47] predict an increasing β 2 deformation for the Dy isotopes towards the N = 104 mid-shell, but with a near saturation of collective behavior and deformation from N = 98 ( 164 Dy). FIG. 10. Time distribution for the yrast 2 + state in 166 Dy, obtained using gates on the decay energy E d = 77 keV and feeding energy E f = 177 keV or E f = 273 keV. The deduced half-life from the fit is given in the legend.

More recent work by Bonatsos et al. uses the proxy-SU(3) scheme to make predictions of the β (and γ ) deformation variable for the Dy isotopes, with increasing N [48]. The Dy deformations are predicted to be among the largest in the region and to saturate at a value of β 0.3 between N = 98 and N = 102.

Self-consistent density-dependent Hartree-Fock calculations with BCS pairing were reported by Rath et al. [7], FIG. 11. Systematics of B(E 2) ↓ for Gd, Dy, Er, and Yb isotopes with 94 N 104; data taken from [22,33,[39][40][41][42][43][44][45][46]. The B(E 2) ↓ values for 164 Dy and 166 Dy calculated here are added as starred data points. The isotopes are slightly offset at each value of N to allow each data point and error bar to be seen. which also predict a saturation of β 2 at ≈0.35 in the range A = 162-170 (N = 96-104) across the Dy isotopic chain. While the energy systematics of the 2 + yrast states suggest a deformation maxima at N = 98 (local) and possibly N = 104 (global) [12], the current work is consistent with the predicted deformation saturation. This is also the first direct B(E 2) measurement in a neutron-rich Dy isotope and provides a bridge for future higher-precision studies towards and across the N = 104 mid-shell valence maximum, possibly following production via high-energy projectile fission reactions as studied in [13][14][15].

APPENDIX: A NOTE ON UNCERTAINTY CALCULATIONS

Error bars on the statistics in each channel are always taken into account in the total uncertainty on a lifetime result, these are assumed to be the square root of the number of counts in each channel. Where cubes or histograms were added together or subtracted from one another, these error bars were propagated by summing in quadrature.

Factors taken into account for the uncertainty determination when using the decay slope fit were the following: the statistical uncertainty on the number of counts in each bin i, δn i ; the uncertainty of the binned likelihood fit, δ fit, given by the fit residuals at the 1σ interval; and the uncertainty on the decay constant parameter due to variation of the constant background parameter, δλ(bg), given by the distribution in λ at the 1σ interval. The standard uncertainty of the half-life was derived by adapting the methodology described in Ref. [49].

For the centroid shift method, the uncertainty on the background corrected centroid is given by

δC t PP = i ∂C t PP ∂n i δn i 2 + i ∂C t PP ∂C i δC i 2 , ( A1
)
where i represents the three background regions P|B, B|P, and B|B, such that δC i and δn i are the uncertainties on the centroids and integrals of the three background regions respectively. δC t PP was added in quadrature with the uncertainty δ PRC = 0.008 ns from the PRC correction, to give the overall uncertainty on τ :

δτ = δC t PP 2 + δ PRC 2 (A2)

FIG. 1 .

 1 FIG. 1. Total energy spectrum at beam energies 71, 76, and 80 MeV, in panels (a)-(c), respectively, for events containing at least one γ ray detected by a Compton suppressed HPGe detector.

FIG. 2 .

 2 FIG. 2. (a) Projection of prompt HPGe-HPGe coincidence matrix. (b) Projection of prompt HPGe-HPGe matrix with N 4 and E > 2 MeV, enhancing fusion evaporation events from 178 W. (c) Projection of prompt HPGe-HPGe matrix with 2 N 3 and E < 2 MeV, enhancing events from Coulomb excitation by inelastic excitation of the 164 Dy target nucleus. These data were taken at a beam energy of 76 MeV.

FIG. 3 .

 3 FIG. 3. Projections from a prompt HPGe-HPGe coincidence matrix, with N 4 for the 2 μs event, after applying backgroundsubtracted HPGe gates on transitions in 164 Dy [panel (a)] and 166 Dy [panels (b)-(d)]. Arrows indicate the energies where gates were set. These data were taken at a beam energy of 76 MeV.

FIG. 4 .

 4 FIG. 4. Level scheme of 166 Dy from the γ -ray transitions observed in the current work following the 164 Dy( 18 O, 16 O) 166 Dy reaction. The relative γ -ray intensities are taken from the 76 MeV beam energy data.

FIG. 5 .

 5 FIG.5. The PRC with reference energy E ref = 344 keV. The deviation of the data points from this curve is shown in the inset, and the 3σ interval of 8 ps is taken as the uncertainty of the PRC.

  (a) shows the LaBr 3 projection from the background-subtracted, 259 keV HPGe-gated E -E -T cube. The LaBr 3 projections after setting LaBr 3 energy gates on the 73 and 169 keV transitions are shown in Figs. 6(b) and 6(c).

  ) and9(d) show the LaBr 3 projections from the E -E -T cubes with HPGe gates on 273 and 177 keV, respectively. The LaBr 3 projections after setting LaBr 3 energy gates on the 77 and 177 keV transitions and on the 77 and 273 keV transitions are shown in Figs. 9(b), 9(c), 9(e), and 9(f) respectively.

FIG. 8 .

 8 FIG. 8. (a) 2D projection of the E -E -T cube showing the coincidence peak at 169-259 keV, and the six background regions used to correct the T centroid. (b) Time distribution for T 1/2 ( 164 Dy, 4 + 1 ) with the decay energy E d = 169 keV and feeding energy E f = 259 keV. (c) 2D projection of the E -E -T cube showing the coincidence peak at 259-342 keV, and the three background regions used to correct the T centroid. (d) Time distribution for T 1/2 ( 164 Dy, 6 + 1) with the decay energy E d = 259 keV and feeding energy E f = 342 keV. These plots were produced using combined data from all three beam energies.

TABLE I .

 I The observed transitions associated with

TABLE II .

 II A summary of the measured T 1/2 and B(E 2) ↓ values for164 Dy. Excitation energy, E ex , is given in keV, T 1/2 is given in ns, B(E 2) ↓ is given in e 2 b 2 , Q 0 is given in eb, and (LIT.) refers to the evaluated literature values[33]. of the other even-even Dy isotopes, for 94 N 100.For164 Dy the values obtained in this work are used.The systematic trends of the B(E 2 ↓) values for even-even nuclei between 64 Z 70 and 94 N 104 are shown in Fig.11. As expected, there is an increasing trend in the B(E 2) ↓ as N approaches N = 104 for all of these nuclei, but E (2 + 1 , 164 Dy) < E (2 + 1 , 166 Dy) implies that the maximum quadrupole deformation occurs at N = 98 for Dy isotopes.

				T 1/2
	J π	E ex	T 1/2	(LIT.)	B(E 2) ↓	Q 0
	2 +	73.393(5)	2.35(6)	2.393(29)	1.14(3)	7.58(9)
	4 + 242.234(7)	0.189(7) 0.201(8)	1.54(6)	7.35(14)
	6 + 501.330(12) 0.022(6) 0.0272(8)	2.0(5)	8.0(11)

those

TABLE III .

 III A summary of the measured T 1/2 and B(E 2) ↓ values for different Dy isotopes. T 1/2 is given in ns and B(E 2) ↓ is given in e 2 b 2

  , respectively.

	Nucleus	E (2 + )	T 1/2 (2 + )	α ICC	B(E 2) ↓	β 2
	160 Dy	86.78	2.02(1)	4.63	1.011(5)	0.3361(8)
	162 Dy	80.66	2.19(2)	6.14	1.060(10)	0.3414(16)
	164 Dy	73.39	2.35(6)	8.890	1.14(3)	0.352(4)
	166 Dy	76.7	2.3(2)	7.480	1.12(11)	0.345(17)

ACKNOWLEDGMENTS

The authors would like to thank the operators of the ALTO facility for providing the reliable beams used during the experiment. Additionally we thank the FASTER collaboration for the technical support given. GAMMA-POOL and LOAN-POOL are acknowledged for loaning the Clover and Phase I HPGe detectors. The FATIMA Collaboration is acknowledged for loaning the LaB 3 detectors. This work was supported by the STFC UK Nuclear Data Network, the STFC (Grants No. ST/L005743/1 and No. ST/P005314), the Marion Redfearn Trust, BMBF (NUSTAR.DA Grant No. 05P15RDFN1), and Spanish MINECO Grant No. FPA2015-65035-P. The research leading to these results has received funding from the European Union's HORIZON2020 Program under Grant Agreement No. 654002. P.H.R., S.M.C., G.L., and R.S. acknowledge support from the UK Department of Business, Energy and Industrial Strategy (BEIS) via the National Measurement System and from the STFC consolidated grant.


L Qi

C Schmitt

M Lebois

A Oberstedt

S Oberstedt

J N Wilson

A Al-Adili

A Chatillon

D Choudhury

A Gatera

G Georgiev

A Göök

B Laurent

A Maj

I Matea

S J Rose

B Wasilewska

F Zeiser

Potential of prompt γ -ray emission studies in fast-neutron induced fission: a first step

Potential of prompt γ-ray emission studies in fast-neutron induced fission: a first step

Introduction

It is well-established that nuclear fission constitutes a particularly interesting phenomenon for both fundamental research and applied science (see Refs. [1,2] for recent reviews). Understanding the evolution of the process from threshold a e-mail: christelle.schmitt@iphc.cnrs.fr (corresponding author) up to moderate excitation energy is, in particular, a challenging problem, as it raises the question of the respective role of nuclear structure in the nascent fragments and nuclear dynamics. An accurate knowledge around and above threshold is also crucial for applications.

So far, models and codes in the domain focus on spontaneous and thermal-neutron-induced fission, for which most numerous and accurate information exists. However, their ability to explain consistently the available data is still limited. In particular, describing neutron and γ -ray emission properties simultaneously remains a problem in most cases (see e.g. Refs. [3][4][5][6][7][8][9]). Part of the difficulty comes from the intricate interplay of the influence of emitter mass A, charge Z , excitation energy E * , and angular momentum L, in determining the neutron and γ -ray observables. These dependences induce natural correlations between fission neutrons and γ rays [10,11]. For a single fissioning system, a wide population (a few hundreds) of primary fragments is generated in the (A, Z , E * , L) space. Varying separately these four variables, or disentangling them, is impossible in practice, what magnifies the complexity of correlations in the integral spectrum. Focus during the last decades has been on the description of neutrons, while γ rays received little attention. However, the understanding of one observable cannot occur in isolation to the other. Furthermore, γ rays on their own are important for understanding specific aspects of the fission process. Fission γ -rays are a key issue in nuclear 123 reactors. The international OECD/NEA agency considers as priority [12] the need to improve the existing simulations of heating caused by γ rays. Recent studies [13][14][15][16] excluded thermal-neutron-induced fission as the cause of the underestimation of γ -ray heating by current calculations. Fast-neutron induced fission may be the cause. A crisp review on the history of prompt fission γ -ray studies, status, open questions and perspectives, can be found in Ref. [17].

The aim of the present work is to contribute to the ongoing worldwide investigation by exploiting the results of a recent experimental campaign [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF][START_REF] Qi | [END_REF][20] on fast-neutron induced fission of 238 U and 239 Pu, including also spontaneous fission of 252 Cf, at the ALTO/LICORNE facility [21], IPN Orsay, France. The results for n+ 239 Pu are presented for the first time. The experimental data are compared to calculations obtained with two semi-empirical codes widely-distributed in the field, with the goal to investigate to which extent the measurements are capable of evidencing differences between the three systems, and correlate it with the underlying physics. The calculations are used to offer an explanation for some experimental observations, whereas some other remain un-explained, as it appears impossible to discriminate between different physics scenarios. Similar comparisons can be found in literature (representative papers are quoted in this paper). The focus was mainly on testing models with benchmark data, and eventually address some physics case. In this context, the present work is instead intended to study in a dedicated and detailed manner to which level of confidence and accuracy this is possible. It shows which specific physics question can, or not, be reliably accessed with certain observables measured in certain conditions. The work sheds light on the influence of critical limitations of current experiments, as well as it points to some required developments.

Measurements

Setup

The Prompt-Fission γ -ray spectrum (PFGS) from fastneutron induced fission of 239 Pu was measured at the ALTO/LICORNE facility, IPN Orsay, France. The reaction p( 7 Li, n) 7 Be was used to generate a quasi-monoenergetic kinematically focused neutron beam of energy E n = 1.8 MeV. To select fission events, a specifically-designed fission chamber was constructed at JRC-Geel, containing the 239 Pu sample [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF]20]. The purity and total mass of the 239 Pu sample was 99.97% and 3.519 mg, respectively. The charge signals of the fission chamber permitted to discriminate fission fragments from α particles. A particularly efficient method based pulse shape discrimination was developed, and permitted to recover 7% of true fission events, which pulse height overlaped with the α bump. Details and spectra have been reported in Ref. [20]. The total number of fission events collected amounts to 5.5 × 10 6 . Prompt fission γ -rays were measured using two types of fast scintillators: 6 individual LaBr 3 (Ce) (cylindrical 2 ×2 and 3 ×3 crystals) detectors located at distances between 34 and 45cm from the target, and the first cluster of the PARIS array [22] encompassing 9 new type of LaBr 3 (Ce)-NaI(Tl) phoswich cells (cubic 2 ×2 ×2 LaBr 3 (Ce) crystals followed with rectangular 2 × 2 × 6 NaI(Tl) crystals) located at 40cm. The measured energy resolution amounted to 3% and 5% at E γ = 661 keV, respectively, for the LaBr 3 (Ce) detectors and PARIS phoswiches. The efficiency at 1.33MeV was measured to be 0.029% for the smallest LaBr 3 (Ce) detectors at closest distance, 0.036% for a PARIS phoswich, and 0.32% for the cluster [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF]. The overall time resolution of the set-up (dominated by the fission chamber) had a Full Width at Half Maximum (FWHM) of ≈ 2 ns. Prompt photons were selected by setting a ± 3 ns wide time window around the γ -ray peak in the time-offlight spectrum of each detector. The experimental threshold was tuned around a few tens of keV, such that it can be set sharp at 100 keV in further analysis. Standard and reaction γ -ray sources, with energies up to 9 MeV, were used for calibration and efficiency determination. We refer to Ref. [20] for further details.

The response function of each detector was obtained from an elaborate simulation of the entire set-up, which was validated by the source data [START_REF] Qi | [END_REF]. The measured γ -ray spectra were unfolded from the corresponding response, and that result can be directly compared to model calculations. The average γ -ray multiplicity M γ and total energy released by photon radiation E γ,tot can also be extracted from the unfolded PFGS as follows: M γ is determined as the integral of the unfolded spectrum, and E γ,tot is obtained from the sum over the product of the spectral yields for each bin in the unfolded spectrum and its energy (viz. first moment of the distribution). Finally, the average energy per photon is derived according to γ = E γ,tot /M γ .

The measurements of fast-neutron induced fission of 238 U and spontaneous fission of 252 Cf were conducted during the same campaign, under the same conditions with the same setup, and analyzed in a similar way [START_REF] Qi | [END_REF].

Experimental results

The mean characteristics of the PFGS for the three reactions discussed in this work are summarized in Table 1, including the average γ -ray multiplicity M γ , total energy released by photons E γ,tot , and average energy per photon γ . The last two columns of Table 1 refer to set-up-dependent parameters. The energy ΔE and time Δt ranges refer to the gates applied to the data in order to define a detected γ -ray as prompt. The results for 239 Pu(n,f) at E n = 1.8 MeV are presented for the first time (with some preliminary data shown in Ref. [20]). Its PFGS is displayed in Fig. 1 separately for the LaBr 3 (Ce) detectors and the PARIS phoswiches. Fastneutron induced fission of 238 U and spontaneous fission of 252 Cf from Refs. [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF][START_REF] Qi | [END_REF] are additionally selected in the discussion of this work to investigate the potential of PFGS for learning about fission. The considered set of measurements is relevant for several reasons. (i) The LICORNE campaign uses quasi-monoenergetic fast neutrons, which permit the population of the primary fragment ( A, Z , E * , L) phasespace in a different way from thermal-neutron-induced fission. Mapping the variable landscape is useful to unravel intricate dependences and correlations. (ii) The beam energy employed corresponds to initial excitation energies in the fissioning system still below neutron threshold, thus avoiding the complexity which multi-chance fission implies at higher bombarding energies. (iii) All three systems are measured and analyzed under identical conditions. The comparison between them is, therefore, robust, independent of systematics errors, which can sometimes complicate the comparison of results collected at different facilities or set-ups. (iv) The prompt fission γ -ray spectrum observable is collected with good efficiency and resolution over the wide dynamical range which fission γ rays can span. (v) Finally, the measurements by Qi et al. [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF][START_REF] Qi | [END_REF][20] contribute to the database required to resolve the problem of heat calculations in reactors, and namely for the n+ 238 U, 239 Pu reactions that are crucial in the context of Generator IV reactor concepts [17].

The mean γ -ray properties extracted from other measurements are also shown in the table. They are consistent with each other. The discrepancy noticed with the DANCE data [24,25] for 252 Cf was ascribed to detection inefficiency in the low-energy region due to absorption effects [26]. Though, we note also that the energy range, time window, Fig. 1 Experimental PFGS for fast-neutron induced fission of 239 Pu for the LaBr 3 (Ce) detectors (full black line) and the PARIS phoswiches (dashed red line). The inset shows the low-energy region. Error bars are shown for the LaBr 3 (Ce) detectors, only, for legibility. They are similar for the PARIS phoswiches and unfolding procedure are different as compared to the other presented measurements. Hence, it is difficult to unambiguously determine the reason for the difference.

The experimental PFGS of n+ 239 Pu, as well as n+ 238 U and 252 Cf(sf) [START_REF] Qi | [END_REF], are overlaid in Fig. 2. Error bars are not shown for legibility reasons; they can be appreciated from e.g. Fig. 5. The upper panel in Fig. 2 shows the entire spectrum measured up to E γ = 6 MeV, and the bottom one restricts to the low-energy region. Structures are clearly visible below E γ ≈ 1 MeV, while a smooth exponential fall-off is observed at higher energy. The structures at low energy are determined by the discrete transitions between low-lying excited states in the last stage of the fission-fragment de-excitation down Fig. 2 Experimental PFGS [START_REF] Qi | [END_REF]20] for spontaneous fission of 252 Cf and fast-neutron induced fission of 238 U and 239 Pu. The upper panel shows the entire measured spectrum, while the lower panel zooms the lower energy range to the yrast line (or to an isomeric state). They do not appear as sharp peaks due to the combined effect of Doppler broadening, intrinsic detector resolution and absence of selectivity on fragment mass. These points will be discussed further below. The exponential decrease in the high-energy region is due to statistical emission which is largely dominated by the giant dipole resonance (GDR) built on excited states. The current data spectrum suffers from limited statistics and does not extend far enough in the E γ range of the GDR peak, but the "low-energy" tail of the latter [27] impacts the highestenergy region accessible to the present experiments.

The comparison of the measured pattern at low E γ shows that, while the intensity of the peaks decreases pretty fast between E γ = 0.15 and 0.80 MeV for n+ 238 U, it remains rather constant over that range for 252 Cf; the behavior is intermediate for n+ 239 Pu. This difference between the three reactions is imputed on the different fragment (A, Z ) populations. Since the heavy fragments are similar [1], namely for the n+ 239 Pu, 238 U reactions, the difference observed in the PFGS may be ascribed to the light fragments. It is interesting to note that a very similar pattern is observed for the PFGS for spontaneous fission of 252 Cf as compared to those of thermal-neutron-induced fission of 235 U and 239 Pu [11].

The comparison of the experimental PFGS in the highenergy region suggests a harder spectrum for n+ 239 Pu. We quantified this difference by performing a fit to the PFGS between E γ = 3 and 6 MeV with an exponentially decreasing function was done: The slope parameter was found to amount to 1.24, 0.97 and 1.20 MeV -2 , for 252 Cf, n+ 239 Pu, and n+ 235 U, respectively; that is, definitively smaller for n+ 239 Pu (the uncertainty on the extracted slopes is below 4%). Again the comparison of 252 Cf and thermal neutroninduced fission of 235 U and 239 Pu suggest a similar trend [11], although less pronounced.

Theoretical modeling

Calculation framework

Modeling fission remains a challenge for nuclear theory [2,28]. While qualitative description can be achieved by fundamental models, quantitative description is missing in most cases. Over the last several years, huge work was invested in the development of phenomenological and (semi-)empirical codes (see Refs. [3][4][5][6][7][8]10,29,30] and therein). These are computationally fast and flexible, as required for efficient implementation in general-purpose transport simulations modeling the interaction of radiation with almost everything (see e.g. Refs. [11,[32][START_REF] Goorley | Initial MCNP6 release overview. MCNP6 version 0.1[END_REF][34]). Although predictive power is a major goal, these codes can also be useful to get insight into the underlying physics [35].

In the present work, calculations were performed with the two semi-empirical codes, FREYA [29] and GEF [10], which generate complete fission events, providing the full kinematic information on the two product fragments, the emitted neutrons and photons. The Monte-Carlo approach is adopted, permitting to naturally preserve correlations. Each code has its own specificities. The features of the codes, and their differences, which are most important for the present concern, are emphasized below.

FREYA is mainly dedicated to the modeling of the fragments de-excitation. It relies on the availability of "external" fragment yields (or reliable estimates) [START_REF]FREYA user manual[END_REF]. On the other hand, the de-excitation of the primary fragments formed at scission is thoroughly calculated. The fragments de-excite first by neutron evaporation. Once this is energetically forbidden, emission of statistical γ -rays starts, until the yrast line (or a long-lived isomeric state) is reached. Noteworthy in our context is the recent implementation in the code of the RIPL3 data base for simulating the end of the decay cascade consisting of characteristic discrete γ -rays. In contrast to FREYA, in GEF the fragment yields are internally computed, based on a powerful semi-empirical modeling. In addition, the competition between neutron evaporation and emission of statistical γ -rays is accounted for. However, the yrast line is not taken from evaluation. Instead, the discrete excited levels characteristic of a nucleus are given by an analytical parameterization. Besides the aforementioned aspects, FREYA and GEF also differ regarding the generation and sharing of excitation energy and angular momentum between the two fragments at scission. The versions of the codes considered in this work are, respectively, the release v2.0.3 for FREYA [29], and GEF2016/V1.2 for GEF [10].

We note that the goal of the present work is not to put FREYA and GEF in competition. Similarly, we did not attempt to adjust parameters to specific reactions. Rather, the aim is to investigate the physics potential behind current experimental data with two different, well-established and representative codes in the field. In addition, FREYA and GEF are freely available, and widely used by the community. Practitioner users can thus evaluate what one shall expect when trying to interpret certain data with these tools. Several comparisons between fragment de-excitation codes like FREYA already exist [11,36,37], including parameter variation studies. Comparisons with GEF, which has its own fragment yield formalism, are scarce [38].

Calculation results

In the calculations, a number of 10 5 events were run for each reaction. Although this work focuses on prompt γ rays, we note that both the used codes give a reasonable description of other fission (fragment and neutron) properties for spontaneous fission of 252 Cf and thermal-induced fission of 235 U and 239 Pu [10,29].

The mean properties of the calculated PFGS are summarized in Table 1, in comparison with the experimental measurements. The γ -ray energy range ΔE and the time window Δt have a critical influence in the comparison between measured and calculated fission γ -ray properties [29,39]. As for the present study, the energy threshold with which the calculations were filtered is identical to the experimental one (100 keV). Regarding time window, the situation is somehow different. The parameter which governs time gating in FREYA is expressed in terms of the longest half-life t max of an excited state so that its decay-out is recorded. It is set equal to the width of the experimental time window Δt, although it does not imply such a sharp gating. In GEF there is no explicit time gating: All transitions are recorded until an isomeric state, as tabulated in JEFF3.1.1, is reached along the decay cascade. According to our simulations [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF] and detailed independent investigations [29,39] on the influence of the set-up-dependent ΔE and Δt parameters, discrepancies of the order of 5-10% can be reached between experiment and predictions for M γ and E γ,tot . Considering the experimental error bars, the complexity of a proper account of energy and time detection limit effects, and the robustness of unfolding procedures [START_REF] Qi | [END_REF], the description of the mean PFGS characteristics by FREYA and GEF is estimated reasonable, and validates their use for the purpose of the present work. Furthermore, the codes have their own limited accuracy, due to the uncertainty of some parameters. According to the literature on FREYA and GEF, we estimate that, for the observables of this work, the calculated uncertainty is 5-10%. We note that best agreement between experiment and calculations in Table 1 is achieved by FREYA for 252 Cf (the default version of the code was tuned on this specific system, see also discussion in Ref. [29]).

The results of the FREYA calculations for the PFGS are presented in Fig. 3. They account for both the Doppler broadening and detector resolution. The GEF results are qualitatively the same. Contrary to the observation drawn from the measurements, the pattern exhibited by the calculated PFGS in the low-energy region is very similar for the three reactions, with the peak intensity steadily decreasing for E γ ∈ [0.15-0.80] MeV, independent of the fissioning system. That is, the singularity noticed in experiment for 252 Cf, with a nearly constant intensity at low energy, is not reproduced. The upper panel of Fig. 3 show that, unsurprisingly, the calculated spectra fall off exponentially above E γ ≈ 2 MeV; but most remarkable is that the calculations describe consistently the difference in hardness of the PFGS for the three systems: The n+ 239 Pu spectrum is unanimously harder. We emphasize that, thanks to the fact that all systems were measured in similar conditions, this difference can be firmly established, and it confirms what could so far only be considered as a prediction by the calculations. A discussion on the origin of the differences in the low-energy structures and high-energy hardness is proposed in Sects. 4.1 and 4.2, respectively.

Discussion

Prompt γ rays constitute a rich source of information in nuclear physics in general. The discrete γ rays emitted below the particle threshold are characteristic of a nucleus and constitute the best observable of its nuclear structure. Along the decay of excited and/or rotating nuclei, γ rays permit the probe of nuclear properties, among which the level-density in the continuum, and angular-momentum-driven effects. In heavy systems, γ -ray emission is in general in competition with neutron evaporation. Neutrons exhaust most of the excitation energy, while γ rays carry off most of the angular Fig. 3 Identical to Fig. 2 but as obtained from the FREYA calculations momentum; both cooling processes are, therefore, necessarily correlated. For the specific case of a nuclear fission reaction, the aforementioned inter-dependences imply that the properties of prompt fission γ rays are a priori sensitive to the energetics of fission (namely the sharing of excitation energy between the two fragments, see e.g. Ref. [40]), to the generation and partition of angular momentum at scission [41], and finally, to the secondary fragment yields and properties [42,43].

Insight into the low-energy structures

As observed above, the calculations do not reproduce the singularity of 252 Cf in the low E γ range. The comparison between the fission-fragment mass distributions for the three systems at low excitation energy [1] permits to highlight the fragment mass region which is intensively produced in 252 Cf fission, and not in the other two systems. Based on this, the deficiency of the calculated PFGS to explain the 252 Cf singularity is tentatively ascribed to the current spectroscopic knowledge of nuclei in the A = 110-120 range which would still not be that good.

The low-energy range of the PFGS exhibits rather broad peaks, rather than sharp lines as produced by the physics. In order to investigate the significance of such a measurement, we propose first to see how these broad peaks are produced, taking FREYA calculations as an example (GEF leads to the same). Since the fragment velocity vector is not available in the measurements by Qi et al. [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF][START_REF] Qi | [END_REF], Doppler effects cannot be corrected for. The corresponding boost is automatically taken into account by the FREYA software, and its influence is illustrated by the red spectrum in Fig. 4, which corresponds to the contribution of Xe isotopes to the low-energy part of the PFGS for the example of fast-neutron induced fission of 238 U. The different peaks are due to the population of various Xe masses, and with different intensities. The physical discrete lines are broadened by the Doppler effect, which amounts to about 3% in this case. The population of numerous Xe isotopes (around 10 with measurable intensity), and their close-lying lines, lead to the development of shoulders for some peaks, as well as the presence of a background. Adding the Sr isotopes, populated as the partners of Xe, gives rise to the blue spectrum. The pattern gets more and more dense, and a natural bunching of the Doppler-broadened lines occurs. Noteworthy also is the substantial increase of the background, and thus the decrease of the peak-to-valley ratio already for a single pair of fragment elements. In the lower panel, the influence of the absence of fragment selectivity is illustrated: The black spectrum is the superposition of the transitions from all fragments (around 300), what increases dramatically the effect of bunching of lines as well as the background. Finally, the detector resolution (around 3% at E γ = 0.662 MeV) is included, leading to the red spectrum where structures are further smeared out. This exercise suggests that the low-energy part of the PFGS as available from the experiments of this work is not sensitive to the post-neutron fragment population in detail. The implications of this limited sensitivity is discussed below.

Since neutrons exhaust most of the excitation energy stored in the primary fragments, they are more direct signatures of E * sharing at scission [3][4][5][6]44]. Emission of γ rays essentially sets in around the neutron separation energy. Hence, the PFGS is expected less sensitive to E * sharing, and various calculations confirm this [45,46]. Nevertheless, due to the strong dependence of neutrons on E * sharing, and the established correlations between neutrons and γ rays (see Ref. [38] and therein), the PFGS can be affected to some extent by the E * sharing mechanism, too. The dependence is indirect, being due to the dependence of the secondary (A, Z ) fragment population on excitation energy partition-Fig. 4 Upper panel: Low-energy part of the PFGS as calculated by FREYA for n+ 238 U restricted to the contributions from Xe fragments (red), and to the contributions from Xe-Sr pairs (blue). Only Doppler effects are accounted for. Lower panel: PFGS including all fragments accounting for Doppler effects (black), as well as intrinsic detector resolution (red) ing. Our study, therefore, shows that the low-energy region of the PFGS from the measurements of Qi et al. [START_REF] Qi | [END_REF]20] is not sensitive to E * sharing at scission for a given system. However, a variant of the experiment [17], supplemented by mass selectivity, clearly establishes the dependence of the low-energy structure pattern on fragment population. That is, when exploited at maximum of its potential, measurements using the same approach and technology can be useful to study the sharing of the excitation energy between the two fragment. Mass selectivity is more critical than resolution in this case.

Although sensitivity to the detailed population for a given system is out of reach, the structures clearly depend on the fissioning system. That is, the experiment may be exploited still to study E * sharing at scission by considering different systems at a time. In Fig. 5, for fast-neutron induced fission of 238 U as an example, the experimental PFGS is compared with FREYA and GEF calculations. The lower panel shows that the positions of the peaks calculated with FREYA match better the experimental ones than GEF does, although there are still differences in terms of intensity. The major difference between FREYA and GEF, and which impacts the low-E γ structures, is the modeling of the discrete excited states. As specified in Sect. 3.1, the latter are taken from the RIPL3 data base for FREYA, while they are based on a fully analytical formalism in GEF, which, in terms of accuracy, can of course, not compete with RIPL3. Therefore, the present study demonstrates that the experiments used here are sensitive to the accuracy in the modeling of discrete excited states. It also confirms that this type of experiments may be exploited to some extent in the context of nuclear structure [17], namely when some mass selectivity and Doppler effects correction are available [47].

Insight into the high-energy region

The high-energy part is less sensitive to uncorrected Doppler effects and intrinsic detector resolution, due to the very low density of discrete lines above 2 MeV. Statistical γ -ray emission (mainly from the GDR) depends on emitter temperature, nuclear level density and photon strength function [48,49]. Except in the vicinity of closed shells, their properties vary in a smooth way with emitter A and Z . For a given fissioning system, a modification of the fragment population within a realistic range is then expected to affect only weakly the high energy tail of the PFGS. We have confirmed this conjecture by comparing the high-energy part of the spectrum obtained from FREYA when using as input two different primary fragment populations, which calculations we mentioned already in Sect. 4.1. Both populations exhibit a very similar exponential fall-off at high E γ . However, while this is true for a given system, it is obviously not, when comparing different fissioning systems, which can be characterized by more dramatic changes in fragment population, and hence temperature, level density, photon strength and GDR properties. In other words, similarly to the comment made for the low-energy side, the comparison of various systems may be exploited to study E * sharing at scission to some extent. This endeavor is out of the scope of this manuscript. A recent work by Chyzh et al. [50] based on Pu fission with different entrance channels may tentatively be interpreted in a similar way.

As seen from the upper panel of Fig. 5 the calculations describe pretty well the n+ 238 U measurement above 2 MeV (the GEF spectrum is slightly too rounded -a feature already noticed in Ref. [10] and which is still un-explained). A similar achievement is observed for the other two systems [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF]. Although the GDR peak of typical fission frag-123 Fig. 5 Comparison between the experimental (red lines) and calculated (blue and black lines for FREYA and GEF, respectively) PFGS [START_REF] Qi | [END_REF] for n+ 238 U. The upper panel shows the full E γ range, while the lower panel restricts to E γ ∈ [0-1] MeV. Shadowed red bands give the range of the experimental error bars ments is located around 15 MeV, Vogt et al. [29] demonstrated the huge impact of the tail of the GDR down to E γ ≈ 3 MeV. In other words, measurements of the type as those by Qi et al. [START_REF] Qi | [END_REF] are presumably sensitive to the properties of the GDR built on excited states, and namely to its width, which dependence on temperature is controversial [51].

As discussed above, an important observation of the measurements is the harder spectrum for fast-neutron induced fission of 239 Pu as compared to spontaneous fission of 252 Cf and fast-neutron induced fission of 238 U. As noted too, calculations consistently describe the dependence of the PFGS hardness on the system, see Fig. 3 (upper panel). According to the good description of the measured exponential fall-off by the calculations, an interpretation for the "hierarchy" in Fig. 6 Average neutron separation energies as a function of secondaryfragment mass number as obtained with FREYA for the three systems considered in this work PFGS hardness is proposed in the following, based on these calculations.

Since γ -ray emission sets efficiently in at the neutronemission threshold, the excitation energy of the fission product at the end of the neutron cascade is essentially given by the neutron separation energy S n [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF]29]. The evolution of the empirical S n value [52] as function of the secondary fragment mass calculated with FREYA (after averaging over Z) is displayed in Fig. 6 for the three reactions studied in this work. A very similar picture is obtained when FREYA is replaced with GEF. Fast-neutron induced fission of 238 U populates on the average more neutron-rich fragments as compared to the other two systems, being therefore characterized by smaller secondary-fragment neutron separation energies. On the average the temperatures after neutron evaporation are thus lower, and the PFGS is expected to be the least hard. The separation energies involved in the 252 Cf and n+ 239 Pu systems are larger. At the same time, the weight of the S1 fission mode, which leads to fragments in the vicinity of 132 Sn is much larger for n+ 239 Pu [10]. The near-to-magic fragments produced more abundantly with n+ 239 Pu are characterized by low level densities, and higher temperatures [44], as compared to the fragments produced in 252 Cf. As a consequence, the PFGS is harder for n+ 239 Pu. The fact that the hardness of the PFGS of fast-neutron induced fission of 238 U is finally similar to the one of 252 Cf (in experiment like in the calculations), see Fig. 3, is explained by the intense S1 mode in 239 U vs. 252 Cf fission, which somehow counterbalances the expectation based on S n alone.

A substantial excess of γ -ray yield between E γ = 4 and 8 MeV was observed several decades ago in spontaneous fission of 252 Cf with the Crystal Ball NaI array, see Refs. [53,54] and therein. Thanks to the availability of mass selection, this so-called "γ bump" was assigned to the emission properties of post-neutron fragments in the vicinity of 132 Sn. Further measurements did not pay much attention to this, due to the experimental difficulty of extending the spectrum to high E γ values with sufficient statistics. The advent of new, efficient scintillators leads to a renewed interest in the γ bump. Very recently, the PFGS extracted by Makii et al. [55] in the commissioning of their new LaBr 3 detectors seem to confirm the occurrence of such an excess of yield also for thermalneutron-induced fission of 235 U. Though, the work shows at the same time that the reliable extraction of the γ bump requires a very careful analysis, since in the inclusive spectrum, i.e. in the absence of mass gating, its signal remains small (see also Fig. 1a, b in Ref. [56]).

Although the experiments of Qi et al. [START_REF] Qi | [END_REF]20] in its present implementation cannot be used to address the origin of the γ bump, due to absence of mass selectivity and low statistics in the corresponding energy region, we propose to discuss the predictions of the calculations in this context. The upper panel of Fig. 7 shows the mass distribution of the postneutron fragments calculated with FREYA contributing to different slices of the PFGS, between E γ = 3 and 6 MeV, for fast-neutron induced fission of 238 U. It is predicted that the contribution of heavy fragments with masses around A = 130-134 clearly dominates from E γ = 4 MeV on. That is, the PFGS for near-to-closed-shell nuclei is harder. A similar result is predicted by FREYA for the other two systems. Calculations by the GEF code, reported in Fig. 122 of Ref. [10], show the same pattern. While the excess of yield measured at Crystal Ball is supported by the calculations to be due to fragments close to 132 Sn, contrary to experimental findings, FREYA and GEF do not exhibit a bump-shaped excess; the calculated spectra are simply harder. One cannot exclude that the calculations miss some specific (possibly exotic) γ strength for the involved nuclei. On the other hand, calculations with the FIFRELIN code [3] predicts a PFGS whose shape resembles more a bump (see Fig. 5.14 in Ref. [START_REF] Regnier | Contribution a l'etude des γ prompts de fission[END_REF]). As compared to FREYA and GEF, the FIFRELIN code models neutron and γ -ray emission within the Hauser-Feshbach theory, and the implementation of RIPL3 discrete levels is slightly different from FREYA. Finding the very origin of the γ bump is therefore expected to benefit from calculations of this kind as for guidance.

Recent measurements [START_REF] Chyzh | [END_REF] at the LANSCE facility with the DANCE array permitted to compare the PFGS in slowneutron (from about thermal to 100 keV) induced fission of 235 U, 239 Pu, and 241 Pu, as well as the 252 Cf standard. The occurrence of various "bumps" from E γ ≈ 0.5 MeV on, and their dependence on fissioning system above E γ ≈ 5 MeV, was revealed. It was suggested that the difference in PFGS between the available systems is to be linked to different level-density and dipole resonance properties of the Fig. 7 Post-neutron fragment mass as obtained with FREYA for n+ 238 U and populating specific region of the PFGS, i.e. with E γ ∈ [3.5-4] (red), [4-4.5] (black), [4.5-5] (blue), [5-5.5] (green), [5.5-6] (violet) MeV. The distributions are normalized to unity for evidencing the relative contribution of the light and heavy fragments depending on the E γ slice corresponding fragment population. Unfortunately, the limited resolution of the BaF 2 scintillators prevented the aforementioned interpretation from being further probed, and presumably supported, by differences in the low-energy structure pattern. In addition, no realistic fission-fragment deexcitation calculation was done to deepen the understanding of the observed differences. Like in the present campaign, no mass selection was available. Nevertheless, the outcome clearly demonstrates the significance in pushing such kind of measurements further.

It has finally to be mentioned that the discussion of the γ bump(s) is probably to be linked with the observation made above about the hardness of the PFGS depending on the reaction system. Clearly, dedicated experiments, with efficient set-ups, some level of mass identification, and involving different fissioning systems, are highly desirable to reach a consistent picture. This seems to be possible in reasonably close future [17,55], with straightforward extension [17] of existing set-ups.

Angular momentum influence

Since γ -ray emission is by far the main mechanism for exhausting angular momentum, it is the observable of choice to trace back the angular momentum generated at scission. The latter, and even more important, the mechanism which is responsible for creating it and partitioning it between the fragments, remains until today a longstanding controversial question (see section III.I in Ref. [10]. Here, we propose a discussion on the possible evidence of sensitivity to angular momentum.

When measuring γ rays, various methods can be used to extract information on angular momentum, among which photon angular distributions and isomeric ratios. Though, the most direct, model-independent way is certainly to identify the excited states populated in the fragments in order to determine the maximum spin value reached. Since the spin straightforwardly impacts the number of γ rays emitted along the descent of the yrast line, M γ is a good signature for estimating the maximum angular momentum reached, too. It is thus the low-energy region which is the most useful part of the PFGS, since it concentrates most of M γ .

Our calculations with GEF predict that the spin acquired by the fragment at scission increase from about 2-7 h over the fragment mass range A = 80-160, given at first order by the moment of inertia, and thus also deformation. The slope of the increase slightly depends on the fissioning system. The calculations by FREYA give a similar result, with, though, a somehow smaller average value, around 3-4h and a weaker system-dependence. Inspection of Table 1 led us to conclude that, within the current experimental status and uncertainties, as well as the accuracy of (still other) model assumptions, FREYA and GEF give on average a good description of M γ . That is, overall the predicted angular momentum looks reasonable, and current M γ data cannot pretend being sensitive to the difference of a couple of h between the two codes. Regarding the PFGS observable, this difference reflects into different intensities for the characteristic γ -ray transitions. Within the experimental limitations in measuring the lowenergy portion of the PFGS discussed above, and the influence of model assumptions, any more precise conclusion regarding the value of L would be highly speculative. Further investigation shows that the major difference between the FREYA and GEF results is in the dependence of M γ on fragment mass [START_REF] Qi | Measurements of prompt γ rays emitted in fission of 238 U and 239 Pu induced by fast neutrons from the LICORNE neutron source[END_REF]. The difference is strongly related to the treatment of the emission of statistical γ rays, and namely to the amount of spin carried away by the latter. Unfortunately, experimental information about the dependence of M γ on mass is very scarce, highly model-dependent and still very controversial (see section IX.F. in Ref. [10]).

Regarding the possible evidence of angular momentum effects, we are therefore forced to conclude that the present implementation of the experimental approach is not sensitive to angular momentum within a couple to several h. The recent study by Rose et al. [59] suggests that, for an inclusive measurement like here to be sensitive to angular momentum, the L's involved need to span over 3-4 h. Model calculations by Litaize et al. [46] suggest that the high-energy part of the PFGS can be sensitive to L at the level of 5 h or so. The recent calculations by Chyzh et al. [50] suggest higher sensitivity. Experimental efforts into the direction of reliable L extraction are definitively needed to settle this point.

Again, we mention that a step beyond the present limitation can be made with a little variant of the set-up [17], giving access to fragment mass within a few units. In the 1960's, Bowman et al. [47] observed that, already with NaI scintillators, fragment spins for most intense channels may be inferred. High-resolution spectroscopy by means of Ge detectors (e.g. Refs. [42,43]) is, of course, best suited to pin down the maximum L populated. Though, lower efficiency in that case hampers the determination of M γ , which is an important quantity, too. Hence, scintillationand Ge-detector based experiments are fully complementary approaches.

Conclusions and perspectives

Prompt γ -ray spectra emitted in fast-neutron induced fission of 239 Pu are presented. A detailed analysis of the low and high energy portions of the spectra, together with fast-neutron induced fission of 238 U and spontaneous fission of 252 Cf, is performed. The consistency of the data set, collected under similar conditions, permits a robust comparison between the three fissioning systems. The latter is proposed to be guided by calculations using the FREYA and GEF semi-empirical models. Differences in the low-E γ structures between the various systems point to the possibility of evidencing the influence of fragment population, which is intimately correlated with neutron evaporation. Similarly, comparison in the high-energy region of the E γ spectra is informative about the fragment properties.

According to the renewal and growing interest of γ -ray emission in fission, the development of more and more elaborate devices and analysis tools, on the experimental side, and the wide popularity of codes which are used for various purposes, on the theoretical side, the present investigation makes a point about the robustness and possibility to address certain physics questions with certain data and models. It sheds light on the influence of the limitations of current methods, as well as it points the potential of the latter when supplemented with the little required development.

To exploit and push further the exploitation to nuclear structure studies and the investigation of energy sharing and angular momentum generation in fission needs mass selectivity. It requires the implementation of position-sens-itive ionization chambers, conserving the 4π efficiency, in conjunction with the high-efficiency PARIS array, both available at the high-intensity fast-neutron beam ALTO/LICORNE. Also the wider mapping of PFGS properties in the actinide region should be performed. Such data will permit to put more stringent constraints on fission models and understanding. Altogether will also constitute valuable input for nuclear applications as set out by the OECD/NEA. 123

Table 1

 1 Characteristics of the PFGS. Experimental results are shown together with the FREYA and GEF calculations. See the text

			M γ (/fission)	E γ,tot (MeV)	γ (MeV)	Ref.	Δt (ns)	ΔE (MeV)
	252 Cf(sf)	Expt.	8.35 ± 0.20	6.64 ± 0.21	0.80 ± 0.02	[19]	5	0.1-6.0
		Expt.	8.30 ± 0.09	6.64 ± 0.10	0.80 ± 0.01	[23]	5	0.1-6.0
		Expt.	8.14 ± 0.40	7.65 ± 0.55	0.94 ± 0.05	[24]	10	0.15-10
		Expt.	8.75	8.52	-	[25]	8	Not specified
		GEF	7.17	6.52	0.91	-	-	0.1-6.0
		FREYA	8.31	7.10	0.85	-	1.5	0.1-6.0
	n (E n =1.9MeV)+ 238 U	Expt.	6.54 ± 0.19	5.25 ± 0.20	0.80 ± 0.04	[19]	5	0.1-6.0
		GEF	6.24	5.84	0.94	-	-	0.1-6.0
		FREYA	7.23	6.18	0.85	-	1.5	0.1-6.0
	n (E n =1.8MeV)+ 239 Pu	Expt.	7.23 ± 0.37	6.71 ± 0.37	0.91 ± 0.04	-	6	0.1-7.0
		GEF	6.72	6.76	1.00	-	-	0.1-7.0
		FREYA	7.38	7.06	0.96	-	1.5	0.1-7.0

Acknowledgements We thank the staff at the ALTO facility for the production of high intensity beams, and smooth running, as well as we acknowledge support from the PARIS collaboration all along the campaign. We thank J. Randrup and K.-H. Schmidt for enlighting discussions about FREYA and GEF, respectively. We are also very thankful to K.-H. Schmidt for critical reading of the manuscript. We acknowledge funding from the ENSAR2 and CHANDA (Project 605203) programmes of the European Commission. This work was also supported by ELI-NP -Phase II, co-financed by the European Regional Development Fund through programme COP ID 1334.

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors' comment: Data are available from the authors upon request.]