1. Model calculations of prompt fission neutron spectra mainly of 235 U(n,f) and also of 232 Th(n,f), 238 U(n,f) Anabella TUDORA University of Bucharest Faculty of Physics

2. I. 235 U(n,f)  Point by Point (PbP) calculation using a new method of TXE partition between fully accelerated fission fragments  PFNS (PbP model and most probable fragmentation approach) III.2 PFNS of 239 Pu (n,f) and 233 U (n,f) (reported in 2010) compared with experimental data provided by IAEA-CRP (January 2011) III.3 238 U(n,f) PFNS in the frame of the PbP model and most probable fragmentation approach II. 232 Th(n,f) (New)  PbP model calculations of prompt neutron and gamma-ray quantities  PFNS (PbP and most probable fragmentation) A.Tudora, IAEA-RC meeting, 13-16.12.2011 III.1 Sensibility of PFNS to,, and σ c (ε) (optical model potentials) exemplified on 235 U(n th,f) and 235 U(n 0.5,f) Remaining time:

3. During the time we have used 2 methods of the TXE partition between complementary fully-accelerated FF: 1. A possible reference method of TXE partition because it is based exclusively on the systematic behaviour of experimental ν(A) data. It is not depending on what is going on during the scission. Exp ν H /(ν L +ν H ) data as a function of A H exhibit a systematic behaviour that was parameterized. available in low energy fission (almost all prompt neutrons are emitted at full acceleration) Systems studied: 233,235 U(n th,f), 239 Pu(n th,f), 237 Np(n,f) En=0.8, 5.5 MeV 252 Cf(SF), 248 Cm(SF) E*(A), a(A), T(A) are calculated  RT(A H ) general parameterization for (n,f) and local param for SF. Obs.: the general parameterization of RT(AH) was used in the PbP calculation for 232 Th(n,f), too. C.Manailescu, A.Tudora, F.-J.Hambsch, C.Morariu, S.Oberstedt Nucl.Phys.A 867 (2011) 12-40

4. A new method of TXE partition based on the calculation of the additional deformation energy at scission and the partition of the total available excitation energy at scission E* sc between complementary nascent fragments assuming statistical equilibrium at scission Basic features of this method easy calculated for each pair Energy conservation at scission At full acceleration So the “asymptotic” excit. energy of a fragment, i.e. after dissipation of the additional deform. energy into excit. energy (intrinsic/single-particle and collect.) but before de-excitation is obtained by and

5. Calculation in two steps 1) calc. of fragment additional deformation energies at scission 2) partition of the total available excitation energy at scission obtained by STEP 1: According to Terrel [ Review Paper Symp.Phys. 1965 vol II ] and Ruben et al. [ Z.Phys. A 338 (`1991) 67 ] the 2 fragments are assumed to be of roughly spheroidal shape, just touching at the scission point, with their long axis along the direction of separation. The deformation energy of each fragment is assumed to be quadratic in the change in radius (from the radius or major semi-axis value at scission to the radius at full acceleration). In other words E def L,H must be understood as an additional deformation at scission that will be relaxed into excitation at full acceleration. Hence, the well separated fully accelerated fragments are less deformed compared to the nascent fragment at scission. between the 2 nascent fragments A.Tudora, IAEA-RC meeting, 13-16.12.2011

7. STEP 2: Partition of available excitation energy at scission assuming statistical equilibrium at scission The magnitude of TXE is ~ 25 - 50 MeV The additional deform. energy relative to the deform. energy at full acceleration does not exceed 10 MeV, so the available excit. energy at scission remains sufficiently high so that the level density of fragments can be described by Fermi-Gas type functions (allowing to express E*=a τ 2 ). Consequently E* sc can be partitioned according to: The generalized super-fluid model (Ignatiuk) can be used because the ratios of level density parameters of complementary fragments provided by the super-fluid model are practically the same as the ratios of effective level density parameters. a sc L,H are effective lev.dens.param. accounting for collective and intrinsic excitations at scission A.Tudora, IAEA-RC meeting, 13-16.12.2011

9. The FG description of lev.dens. at available excit. energies at scission is not in contradiction with other methods of intrinsic energy partition that are based on the lev. dens. described by the constant T function. Because the cumulative numbers of levels given by FG and CT are practically the same at E* of interest

10. Not only the cumulative numbers but also the total level densities ρ(E*) exhibit the same behaviour: CT and FG are practically equal in the E* range of about 2-3 MeV above the matching energy value. A.Tudora, GAMMA-1, Novi Sad Nov.2011

11. First validation of this method: comparison of E*(A) calculated with this method with the indirect “experimental” E*(A) obtained from experimental ν(A) (by partitioning TXE in the ratio ν L /ν H obtained from experimental ν(A) data) Studied systems: 233,235 U(n th,f), 239 Pu(n th,f), 237 Np(n,f) at En=0.8 MeV and 5.5 MeV and 252 Cf(SF) A.Tudora, IAEA-RC meeting, 13-16.12.2011

15. Second validation: Prompt neutron emission quantities as a function of fragment (obtained by using this TXE partition method) compared with experimental data: A.Tudora, IAEA-RC meeting, 13-16.12.2011

17. Calculated ν(A) confirm the interesting experimental behaviour of the prompt multiplicity increase with En for heavy fragments only

18. Fig.14 from A.Tudora Ann.Nucl.Energy 33 (2006) 1030 PREDICTION: 5 years ago the behaviour of ν(A) with the increase of E was reported.

19. Applying the two TXE partition methods, also the prompt γ-ray energy as a function of fragment (provided by the PbP model concomitantly with prompt neutron quantities) describes very well the unique experim. data: A.Tudora, GAMMA-1, Novi Sad Nov.2011

20. Discussion in connection with other TXE partition methods Present results compared with theoretical results ob. within the 2 center Wood-Saxon shell model (M.Mirea, Phys.Rev.C 83 (2011) 054608) reporting for a pair with A H =132 E* HF ~ 5 MeV and E* LF ~ 10 MeV. Our results are in good agreement with these ones, i.e. for a pair with A H =132 the ratio E sc L /E sc H =1.95 for 235 U(n th,f). The present method is in quantitative terms almost equivalent to the method of O.Litaize, O.Serot Phys.Rev.C 82 (2010) 054616 also using statistical equilib. at scission, FG description of lev. dens. and superfluid model. They consider that at full accel. after relaxation of the deformation energy TXE is Erot+Eintr. Erot is calculated and Eintr=TXE-Erot is partitioned. Here Edef is calculated and Esc=TXE-Edef is partitioned. The method Litaize-Serot needs adjustments of the momentum of inertia to describe the experimental ν(A) of 252 Cf(SF). Our method does not need any adjustment or experimental data. We use only data provided by recommended libraries from RIPL: for instance shell corr. (Moller, Nix, Myers, Swiatecki), HFB-14, FRDM, Amédée and so on. Also if experim.TKE(A) are not available then approaches can be used. A.Tudora, IAEA-RC meeting, 13-16.12.2011

21. 1. The TXE partition based on the systematic behaviour of experimental ν H /ν pair (A H ) has the advantage to be not dependent on what is is going on during the scission. For this reason it can be taken as a possible reference method. The parameteriz. of RT(A H ) for (n,f) at moderate En allows to predict prompt neutron emission data and γ-ray energies for fissioning systems that are not far from the studied ones. 2.The method of TXE partition based on the calculation of additional deformation energies of nascent fragments and the partition of the available excitation energy at scission assuming the statistical equilibrium of nascent fragms. is more predictable than the first method because it does not need any experimental data and adjustments of parameters. Obviously the exp.ν(A) is better described when the reference meth. based on the ν H /ν pair parameterization is used but the present one is more predictable. A.Tudora, GAMMA-1, Novi Sad Nov.2011

22. I.2 PFNS of 235 U(n,f) compared with experimental data  at En=th provided by IAEA-CRP in January 2011  at other En taken from EXFOR Calculation with  PbP model using  experimental Y(A,TKE) of Straede (IRMM) measured from thermal up to 5.5 MeV with a step of 0.5 MeV and also  recent preliminary Y(A,TKE) measured at IRMM at En=th  Most probable fragmentation approach using:  average parameters obtained from the PbP treatment for the main fissioning nucleus 236 U and for 3-nd compound nucleus 234 U and values provided by the systematic for other fission chances  fission c.s. ratios RF from evaluations (for instance BRC) A.Tudora, IAEA-RC meeting, 13-16.12.2011

23. As usually in the PbP treatment the FF range was chosen as following: the entire mass range covered by the experimental Y(A,TKE) distrib. with a step of 1 mass unit. For each mass number 2 fragments are chosen with the charge numbers Z taken as the nearest integers above and below the most probable charge Zp (determined from the “unchanged charge distribution” UCD corrected with a the experim. charge polarization ΔZ (given in the book edited by C.Wagemans, Fig.85, p.397, A.C.Wahl) Details of the PbP model were the subject of other presentations and published papers. Here we mention only that a triangular form of P(T) is used. For all FF involved the CN cross-sections of the inverse process of evaporation from FF are obtained from optical model calc. (SCAT2) with optical potential parameterizations appropriate for nuclei that are FF (B-G, K-D, W-H etc.). The level density parameters of fully accelerated FF are provided by the generalized super-fluid model of Ignatiuk, the calc. being performed at the excitation energy values obtained from the present TXE partition method. As previously mentioned total average prompt neutron and γ-ray quantities practically are not sensitive to the TXE partition

24. A.Tudora, IAEA-RC meeting, 13-16.12.2011

35. The present PbP model and parameters used for PFNS calculation, meaning exp. Y(A,TKE), optical model parameterization for σ c (ε), TXE partition, P(T) and so on, are also validated by the very good agreement with experimental data of other total average prompt fission quantities, for instance: (En) P(ν) A.Tudora, IAEA-RC meeting, 13-16.12.2011

36. A.Tudora, B.Morillon, F.-J.Hambsch, G.Vladuca, S.Oberstedt, Nucl.Phys.A 756 (2005) 176-191

37. A.Tudora, GAMMA-1, Novi Sad Nov.2011

38. A.Tudora, F.-J.Hambsch, Ann.Nucl.Energy 37 (2010) 771-777

39. A.Tudora, B.Morillon, F.-J.Hambsch, G.Vladuca, S.Oberstedt, Nucl.Phys.A 756 (2005) 176-191

40. A.Tudora, IAEA-RC meeting, 13-16.12.2011

41. The behaviour of spread and scarce experimental data at the spectrum queue, measured at En = 14 –15 MeV (for a few nuclei ( 235 U, 238 U, 232 Th) shows a spectrum increase at around 7-8 MeV emitted neutron energies (where the pre-equilibrium pick is present). The very good description of this experimental behaviour in the case of 235 U(n,f) at 14.7 MeV when the (n,xn) spectra provided by Gnash are used, proves that (n,xn) spectra obtained from Empire, Talys, Gnash calculations (from which the contribution of neutrons leading to excitation energies of the residual nucleus less than the fission barrier height were subtracted) seem to be more appropriated to describe neutrons evaporated prior to the scission than the Weisskopf-Ewing spectra. The consistency of a PFNS evaluation is increased if not only RF but also the (n,xn) spectra are provided by the respective evaluation of neutron induced cross-section.

42. II. PbP model and most probable fragmentation approach applied on 232 Th(n,f) For the first time PbP calculation for 232 Th(n,f) are done. using the experimental Y(A,TKE) distributions measured at 6 incident neutron energies (from 1.6 up to 5.8 MeV) available in the EXFOR library A.Tudora, IAEA-RC meeting, 13-16.12.2011

44. C.Manailescu, A.Tudora, F.-J.Hambsch, C.Morariu, S.Oberstedt Nucl.Phys.A 867 (2011) 12-40 232 Th(n,f) PbP calculations: FF range: A range covered by experim. Y(A,TKE) and 2Z/A Triangular form of P(T) CN cross-sections of the inverse process of neutron evaporation from FF, provided by SCAT2 with the optical model potential of Becchetti-Greenless Level density parameters calculated with the generalized super fluid model at the excitation energies of FF resulted from the TXE partition method recently reported (meaning the general parameterization RT(A H ) for (n,f) and moderate En) Prompt neutron quantities and prompt γ-ray energies are obtained in good agreement with all existing experimental data A.Tudora, IAEA-RC meeting, 13-16.12.2011

45. A.Tudora, GAMMA-1, Novi Sad Nov.2011

47. A.Tudora, IAEA-RC meeting, 13-16.12.2011

49. Most prob.fragmentation approach  average values of model parameters obtained from the PbP treatment

50. A.Tudora, IAEA-RC meeting, 13-16.12.2011

52. Most prob. fragm. approach at higher En where more fission chances are involved  RF are needed.

53. A.Tudora, IAEA-RC meeting, 13-16.12.2011 Examples of PFNS calculations:

54. A.Tudora, IAEA-RC meeting, 13-16.12.2011

55. A few conclusions focusing PFNS  PbP model results describe well PFNS experimental data of 235 U(n,f), 239 Pu(n,f), 233 U(n,f), 238 U(n,f) and 232 Th(n,f)  Average values of model parameters obtained from PbP treatm. together with RF (from cross-section evaluations) entering the most probab. fragm. approach lead to PFNS in good agreement with experimental data  At high En (14-15 MeV) the agreement with PFNS exp. data at the spectrum queue is improved when for neutron evaporation prior to the scission the (n,xn) spectra provided by GNASH or EMPIRE, TALYS are used instead of Weisskopf-Ewing spectra.  All prompt neutron quantities and prompt gamma-ray energies obtained concomitantly with PFNS are in good agreement with all existing experimental data (consistency). Without adjustments of parameters, assuring prediction.

56. (TKE) PbP calc. done 2007 in good agreement with exp.data measured later in 2010 by Sh.Zeynalov. So, PbP can predict these kind of data !

59. III.1 Sensibility of PFNS to model parameters and σ c (ε) (optical model potentials) exemplified here for 235 U(n th,f) and 235 U(n 0.5,f) A.Tudora, IAEA-RC meeting, 13-16.12.2011

60. σ c (ε) optical mod. parameteriz. or simplified formulae lead to a pronounced change of PFNS shape  sometimes in disagreement with experimental shape A.Tudora, IAEA-RC meeting, 13-16.12.2011

63. 40% increase / decrease of  maximum 22% increase / 19% decrease at the PFNS queue (20 MeV) A.Tudora, IAEA-RC meeting, 13-16.12.2011

64. 40% increase / decrease of  maximum 16% decrease / 18% increase at the PFNS queue (20 MeV) A.Tudora, IAEA-RC meeting, 13-16.12.2011

65. 50% increase / decrease of =A CN /  maximum 2-3% decrease/increase at the PFNS queue (20 MeV) A.Tudora, IAEA-RC meeting, 13-16.12.2011

66. The variation of average parameter values practically does not change the PFNS shape, only the magnitude A.Tudora, IAEA-RC meeting, 13-16.12.2011

67. PFNS sensitivity to parameters: In the case of “classical” LA model (1-st fission chance) - σ c (ε) (different OM parameterizations, Iwamoto formula or constant σ c )  major change of PFNS shape -,,  influence only the spectrum magnitude (especially at the queue)  very low sensitivity to Multiple fission chances: -RF (fission probability of each compound nucleus) -(n,xn) spectra of n evaporated prior to the scission New form of P(T)  more pronounced PFNS increase at low E and also a slight increase at the queue Anisotropy (b param.)  increase of PFNS more visible at low E Consideration of scission neutrons (with an amount of about 1.1% according to the literature)  PFNS increase at low E, improving the agreement with existing experimental data

68. III.2 PFNS of 239 Pu(n,f) and 233 U(n,f) reported in the progress-report IAEA-CRP 2010 compared with experimental data provided by IAEA-CRP (in January 2011) A.Tudora, IAEA-RC meeting, 13-16.12.2011 Experimental data provided by IAEA (2011) are well described by the model calculations reported in 2010

69. A.Tudora, IAEA-RC meeting, 13-16.12.2011

72. III.3 238 U(n,f) PFNS in the frame of the PbP model and most probable fragmentation approach  First PbP treatment made in 2001 (the aim being multi-modal calculations) using experimental Y(A,TKE) measured at IRMM G.Vladuca, A.Tudora Ann.Nucl.Enegy 28 (2001) 2 papers, 1653, 1643 F.-J.Hambsch, G.Vladuca, A.Tudora, S.Oberstedt, Nucl.Phys.A 709 (2002) 85  Most probable fragmentation – calc. up to En = 80 MeV (2003) this being the first validation of the extended model that takes into account the fission of secondary nucleus chains and paths formed by charge particle emission (at high En, above 20 MeV) A.Tudora, G.Vladuca, B.Morillon, Nucl.Phys.A 740 (2004) 33-58 PbP calculations re-taken in 2008 using new experimental Y(A,TKE) data measured at IRMM with a fine energy grid below En = 2 MeV A.Tudora, IAEA-RC meeting, 13-16.12.2011

73. A.Tudora, IRMM 2008 New PbP calculations below 1.3 MeV confirmed the model prediction (2003)

74. A.Tudora, IRMM 2008

75. Present calc. with σ c (ε) of K-D (middle) and B-G (bottom) in comparison with ENDF/B-VII (upper part) A.Tudora, IAEA-RC meeting, 13-16.12.2011

78. RF of 1-st and 2-nd chance provided by different evaluations are different at En = 5, 6, 7 MeV

79. A.Tudora, IAEA-RC meeting, 13-16.12.2011