IAEA Research Contract No Prompt fission neutron spectrum calculations in the frame of extended Los Alamos and Point by Point models First year Application on 233,232 U(n,f) and 239 Pu(n,f) Preliminary results Professor Dr. Anabella TUDORA Bucharest University, Faculty of Physics Bucharest-Magurele, POB MG-11, R-76900, Romania IAEA-NDS, April 2010

I. Basic features of prompt neutron emission models used II. 239 Pu(n,f), 233 U(n,f), 232 U(n,f) preliminary results 1. Point by Point model calculation of prompt neutron quantities: total average prompt neutron multiplicity and spectrum, ν(A,TKE), ν(A), P(ν), (A), (TKE) and so on - discussion about FF experimental distributions Y(A,TKE) - 2 methods of TXE partition between the 2 fragments forming a pair - different optical model parameterizations to calculate the compound nucleus cross-section of the inverse process σ c (ε) of each fragment - average model parameter values obtained from PbP treatment 2. Most probable fragmentation approach: prompt neutron multiplicity and spectrum calculations 3. Discussion of different fission cross-section evaluations that can be used (as fission c.s. ratios) to calculate PFNM and PFNS at incident energies where multiple fission chances are involved Content of the presentation

Basic features of models based on neutron evaporation from fully-accelerated fission fragments (Los Alamos type models) SCM, one fragment SCM, one fragmentation, “most probable fragmentation” approach. :

LS, one fragment Obs.:Most prob.fragmentation around A H =140 where ν H = ν L, fact observed for all fissioning systems with experimental sawtooth data. Madland & Nix assumption (Nucl.Sci.Eng.81(1982)213) is correct. CN cross-section of the inverse process: DI mechanism, SCAT2 code with optical model parameterizations appropriate for FF nuclei region: Becchetti-Greenless, Wilmore-Hodgson, Koning-Delaroche, as well as the simplified σ c form proposed by Iwamoto. Total spectrum

New form of FF residual nuclear temperature distribution (Vladuca and Tudora, Ann.Nucl.Energy 32 (2005) ) With conditions: - continuity in T=α - P(T=β)=0 - normalization on 1 - =2Tm/3 parameterization in the computer code:

Obviously for s=1 P(T) of LA Madland & Nix is re-obtained Anisotropy effect: the most important emission of prompt n. is from fully-accelerated FF but n. evaporation during fragment acceleration is also possible, leading to a non-isotropic spectrum in CMS. Another source of non-isotropic neutrons can be the emission at the scission moment (scission-neutrons). According to Terrel the anisotropy of neutron emission if present is symmetrical about 90 o and the SCM spectrum could be described by: b = anisotropy parameter

With the new P(T) and anisotropy taken into account, the prompt neutron spectrum in LS is :

In the case where only one fissioning nucleus is involved: SF and neutron induced fission in En range of the first chance a)“Most probable fragmentation approach” with average values of model parameters (,,,, =Ac/ ) b) “Multi-modal” fission concept: total PFNM and PFNS calculated as superposition of the multiplicity and spectrum of each mode weighted with the modal branching ratios. Average model parameters are determined for each mode. c) Point by Point (PbP) model: the entire FF range covered by the Y(A,TKE) distribution is taken into account. Total PFNM and PFNS are calculated as superposition of the multiplicity and spectrum of each pair weighted with the charge and mass distributions of FF. The PbP treatment is the most accurate because it takes into account the full range of possible fragmentations while the other two approaches consider only one ore few fragmentations (subsets) with average model parameters

When more fission chances are involved: only “most prob. fragm”. approach is used because it is impossible to distinguish Y(A,TKE) of each chance and more, the secondary CN are formed at many excitation energies  too large amount of calculations. Fissioning nuclei of the main chain (formed by neutron evaporation from the precursor) – LA classical:

Evaporation spectrum of neutrons emitted prior to the scission:  Weisskopf-Ewing spectrum as in the classical LA model  evaporation spectrum obtained from (n,xn) spectra provided by GNASH-FKK (or other codes like Talys, Empire), from which the contribution of neutrons leading to excitation energies of the residual nucleus less than the fission-barrier height were substracted. ( Tudora et al., Nucl.Phys.A 756 (2005) 176 ) Most probab. fragm. at high En – the fission of secondary CN chains formed by charged particle emission is taken into account as following: (Tudora et al., Nucl.Phys.A 740 (2004) 33-58) 2) Protons way (fissioning nuclei formed by p. emission from CN of the main ch. 3) Neutrons via protons way (fiss.nuclei formed by n evap. from the nuclei formed by p. emission 4) Deuterons way (fiss. nuclei formed by d. emission from the nuclei of the main chain 5) Alpha way (fiss. nuclei formed by alpha emission form the nuclei of the main chain 6) Neutrons via alpha way (fiss. nuclei formed by n. evaporation from the nuclei formed by alpha emission

Secondary nucleus chains and paths (ways) – Excitation energies, recursive formulae: Paths: k=2 (p) and k=5 (α) c=chain II (formed by p, nvp, d) and III (α and nv α) Paths: k=4 (d) S k p or α separation energy from “i” precursor of main ch. Paths: k=3 (nvp) and k=6 (nvα)

Total and partial fission cross-section ratios production cross sections of the j-th secondary nucleus by proton (σ 2 j ), neutron (σ 3 j ) and deuteron (σ 4 j ) emission and respectively by alpha and neutron via alpha emission Prompt neutron multiplicity: k=1(n), 3(nvp) and 6(nvα) i from n=1 for n, n=2 for nvp and nvα k=2(p), 4(d) and 5(α) i from n=1 for (p) and n=2 for (d)

Total prompt neutron spectrum for k=1(n), 3(nvp) and 6(nvα) Total prompt neutron spectrum for k=2(p), 4(d) and 5(α) the individual PFNS of the i-th fissioning nucleus of the k way the evaporation spectrum of neutron emitted prior to the scission for secondary nucleus ways only Weisskopf-Ewing Details of the model in: A.Tudora, G.Vladuca, B.Morillon, Nucl.Phys.A 740 (2004) 33-58

Computer codes: 1. SPECTRUM first version (2000) ( Vladuca and Tudora, Computer Phys. Communic.125 (2000) ) Program Library of CPC id. ADLH (2000) - Most prob. fragm, σ c =variab, multiple fission chances, main CN chain - Average model parameters dependence on En (or E*) made for SF and neutron or proton induced fission (one incident energy) 2. SPECTRUM second version (2002) - new P(T) form, anisotropy, possibility to use evaporation spectra of neutrons emitted prior to the scission provided by GNASH-FKK or other nuclear reaction codes (like Talys, Empire) For SF and neutron or proton induced fission (multiple incident energies) 3. SPECTRUM extended version (2004) Including the extended model with fission of secondary CN chains and ways (paths) formed by charged particle emission (high En) All versions allow also the options: σ c =const and σ c =the simplified form of Iwamoto

4. SPECTRUM with multiple fragmentations (2002) Including 2 options: A. Multi-modal fission approach B. Point by Point approach Dimensioned for 300 pairs (meaning 600 fragments) Auxiliary input files for all versions: σ c provided by SCAT-2 code with different optical model parameterizations appropriated for FF nuclei Fission c.s. ratios RF taken from evaluations (endf) or from cross-section calculations (ECIS + STATIS + GNASH-FKK) For the version with multiple fragmentations: Model parameters of fragmentations provided by the codes:  MMPAR: for multi-modal fission approach  PAIRPAR: for PbP approach

POINT BY POINT model FF pair range: all mass pairs {A L, A H } covered by Y(A, TKE) (with the step of 1 mass unit) are taken into account. For each mass pair 2Z/A, 4Z/A, 6Z/A… are taken with the charge number Z as the nearest integer values above and below the most probable charge Zp (UCD with charge polarization ΔZ). Usually 2Z/A are taken because P(Z) is a narrow distribution. For each FF pair “i” (meaning LF i, HF i ) quantities as: number of prompt neutrons, prompt neutron spectrum, average prompt neutron energy in CMS and so on are calculated. PbP provides all multi-parametric data (quantities referring to each FF) these quantities do not depend on FF distributions Y(A, Z, TKE) And can be compared with experimental data. Such quantities are: the multi-parametric matrix ν(A,TKE), ν pair (A), sawtooth ν(A), ε(A), Eγ(A), TXE(A) and so on.

PbP is a powerful model. The TXE partition between LF and HF forming a pair is almost avoided because the model is working under the concept of FF pair. The only one limitation is the need of Y(A,TKE) PbP provides all total average quantities (depending on FF distrib.) that can be compared with existing experimental data too. Such as, N(E), (TKE), (TKE), P(ν) etc. Special mentions: P(ν) very sensitive quantity - the PbP model is (to our knowledge) the only able to provide P(ν) results in very good agreement with experimental data for all fissioning systems having experimental P(ν) data (SF and neutron induced fission) : 252 Cf(SF), 248,244 Cm(SF), 240,242 Pu(SF), 235 U(n th,f) and 239 Pu(n th,f) Tudora, Ann.Nucl.Energy 37 (4) (2010) ( for 252 Cf, 248,244 Cm(SF)) Tudora, Hambsch Ann.Nucl.Energy (2010) in press (7 fissioning systems) PbP describes very well experimental (TKE) data too: 252 Cf(SF), 248,244 Cm(SF), 233,235 U(n th,f) Tudora, Ann.Nucl.Energy 35 (2008) 1-10

Because at this meeting many results concerning 235 U(n th,f) and 252 Cf(SF) were presented, I added few of my previous results concerning P(ν) and Eγ(A) Fig.3 from A.Tudora, F.-J.Hambsch, Ann.Nucl.Energy (2010) in press

Fig.1 from A.Tudora, F.-J.Hambsch, Ann.Nucl.Energy (2010) in press

Tudora A., Ann.Nucl.Energy 35 (2008) 1-10

Tudora, Morillon, Vladuca, Hambsch…Nucl.Phys.A 756 (2005)

PbP model parameters and average parameter values param i : Er i, TKE i, Sn i, C i Level density parameter of each FF Super-fluid model (Ignatiuk) Δ(Z,A) pairing δW shell-corrections (Moller&Nix RIPL) Systematics of average param. Tudora, Ann.Nucl.Energy 36 (2009) 72 if equal T of LF and HF

TXE partition between the two fragments of the pair  Lemaire,Talou, Madland (Los Alamos) a L, a H super-fluid model, iterative procedure The two FF have the same Tm (thermodynamic equilibrium)  Tudora (Bucharest) a L, a H super-fluid model. ν H /(ν L + ν H ) parameterization obtained on the basis of the systematic behaviour of experimental sawtooth data Not equal Tm of the two fragments Lemaire et al. Phys.Rev.C 72 (2005) Tudora Ann.Nucl.Energy 33 (2006)

Simulations to obtain Y(A) of FF (pre-neutron) in neutron induced fission Experimental P(Z) data of FF (pre or post neutron) can be used in the frame of the PbP treatment to obtain Y(A) of FF:  Experimental P(Z) for 234 U electromagnetic induced fission (Schmidt et al., Nucl.Phys.A 665 (2000) )  PbP treatment to obtain Y(A) of FF for 233 U(n,f) A.Tudora, Ann.Nucl.Energy 37 (2010)  Experimental P(Z) of post-n FF for 239 Pu(n th,f) measured by Gonnenwein (Cosi fan Tutte, Kaufmann et al., Proc.Int.Conf.NDT (1991), 133 )  PbP tratment to obtain Y(A) of FF for 239 Pu(n th,f)  Exp.P(Z) of 233 U electrmg.ind.fiss. and of 232 U(n th,f) used to obtain Y(A) of FF  PbP model to calculate prompt neutron emission data for 232 U(n,f)

A.Tudora, Ann.Nucl.Energy 37 (2010) 43-51

PROMPT NEUTRON EMISSION DATA FOR 239 Pu(n,f), 233 U(n,f), 232 U(n,f) PRELIMINARY / PARTIAL RESULTS

239 Pu(n,f) POINT BY POINT MODEL CALCULATION  Experimental FF distributions Y(A,TKE), from EXFOR: - more data sets at En=th: IRMM (Hambsch), Wagemans 1984/2010, Surin 1971 CCPFEI, Akimov 1971 CCPFEI, Tsuchiya 2000 JPBKTO - Y(A) Akimov et al.: En=0.72 MeV, 1.72 MeV, 2.72 MeV, 4.48 MeV TKE(A) obtained from experimental as a function of En and renormalization to the shape of TKE(A) at thermal En  CN cross-section of the inverse process: SCAT2 code with more optical model potential parameterizations: Becchetti-Greenless, Wilmore-Hodgson, Koning-Delaroche  TXE partition, two methods: ν H /(ν L + ν H ) parameterization (Tudora, 2006) Iterative procedure of Lemaire et al., 2005

239 Pu(n th,f) multi-parametric representation of the PbP calculated matrix ν(A,TKE) A.Tudora, F.-J.Hambsch, Ann.Nucl.Energy (2010) in press

PbP calculations at En=th: all experimental FF distributions were used, best agreement of PbP results with multiplicity and spectrum experimental data were obtained for FF distrib of IRMM and Surin. (Tudora, Ann.Nucl.Energy 37 (2010) 43-51) PbP details Y(A) IRMM, ΔZ=0 th ENDF/B-VII TKE(A) IRMM, opt.K-D, TXE Tudora % TKE(A) IRMM, opt.K-D, TXE Lemaire et al % TKE(A) IRMM, opt.B-G, TXE Tudora % TKE(A) Wagemans, opt.B-G, TXE Tudora % PbP calculation at other En: - σ c (ε) Becchetti-Greenless parameterization - TXE partition – the iterative procedure Lemaire et al., 2005

En (MeV) (MeV) th (Wagem) th (IRMM) (Tudora) (Tudora) (Lemaire) Pu(n,f) average model parameter values obtained from PbP treatment

239 Pu(n,f) MOST PROBABLE FRAGMENTATION APPROACH Using average model parameter values obtained by PbP treatment

Iwamoto spectrum shape close to the case σ c =const

Most probable fragmentation approach – calculation at En where more fission chances are involved (up to En = 20 MeV, only the fission of CN of the main chain are important) Fission cross-section ratios are needed. RF provided by evaluations (MF=3, MT=18, 19, 20, 21, 38) In the case of n+ 239 Pu, fission chance cross-sections are given in ENDF/B-VII, JENDL/AC and CENDL3.1 (in these libraries the upper limit En = 20 MeV). Only BRC evaluation in JEFF3.1 is given up to 30 MeV. Observation: in all evaluations (excepting BRC) the fission chance cross-sections are obtained by renormalization of σ(n,xnf) model calculation results to the total fission cross-section (MT=18). And the evaluated total fission c.s. are not pure model calculations, adjustments to describe experimental data were made. provided by BRC are preferable.

Previous calculations using RF of BRC evaluation, 30 MeV

Same previous calculations using RF of BRC,this time up to 20 MeV

233 U(n,f) PbP model calculations FF distributions -at En = th: Y(A,TKE) of Nishio (JPNKTO, 1998), Surin (CCPFEI, 1971), Baba (JPNKTO, 1997, incomplete FF mass range). Y(A) Pleasonton (incomplete FF mass range), TKE(A) Zakharova (CCPNIR, 1973). FF distributions of Nishio and Baba very close to each other. -at En = 5.42 MeV: FF distributions Surin – Y(A) very high ratio pick to valley (the symmetric fission yield is to low) TXE partition:  ν H /ν pair parameterizations of Tudora done in 2006 (Ann.Nucl.Energy 33, ) and new parameteriz. (February 2010)  Lemaire, Talou et al. method (equal residual nuclear temperature of FF forming a pair).

PbP calc. ΔZ=0.5 Y(A,TKE) Nishio th Dev.ENDF/B-VII Optical pot.B-G, TXE Tudora % Optical pot.B-G, TXE Tudora % Optical pot.B-G, TXE Lemaire % Optical pot.K-D, TXE Tudora % Optical pot.B-G, TXE Tudora 2010 Y(A,TKE) of Surin % Prompt neutron multiplicity resuts at thermal En:

Tudora, Ann.Nucl.Energy 33 (2006)

Most probable fragmentation approach calculations

Tudora, Ann.Nucl.Energy 36 (2009) 72-84

A. Tudora, Annals of Nuclear Energy 37(1) (2010) Fig.9: 232 U(n th,f) PbP spectrum calculation for the 3 studied cases given in logarithmic scale (upper part) and as ratio to Maxwellian spectrum with TM=1.33 MeV (lower part)

A.Tudora, Annals of Nuclear Energy 37(1) (2010) Fig.10: 232 U(n,f) total average prompt neutron multiplicity up to En = 20 MeV calculated in the 3 studied cases in comparison with ENDF/B-VII, JEFF3.1 and JENDL3.3 evaluations.