IRMM - Institute for Reference Materials and Measurements

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1 Reaction cross sections and prompt neutron emission and spectra calculations for 238 U(n,f) and 237 Np( Np(n,f n,f) F.-J. Hambsch, A. Tudora 1, S. Oberstedt 1) Bucharest University, Faculty of Physics, RO Bucharest, Romania IRMM - Institute for Reference Materials and Measurements Geel - Belgium

2 Content Introduction Theoretical modeling Neutron induced cross sections ( 238 U(n,f)) PbP calculations for 238 U(n,f) Neutron induced cross sections ( 237 Np(n,f)) PbP calculations for 237 Np(n,f) Conclusions

3 Introduction Model prediction of mass distributions Investigate the predictive power of the model

4 Introduction Mono-energetic neutron source 7 MV Van-de-Graaff accelerator GELINA neutron TOF spectrometer energetic neutron source MeV electron accelerator 7 LiF(p,n) 7 Be, TiT(p,n) 3 He, D 2 (d,n) 3 He, TiT(d,n) 4 He DC (I p,d < 50 µa), pulsed beam available non-t beam line Φ n < 10 9 /s/sr NEPTUNE NEPTUNE isomer spectrometer ionisation chambers, NE213 neutron/gamma-ray detectors, BF 3 counters, HPGe detectors Bonner spheres fast rabbit systems (T 1/2 > 1s) for activation studies MeV electron accelerator repetition frequency: Hz neutron pulse: 2 µs - 1 FWHM Φ n = Hz 12 different flight paths with a length between 8 and 400 m ionisation chambers, C 6 D 6 detectors high-resolution γ-ray detectors fission chambers for flux monitoring

5 Theoretical modeling of reaction cross sections Theoretical modeling of reaction cross sections and prompt neutron multiplicity and spectra

6 Concept of the model calculations Experimental input: fission-mode branching ratio (w m ) as a function of the incident neutron energy ENDF/B-VI fission cross section data Statistical treatment of the CN mechanism within the code STATIS extended for MM-RNR model (NP A707 (2002) 32) one CN ( incident neutron energies below 2 nd chance fission) 3 most dominant fission modes : asymmetric S1, S2 and symmetric SL parabola-shaped inner and outer barriers elastic and inelastic neutron scattering, radiative capture, fission Direct interaction with ECIS code (coupled channel method, Raynal CEA-N-2772, 1994): total cross-section, partial direct scattering cross-sections for the first four rotational bands and the neutron transmission coefficients

7 Multi-modal fission barrier Barrier height (MeV) U(n,f) V A = 6.40 MeV hω A = 0.73 MeV V I = 1.31 MeV hω I = 0.78 MeV without fission modes V B = 5.71 MeV hω B = 0.50 MeV S1 V B = 6.70 MeV hω B = 1.20 MeV S2 V B = 6.08 MeV hω B = 0.51 MeV SL V B = 9.05 MeV hω B = 2.10 MeV Deformation (relative unit)

8 238 U(n,f)

9 Fission Cross-section for 238 U(n,f) U(n,f) Fission cross section (b) E-3 1E-4 1E-5 1E-6 V A =6.40MeV hω A =0.70 MeV V I =1.50 MeV hω I =1.00 S2 V B =6.10 MeV hω B =0.48 MeV; Goverdovski S1 V B =6.65 MeV hω B =1.20 MeV; Goverdovski SL V B =9.00 MeV hω B =2.10 MeV 1E E n (MeV) EXFOR (other) Blons DFilippe ENDF/B-VI Present evaluation S1 S2 SL

10 Branching Ratio for 238 U(n,f) w(% %) U-238 S1 russian S1 IRMM S2 russian S2 IRMM SL IRMM E(M ev)

11 238 U Mass Distribution at E n =1.2 MeV U(n,f) 10 0 Y(%) exp.data IRMM at En = 1.2 MeV sum S1 S2 SL A

12 238 U Mass Distribution at E n =0.9 MeV U(n,f) 10 0 Y(%) E n = 0.9 MeV S1 S2 Sl sum A

13 Fission mode weights S1 mode weight (%) This work d min >11.8 fm Vivés et al. Goverdovski Theoretical predictions σ f (E n ) 238 U(n, f) Calc E n (MeV) E-3 Cross-sec ction (b)

14 Improved barrier parameters Fission cross section (b) U(n,f) "experimental" modal cross-sections S1 S2 present calculation S1 S2 sum of modal fission c.s. sets given as absolute data ( ) Difilipo 80 USALAS sets given as ratio to 235U ( ) Meadows 89 USALAS Merla 91 GERDRE Shcherbakov 2001 RUSLIN Lisowski 91 USALAS (as ratio U235) En (MeV) w(%) w(%) IRMM 2008 S1, S2 IRMM 2000 S1, S2, SL 238 U(n,f) 20 present calculation S1, S2, SL IRMM 2008 S1, S present calculation 0 S1, S En (MeV)

15 Point by point (PbP) calculations Assumption: Neutron evaporation from fully accelerated fission fragments (Los Alamos model) PbP takes into account the full range of possible fragmentations of the fissioning nucleus FF mass and total kinetic energy distributions are input quantities for the PbP calculations above the second chance threshold only most probable fragmentation used split of the total excitation energy between the two fragments of each pair is based on ν H /ν pair ratio mass excesses are based on Audi and Wapstra

16 Prompt neutron multiplicity PFNM U(n,f) Tudora NPA 2004, JEFF3.1 Madland NPA 2006 Systm. of param. PbP 2006 PbP 2008 data renormalized to 252 Cf(SF) or 235 U(n th,f) Asplund-Nilsson 64 SWDFOA Mather 65 UKALD Nurpeisov 75 CCPFEI Malynovsky 83 CCPFEI Frehaut 80 BRC Fr average param. (IRMM 08) data without renormalization Batchelor 65 UKALD Savin 72 CCPKUR Vorob'jova 74 CCPFEI BaoZongyu 75 CPRAEP other data sets from EXFOR other data requiring renorm Manero and Konshin 72 eval En (MeV)

17 Prompt fission neutron spectrum PFNS (1/MeV) PbP calc. using as input Exp. Y(A), TKE(A) 2008 En = 2 MeV PbP calc. using as input Exp. Y(A), TKE(A) En =3 MeV Baba 1989 JPNTOH set 1, set 2 Boykov 1991 RUSFEI (En = 2.9 MeV) 10-1 PbP calc. using as input 10-2 En =5 MeV Exp. Y(A), TKE(A) 2002 Trufanov 2001 RUSFEI (given as ratio to 252 Cf(SF)) E (MeV)

18 Level densities and share of TXE Level density parameter (MeV -1 ) U(n,f) En = 1.4 MeV A / 11 Level density parameter: superfluid model (Ignatiuk) E* L /E* H =ν L /ν H Tudora 2006 E* L /E* H =a L /a H Talou A of FF NUP of FF pair NUP of FF U(n,f) En = 1.4 MeV 3.0 E* L /E* H =ν L /ν H Tudora E* L /E* H =a L /a H Talou 2005 (iterations) A of FF

19 237 Np(n,f)

20 237 Np fission cross section up to 50 MeV 2.5 present calculation NPA 767(2006) 112 ENDF/B-VII (2008) JEFF3.1, JENDL Np(n,f) 237 Np(n,f) NPA 767(2006) present calculation 2.5 Fission cross-section (b) Plattard 75 FRSAC Moore 72 USALAS (nucl.expl.) Henkel 57 USALAS Gokhberg 59 CCPFEI White 65 UKALD, Behrens 82 USALRL Varnagy 82 HUN Goverdovski 85 CCPFEI EXFOR (2006): Merla 91 GERDRE the other sets of EXFOR Shcherbakov 2001 Dubna (absolute data) Shcherbakov (as ratio) with 235U BRC eval. Meadows 83 USALAS Kanda 85 JPNTOH Terayama 86 JPNTOH Kuprijanov 78 CCPFEI EXFOR, with standard U-235 Tovesson 2008 USALAS Tovesson 2007 USALAS Tassan-Got 2008 (ntof) Shcherbakov 2001 RUSLIN Behrenz 82 USALRL Fission cross-section (b) EXFOR, with standard U-235 EXFOR (2006): Tovesson 2008 USALAS Merla 91 GERDRE Tovesson 2007 USALAS Shcherbakov 2001 Dubna (absolute data) Tassan-Got 2008 (ntof) Shcherbakov (as ratio) with 235U BRC eval. Plattard 75 FRSAC Shcherbakov 2001 RUSLIN Moore 72 USALAS (nucl.expl.) Behrenz 82 USALRL Henkel 57 USALAS Meadows 83 USALAS Gokhberg 59 CCPFEI White 65 UKALD, Behrens 82 USALRL Varnagy 82 HUN Goverdovski 85 CCPFEI Kanda 85 JPNTOH Terayama 86 JPNTOH Kuprijanov 78 CCPFEI the other sets of EXFOR En (MeV) En (MeV)

21 Capture cross section Np(n,γ) ENDF/B-VI JENDL3.3 and JEFF3.1 ENDF/B-VII.0 (n,γ) cross section (b) EXFOR, Lindner 76 USALAS Stupegia 67 USAANL Trofimov 83 CCPRI,, Buleeva 88 CCPFEI Criccho 82 FR(Rapsodie) and Trofimov 87 CCPRI Weston and Todd 81 ORL previous evaluation NPA 767 (2006) 112 present calculation En (MeV)

22 Prompt neutron multiplicities Prompt Fission Neutr ron Multiplicity EXFOR data without renorm. Boykov 1994 RUSRI Malinovski 1983 CCPFEI Mueller 1981 GERKFK Taieb 2007 USALAS Thierens 80 BLGGHT and Borzakov 2000 ZZZDUB ENDF/B-VII 237 Np(n,f) calculation 2009 PbP most probab. fragm. EXFOR data with renorm. 252 Cf(SF)=3.759 Khokhlov 1994 RUSEPA Veeser 1978 USALAS Frehaut 1982 FR BRC En (MeV) Prompt Fission Neutron Multiplicity EXFOR data without renorm. Boykov 1994 RUSRI Malinovski 1983 CCPFEI Mueller 1981 GERKFK Taieb 2007 USALAS Thierens 80 BLGGHT and Borzakov 2000 ZZZDUB EXFOR data with renorm. to 252 Cf(SF)=3.759 Khokhlov 1994 RUSEPA Veeser 1978 USALAS Frehaut 1982 FR BRC 237 Np(n,f) total prompt neutron multiplicity contributions of: Np main nucleus chain U secondary chain "proton" path U secondary chain "neutron via proton" path En (MeV)

23 Prompt fission neutron spectra Prompt Fission Neutron Spectrum (1/MeV) 10 0 En=7.8 MeV En=4.9 MeV most probable fragm. approach using 238 Np param. of systematics using 238 Np param from PbP 2009 Trufanov 1992 RUSFEI ENDF/B-VII (Madland 84) 237 Np(n,f) Trufanov 1992 RUSFEI 10 0 En=0.52 MeV Kornilov 1997 RUSFEI ENDF/B-VII (Madland 84) PbP 2009 most prob fragm. with param.pbp PbP 2009 most prob fragm. with param PbP E(MeV)

24 Conclusions Model calculations within a statistical model in good agreement with many experimental results, but predictive power of the model is limited. Point by point calculation of the prompt fission neutron multiplicities and spectra gives good agreement with experimental data.

25 Thank you for your attention