Sub-barrier resonance fission and its effects on fission fragment - PowerPoint PPT Presentation

Sub-barrier resonance fission and its effects on fission fragment properties exemplified on 238 U(n,f) and 234 U(n,f) Anabella Tudora University of Bucharest, Faculty of Physics F.-J.Hambsch, S.Oberstedt EC-JRC-IRMM, Geel, Belgium WONDER-2012, Aix-en-Provence

I. Correlation between the sub-barrier resonant behaviour of fission xs of non-fissile (fertile) actinides ( pre-scission stage ) and the non-statistical fluctuations of their FF and prompt neutron data ( post-scission stage ) around En of sub-barrier resonances II. Pre Pre- -scission stage scission stage: calculation of neutron induced xs focusing the fission xs., in the frame of the refined statistical model for fission with sub-barrier effects (Vladuca et al, STATIS code). Applied in this work to n+ 234,238 U; extended to take into account the multi-modal fission (exemplified here for n+ 238 U). scission stage: the prompt neutron and γ -ray emission is III. Post Post- -scission stage treated in the frame of the Point-by-Point (PbP) model. Total FF and prompt neutron quantities as a function of En obtained by averaging the PbP results as a function of fragment over the FF distributions reveal variations around En of sub-barrier resonances of the fission cross-section. WONDER-2012

Fission cross section (b) 0.08 238 U(n,f) Meadows 89 USALAS Merla 91 GERDRE calculation (STATIS, GNASH) 0.06 Shcherbakov 2001 RUSLIN visible fluctuations of FF Lisowski 91 USALAS (as ratio U235) 0.04 properties around En where given as absolute data (1983-1957) 0.02 the fission cross-section exhibits Difilipo 80 USALAS given as ratio to 235U (1985-1972) 0.00 sub-barrier resonances experimental <TKE> (IRMM) 238 U(n,f) 2 171.0 170.5-0.14*En-0.009*En <TKE> (MeV) Here experimental <TKE> (En) 170.5 measured at IRMM 170.0 169.5 0.5 1.0 1.5 2.0 2.0 Fission cross section (b) 234 U(n,f) En (MeV) model calc. 2011 (Statis code) ENDF/B-VII 1.5 JENDL4(Ac) given in EXFOR as absolute data James 77 USAORL 1.0 Lowry 54 USALAS Lamphere 53 USAORL given in EXFOR as ratio to 235U Paradela 2006 IN2P3/IPN Behrenz 77 USALRL given in EXFOR as ratio to 235U Meadows 78 USAANL 0.5 , White 65 UKALD , Goverdovski 87 RUSFEI , , Lamphere 62 USAORL Kanda 86 JPNTOH Fumitoshi 88 JPNTOH Fursov 91 RUSFEI Lisowski 91 USALAS 0.0 234 U(n,f) 171 <TKE> (MeV) 170 EXFOR Goverdovskiy 87 RUSFEI 235 U <TKE> th =170.5 MeV renorm. IRMM 2011 (Al-Adili et al.) Tudora et al., Nucl.Phys.A 890-891 (2012) 77 169 0.0 0.5 1.0 1.5 2.0 2.5 3.0 WONDER-2012 En (MeV)

The correlated behaviour of the fission xs and FF properties is better outlined in the cases 238 U(n,f) and 234 U(n,f) because these fertile nuclei benefit of experimental FF data measured at many En with a fine grid in the region of sub-barrier resonances (measurements performed at IRMM for both 234,238 U(n,f)) The correlated behaviour can be observed in the case of 232 Th(n,f) too, but unfortunately the existing experimental FF data are measured only at a few En without a fine grid around En of sub-barrier resonances of the fission cross-section as in the cases of 238,234 U(n,f). The correlation makes the link between the two stages of fission PRE- and POST-SCISSION usually treated by 2 different classes of models WONDER-2012

scission: one single nucleus � the evolution of this CN on the fission path, with Pre- -scission Pre the change of shape from g.s. (equilibrium) deformation passing trough different stages of deformation up to the rupture point. In this stage the neutron induced fission is in competition with other channels (n,n), (n,n’), (n, γ ), treated by the modeling of nuclear reaction mechanisms. The main quantity of this stage is σ f obtained concomitantly with σ el , σ in , σ γ as a function of En. (here of interest only the En range where one CN in formed) scission: many nuclei ( FF resulted from many possibilities of CN fragmentation), Post- -scission Post each FF emitting prompt neutrons and gammas according to its structure properties and excitation energy partition. This stage of prompt fission is characterized by quantities referring to both FF and prompt neutrons and gammas as a function of En. These quantities can be as a function of fragment (TKE(A), ν (A), ε (A) etc. at a given En) or can be average quantities as a function of En (<TKE>, <Er>, < ν p >, spectra, <E γ > and so on) The correlation between σ f (pre-scission/one nucleus) and quantities of post-scission (involving many nuclei ) can be quantitatively analyzed in a consistent and coherent manner by taking into account the behaviour of average prompt fission quantities (obtained by averaging the quantities as a function of fragment over the FF distributions) Sub-barrier resonances of σ f � reflected by an increase of the fission channel population in the pre-scission stage � leading to an increase of FF distributions in the post scission stage at En values of resonances. Variation of Y(A) exemplified for the FF range (PbP treatment) � <A H >, <Er> WONDER-2012

0 0 10 10 Relative Channel Population -1 10 Relative channel population -1 10 -2 10 238 U n+ Channel population by CN mechanism fission channel -3 10 gamma-capture channel 234 U elastic channel n + inelastic channel -2 10 Channel population by -4 10 CN mechanism 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 fission channel En (MeV) gamma-capture channel ∑ σ = σ π π elastic channel CN ( E ) ( E , J ) P ( E , J ) α α α α inelastic channel ' ' π -3 J 10 ∑ 0.1 1 σ π = π π CN 2 J D ( E , J ) g T ( E , J ) α α α α lj En (MeV) lj In the En range where only the first fission chance is involved (that is of interest in this case) the total relative population of a given channel (such as fission, gamma capture, elastic and inelastic scattering by CN mechanism) can be given by the ratio of the respective channel cross section to the CN formation cross section = σ α σ P ( E ) ( E ) ( E ) α n ' n ' CN WONDER-2012

140.0 238 U(n,f) 139.8 139.6 <AH> 139.4 <A H > by averaging over experimental Y(A) 139.2 appropriate fit 139.4788+0.04864*En 139.0 238 U(n,f) 186.8 <Er> (from PbP treatment) <Er> (MeV) 186.6 2 186.63588-0.13291*En+0.01331*En 186.4 186.2 186.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 En (MeV) The variation of Y(A) around En of sub-barrier resonances (0.95 MeV, 1.25 MeV) is visibly reflected by the behaviour of <A H > and <Er> as a fucntion of En: <Er> is obtained by averaging Q-values of FF pairs (forming the FF range of the PbP treatment) over Y(A) and P(Z) distributions. Q-values and P(Z) do not change with En � Consequently the <Er> dependence on En is given only by Y(A) Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

140.0 234 U(n,f) <AH> obtained by averaging 139.5 over experimental Y(A) IRMM <AH> (MeV) 139.0 138.5 138.0 171.5 exp. IRMM (Al-Adili et al. 2011) <TKE> (MeV) 171.0 170.5 170.0 170.86234-0.17299*En 169.5 169.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 En (MeV) 234 U(n,f) Non-statistical fluctuations of quantities characterizing the FF are observed around the incident energies where the fission xs exhibits sub-barrier resonances (for instance visible variations are around 0.35 MeV and especially at around 0.8 MeV where the fission cross-section exhibits a high resonance) A.Tudora Report ERINDA (IRMM) August 2012 WONDER-2012

189.0 188.02744+0.05054*En 234 U(n,f) 188.5 <Er> (MeV) 188.0 PbP treatment ( 2Z/A, Δ Z=0.5 ) obtained by averaging Er of FF pairs 187.5 over experimental Y(A) IRMM 187.0 PbP treatment ( 2Z/A, Δ Z=0.5 ) 11.40 234 U(n,f) obtained by averaging <a> of FF pairs 11.35 <C>=A 0 /<a> over experimental Y(A) IRMM <C> (MeV) 11.30 11.25 11.20 11.230+0.0056*En 11.15 11.10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 En (MeV) A.Tudora Report ERINDA (IRMM) August 2012 WONDER-2012

5.42 234 U(n,f) 5.40 Average separation energy of the first neutron from FF <Sn1> (MeV) 5.38 5.36 5.34 PbP treatment ( 2Z/A, Δ Z=0.5 ) 5.32 by averaging <Sn1> of FF pairs over experimental Y(A) IRMM 5.30 5.28 28 234 U(n,f) 27 <TXE> (MeV) 26 25 24 23 <TXE>=<Er>+Bn+En-<TKE) 22 21 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 En (MeV) • <Sn1> dependence on En is given only by Y(A) (Sn1 of pairs do not change with En). • <TXE> variations around 0.5 and 0.8 MeV still visible even if in the figure they seem to be less pronounced (really these variations are of the same order of magnitude as the variations of other quantities mentioned above) A.Tudora Report ERINDA (IRMM) August 2012 WONDER-2012

27 238 U(n,f) 26 <TXE>=<Er>+En+Bn-<TKE> <TXE>=20.89661+1.09166*En 25 <TXE> (MeV) 24 23 22 21 20 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 En (MeV) <TXE> variations (at around 0.95 and 1.25 MeV) seem to be less pronounced compared to other quantities (like <Er>, <A H >) because the difference between <Er> and <TKE> varies less than <TKE>. Really the <TXE> variations are almost of the same order of magnitude as of other quantities mentioned above. Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012