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

Sub-barrier resonance fission and its effects on fission fragment properties

Anabella Tudora

University of Bucharest, Faculty of Physics

F.-J.Hambsch, S.Oberstedt

EC-JRC-IRMM, Geel, Belgium

exemplified on 238U(n,f) and 234U(n,f)

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+234,238U; extended to take into account the multi-modal fission (exemplified here for n+238U).

• III. Post

Post-

• scission stage

scission stage: the prompt neutron and γ-ray emission is 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

• f the fission cross-section.

WONDER-2012

0.5 1.0 1.5 2.0 169.5 170.0 170.5 171.0

experimental <TKE> (IRMM) 170.5-0.14*En-0.009*En

2

238U(n,f)

<TKE> (MeV) En (MeV)

0.00 0.02 0.04 0.06 0.08

given as absolute data (1983-1957) Difilipo 80 USALAS given as ratio to 235U (1985-1972) Meadows 89 USALAS Merla 91 GERDRE Shcherbakov 2001 RUSLIN Lisowski 91 USALAS (as ratio U235)

calculation (STATIS, GNASH) 238U(n,f)

Fission cross section (b)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 169 170 171

234U(n,f) EXFOR Goverdovskiy 87 RUSFEI renorm.

235U <TKE>th=170.5 MeV

IRMM 2011 (Al-Adili et al.)

<TKE> (MeV) En (MeV)

0.0 0.5 1.0 1.5 2.0

model calc. 2011 (Statis code)

ENDF/B-VII JENDL4(Ac) 234U(n,f)

given in EXFOR as ratio to 235U Behrenz 77 USALRL Meadows 78 USAANL , Goverdovski 87 RUSFEI Kanda 86 JPNTOH Fursov 91 RUSFEI given in EXFOR as ratio to 235U , White 65 UKALD , , Lamphere 62 USAORL Fumitoshi 88 JPNTOH Lisowski 91 USALAS given in EXFOR as absolute data James 77 USAORL Lowry 54 USALAS Lamphere 53 USAORL Paradela 2006 IN2P3/IPN

Fission cross section (b)

visible fluctuations of FF properties around En where the fission cross-section exhibits sub-barrier resonances Here experimental <TKE> (En) measured at IRMM

Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

The correlated behaviour of the fission xs and FF properties is better outlined in the cases 238U(n,f) and 234U(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 234,238U(n,f)) The correlated behaviour can be observed in the case of 232Th(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 238,234U(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

Pre Pre-

• scission

scission: one single nucleus the evolution of this CN on the fission path, with 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 σf obtained concomitantly with

σel, σin, σγ as a function of En. (here of interest only the En range where one CN in formed)

Post Post-

• scission

scission: many nuclei (FF resulted from many possibilities of CN fragmentation), 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>, <νp>, spectra, <Eγ> and so on) The correlation between σf (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 σf 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) <AH>, <Er>

WONDER-2012

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 10

• 4

10

• 3

10

• 2

10

• 1

10 Channel population by CN mechanism

n+

238U

fission channel gamma-capture channel elastic channel inelastic channel

Relative Channel Population En (MeV)

) , ( ) , ( ) (

' '

π π σ σ

α π α α α

J E P J E E

J CN

∑

=

) , ( ) , (

2

π π π σ

α α α α

J E T g J E

lj lj J CN

∑

= D

) ( ) ( ) (

' '

E E E P

CN n n

σ σ α

α

=

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

0.1 1 10

• 3

10

• 2

10

• 1

10

n +

234U

Channel population by CN mechanism

fission channel gamma-capture channel elastic channel inelastic channel

Relative channel population En (MeV)

WONDER-2012

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 186.0 186.2 186.4 186.6 186.8

238U(n,f) 186.63588-0.13291*En+0.01331*En

2

<Er> (from PbP treatment)

<Er> (MeV) En (MeV)

139.0 139.2 139.4 139.6 139.8 140.0

238U(n,f)

<AH> by averaging over experimental Y(A) appropriate fit 139.4788+0.04864*En

<AH>

The variation of Y(A) around En of sub-barrier resonances (0.95 MeV, 1.25 MeV) is visibly reflected by the behaviour of <AH> 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

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 169.0 169.5 170.0 170.5 171.0 171.5

170.86234-0.17299*En

• exp. IRMM (Al-Adili et al. 2011)

<TKE> (MeV) En (MeV)

138.0 138.5 139.0 139.5 140.0

<AH> obtained by averaging

• ver experimental Y(A) IRMM

234U(n,f)

<AH> (MeV)

234U(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

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 11.10 11.15 11.20 11.25 11.30 11.35 11.40

11.230+0.0056*En

<C>=A0/<a>

234U(n,f)

PbP treatment (2Z/A, ΔZ=0.5)

• btained by averaging <a> of FF pairs
• ver experimental Y(A) IRMM

<C> (MeV) En (MeV)

187.0 187.5 188.0 188.5 189.0

188.02744+0.05054*En

234U(n,f)

PbP treatment (2Z/A, ΔZ=0.5)

• btained by averaging Er of FF pairs
• ver experimental Y(A) IRMM

<Er> (MeV)

A.Tudora Report ERINDA (IRMM) August 2012 WONDER-2012

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 21 22 23 24 25 26 27 28 <TXE>=<Er>+Bn+En-<TKE)

234U(n,f)

<TXE> (MeV) En (MeV)

5.28 5.30 5.32 5.34 5.36 5.38 5.40 5.42

Average separation energy of the first neutron from FF

PbP treatment (2Z/A, ΔZ=0.5) by averaging <Sn1> of FF pairs

• ver experimental Y(A) IRMM

234U(n,f)

<Sn1> (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

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 20 21 22 23 24 25 26 27

238U(n,f)

<TXE>=20.89661+1.09166*En <TXE>=<Er>+En+Bn-<TKE>

<TXE> (MeV) En (MeV)

<TXE> variations (at around 0.95 and 1.25 MeV) seem to be less pronounced compared to

• ther quantities (like <Er>, <AH>) 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

• ther quantities mentioned above.

Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

1.0 1.5 2.0 2.5 3.0 3.5 4.0 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

PbP 2012 (using Y(A), TKE(A) IRMM 2008)

238U(n,f)

data without renormalization Batchelor 65 UKALD Savin 72 CCPKUR Vorob'jova 74 CCPFEI BaoZongyu 75 CPRAEP data renormalized to

252Cf(SF) or 235U(nth,f)

Asplund-Nilsson 64 SWDFOA Mather 65 UKALD Nurpeisov 75 CCPFEI Malynovsky 83 CCPFEI Frehaut 80 BRC Fr

• ther data sets from EXFOR
• ther data requiring renorm

Manero and Konshin 72 eval.

PFNM En (MeV)

Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1

ENDF/B-VII.1 (Maslov) JEFF3.1.2 (Maslov) JENDL4 PbP 2Z/A, ΔZ=0.5 most prob. fr. with param from PbP most prob. fr. with param from systematic

234U(n,f)

Mather 65 UKALD Manero, Konshin 72 ZZZIAE (2.361+0.135En)

Prompt Nu En (MeV)

A.Tudora Report ERINDA (IRMM) August 2012 WONDER-2012

The PbP result of total average prompt neutron multiplicity (obtained by averaging the PbP matrix ν(Z,A,TKE) over the recent experimental Y(A,TKE) (IRMM) reveals visible non-statistical fluctuations around the En where the fission xs exhibits sub-barrier resonances.

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0

calc.2011 (STATIS)

given in EXFOR as ratio to 235U Behrenz 77 USALRL Meadows 78 USAANL , Goverdovski 87 RUSFEI Kanda 86 JPNTOH Fursov 91 RUSFEI given in EXFOR as ratio to 235U , White 65 UKALD , , Lamphere 62 USAORL Fumitoshi 88 JPNTOH Lisowski 91 USALAS given in EXFOR as absolute data James 77 USAORL Lowry 54 USALAS Lamphere 53 USAORL Paradela 2006 IN2P3/IPN

Fission cross section (b) En (MeV)

2.4 2.5 2.6 2.7 2.8

PbP (2012) 2Z/A, ΔZ=0.5 most probable fragm. (2012)

234U(n,f) Mather 65 UKALD Manero, Konshin 72 ZZZIAE (2.361+0.135En)

Prompt multiplicity

A.Tudora Report ERINDA (IRMM) August 2012 WONDER-2012

In both cases 238, 234U(n,f) the sub-barrier resonances of the fission xs, reflected by an increase of fission exit channel population at the respective En values, lead in the post-scission stage to an increase of FF distributions around the En of

• resonances. This fact was proven by the fragment observables and prompt

neutron data obtained by averaging the quantities corresponding to fragment pairs over the fragment distributions Y(A), P(Z), such as <Er>, <Sn1> and so on and also by the experimental <TKE> data. All these quantities exhibiting visible variations around the En of resonances.

The sub-barrier fission xs resonances of 234U (placed at around 0.3 MeV,

0.5 MeV and 0.8 MeV) are much more pronounced (especially the

resonance at 0.8 MeV is very high) compared to the resonances of 238U

(placed at around 0.95 MeV and 1.25 MeV).

Consequently the effect in the properties of fragments and in the prompt neutron emission data is also more pronounced in the case of 234U compared to 238U, as it is proved by the present results.

To synthesize:

WONDER-2012

The multi

multi-

• modal fission concept

modal fission concept also can give an explanation of the

correlation between the sub-barrier resonances of the fission xs and the pronounced variation of experimental <TKE> and of other FF and prompt neutron data at almost the same En values. In the frame of the multi-modal fission the coherence coherence between the stages of pre-scission (one fissioning nucleus) and post-scission (many nuclei, FF) is assured by the behaviour of the modal fission xs (usually of S1, S2, SL modes) as a function of En directly correlated with the behaviour of both modal prompt fission quantities as a function of En:

• the modal distributions (Ym(A), TKEm(A), σTKEm(A)) and
• the modal average quantities (such as <TKE>m, <Er>m and so on)

the index m means S1, S2, SL

WONDER-2012

0.5 1.0 1.5 2.0 20 40 60 80

IRMM (2008) S1, S2

238U(n,f)

Modal weight w (%) En (MeV)

0.00 0.02 0.04 0.06 0.08

"experimental" modal xs using modal w IRMM 2008 S1 S2

given as absolute data (1983-1957) Difilipo 80 USALAS given as ratio to 235U (1985-1972) Meadows 89 USALAS Merla 91 GERDRE Shcherbakov 2001 RUSLIN Lisowski 91 USALAS (as ratio U235)

calculation S1 S2 sum of modal fission xs

238U(n,f)

Fission cross section (b)

• Calculated fission mode xs exhibit resonances at around 0.95 and 1.25 MeV
• The experimental fission mode weights (branching ratios) exhibit pronounced

variations around the fission xs resonances an increase of the S1 weight and a respective decrease of the S2 weight

Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

The average TKE of S1 mode (<TKE>S1) has always the highest value (because of the split in almost spherical fragments in connection with the closed shells N=82 and Z=50 and the lowest distance between their charge centers) the increase of <TKE>S1 around the resonance energies determines the behaviour of the total <TKE>.

120 125 130 135 140 145 150 155 160 140 150 160 170 180 190

En = 0.925 MeV

exp.IRMM, TKE(A) (sum) TKE(A) S1, TKE(A) S2

TKE (MeV) AH

150 160 170 180 190

238U(n,f)

En = 0.9 MeV

exp.IRMM, TKE(A) (sum) TKE(A) S1, TKE(A) S2

TKE (MeV)

This fact is illustrated in the following example where 2 consecutive closed En values (0.9 and 0.925 MeV) at which experimental <TKE> data exhibit a visible variation (increase) with En are taken.

WONDER-2012

120 125 130 135 140 145 150 155 160 1 2 3 4

S2 S1

YS2(A) 0.9 MeV YS2(A) 0.925 MeV YS1(A) 0.9 MeV YS1(A) 0.925 MeV

Y (%) AH

40 80 120 160

S2 S1

TKES2(A)*YS2(A) 0.9 MeV TKES2(A)*YS2(A) 0.925 MeV

238U(n,f)

TKES1(A)*YS1(A) 0.9 MeV TKES1(A)*YS1(A) 0.925 MeV

Ym*TKEm (MeV)

Upper part: S1 and S2 contributions to total <TKE> given by Ym(A)*TKEm(A) with

m Am m CN m CN m

TKE A A A A A A A TKE > < − > < − > < − =

2

) ( ) ( ) ( σ

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ > < − − =

2 2

2 ) ( exp 2 ) (

Am m Am m m

A A w A Y σ π σ

Lower part

Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

II Neutron induced Neutron induced xs xs calculation calculation, with the fission channel treated

• classically (without modes): n+234, 238U
• multi-modal fission concept: n+238U

In the En range where only the first fission chance in involved DI mechanism CC (ECIS) + deformed OM parameterizations (with dispersion) CN mechanism statistical model with sub-barrier effects (STATIS code) including the extended model in the frame of the MM fission concept (5 channels in competition neutron scattering, capture and 3 fission channels S1, S2, SL)

After incident neutron absorption, the CN is populated in class I states. From these states it can decay by neutron emission, gamma transitions and “direct fission” or it can undergo a shape change by transition to a class II state (absorption in the isomeric well). The flux fraction absorbed in the second well is described by an absorptive (imaginary) potential in the deformation region of the second well. This absorbed fraction can decay i) by fission penetrating the outer barrier (the so-called “indirect fission”), ii) by radiative transition to the isomeric state followed by “isomeric fission” or iii) by another change of shape returning to a class I state after penetrating the inner fission barrier. The fission probability is given by the sum of three components: the direct, indirect and isomeric fission. If the fission-mode concept is taken into account, then the fission probability through each mode is also taken as a sum of the direct, indirect and isomeric fission components. For each transition state a double-or triple-humped barrier is taken (parabolas). The dumping of vibrational states in the isomeric well is taken by the imaginary part of the potential in the region of the second well (also parabolic shape with respect to the deformation parameter).

WONDER-2012

0.01 0.1 1 10 4 6 8 10 12 14 16

Capote et al (iref=2408) Vladuca et al (iref=600)

238U(n,tot) Abfalterer 2001 USALAS Poenitz 81 USAANL Schwartz 74 USANBS Hayes 73 USARPI Mubarakmand 74 PAKNIL Cabe, Cance 73 BRC Baba 73 JPNTOH Whalen 71 USAANL Foster 71 USABNW Peterson 60 USALRL Bratenahl 58 USALRL

Total cross-section (b) En (MeV)

30 60 90 120 150 180 10

• 3

10

• 2

10

• 1

10 10

1

En = 3.4 MeV

Capote Vladuca

238U(n,n)

Haouat 82 BRC

Differential cross-section (b/st)

θCMS (deg)

CC calculations (ECIS) Coupled levels 0+, 2+, 4+, 6+, 8+ β2, β4, β6 Moller and Nix (RIPL3) More deformed optical potentials were investigated: BRC, Capote, Soukhovitsky etc.(RIPL3) The best agreement with experimental total xs and exp.differential elastic and inelastic xs (at En where the contribution of the CN mechanism is negligible) was obtained for the case of

• ptical model parameterization
• f Capote et al.

Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

60 120 10

• 2

10

• 1

10 10

1

En = 3 MeV

(n,n)+(n,n'1,2,3) Capote Vladuca 238U(n,n) and (n,n') Annand 85 UKEDG

Differential cross-section (b/st)

60 120 180 En = 4 MeV

(n,n)+(n,n'1) Capote Vladuca Knitter 71 IRMM

θCMS (deg) 60 120 180

(n,n)+(n,n'1) Capote Vladuca

En = 4.5 MeV

Knitter 71 IRMM

60 120 10

• 3

10

• 2

10

• 1

10 10

1

(n,n)+(n,n'1) Capote Vladuca

En = 5 MeV

Knitter 71 IRMM

Differential cross-section (b/st)

60 120 180 En = 14 MeV

CC calculation at En = 14 MeV (n,n)+(n,n'1,2,3,4) Capote Vladuca

238U(n,n) and (n,n')

Sh.Guanran 84 CPRAEP Qi Huiquan 91 CPRTSI Li Jingde 86 CPRSIU Voignier 68 FRVNV Hansen 86 USALRL

θCMS (deg) 60 120 180 En = 15 MeV

CC calculation at En = 15 MeV (n,n)+(n,n'1,2,3,4) Capote Vladuca

Guzhovskiy 61 CCPKUR Qi Huiquan 93 CPRTSI Wan Dairong 90 CPRSIU

Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

10

• 2

10

• 1

10 10

1

2 4 6 8 10 12 14 16 18

Grigoriev 81 CCPFEI (n,sct) ENDF/B-VII JEFF3.1 JENDL4

Li Jingde 86, Shen Guanran 84, Voignier 68

DI (ECIS pot. Capote) + CN (STATIS) 238U(n,n)

EXFOR Litvinsky 90, Murzin 87,Tsang 78, Allen 56 Barnard 66 UKHAR Batchelor 65 UKALD Haouat 82 BRC

Elastic cross-section (b) En (MeV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

ENDF/B-VII JEFF3.1 JENDL4

238U(n,n')

present calculation DI (ECIS, pot.Capote) + CN (STATIS)

EXFOR Tsang 78, Andreev 61, Cranberg 58, Makarenko 89 Kegel 78 USALTI Glazkov 63 RUSFEI Batchelor 56 UKHAR

Inelastic cross section (b) En (MeV) Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

10

• 2

10

• 1

10 0.0 0.2 0.4 0.6 0.8 1.0

present calculation

238U(n,γ)

EXFOR Moxon 2006 UKHAR Voignier 92 FR BRC E.Quang 91 USAMHG exp.data 1988-1944

Capture cross section (b) En (MeV) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 0.0 0.2 0.4 0.6

present calculation S1, S2, SL, sum

"experimental" modal fission xs: S1 S2 SL

238U(n,f)

En (MeV)

0.01 0.1 1 10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10

present calculation: S1 mode, S2 mode, SL mode sum of modal fission xs "experimental" modal cross-sections obtained by multiplying ENDF/B-VII (MT=18) with experimental modal weights: S1, S2, SL 238U(n,f)

Fission cross section (b)

239U: γ-channel, normalization constant

<D0> = (20.26+-0.72) eV <Γ0> = (23.360+-0.031) meV (Mughabghab)

• Inner barrier (AS) 6.40 0.73

Isomertic well 1.31 0.78 Outer barrier (SA) 5.71 0.50 Outer barr. S1(SA) 6.70 1.20 Outer barr. S2(SA) 6.08 0.51 Outer barr. SL(AS) 9.05 2.10

• Tudora et al., Nucl.Phys.A 890-891 (2012) 77

Symmetries Heights and curvatures (MeV)

WONDER-2012

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 10 10

1

10

2

10

3

10

4

a=28.197 (Mughabghab <D0>=3.5 eV) T=0.4016, Er=4.3503, E0=-0.1884, NL=15 238U

Experimental level scheme (RIPL3)

Cumulative number of levels E* (MeV)

10 10

1

10

2

10

3

10

4

10

5

a=30.581 (Mughabghab <D0>=20.26eV) T=0.3827,Er=3.9176, E0=-0.6723, NL=18 239U

Experimental level scheme (RIPL3)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 10 10

1

10

2

10

3

10

4

10

5

Symmetry barrier B: SA for S1 and S2 AS for SL B mode S1 and S2 (SA): T=0.417, Erac=4.6581, E0=-1.152, KB=2.218, (NL=80) B mode SL (AS): T=0.417, Erac=4.6581, E0=-1.152, KB=8.530 (NL=20)

barr B modes S1 and S2 barr.B mode SL

Cumulative number of levels E* (MeV)

10 10

1

10

2

10

3

10

4

10

5

a=30.581 (Mughabghab <D0>=20.26eV) Symmetry: barrier A: AS barrier B: SA A: T=0.405, Erac=4.3913, E0=-0.9769, KA=8.096, (NL=70,Ec=0.213) B: T=0.410, Erac=4.5014, E0=-1.0488, KB=2.173, (NL=70,Ec=0.245)

discrete transitional states (Jmax=8.5): barr.A barr.B 239U

⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎨ ⎧ = symmetry any ut witho 8 (AS) 2 (SA) 2 (SS)

2 2 2 3 2 2 2 2

σ σ π σ σ π σ σ σ σ

f f f f f

K

Enhancement factors relative to the equilibrium deformation

Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

10

• 3

10

• 2

10

• 1

10 10

1

5 10 15 20 25

CC ECIS using the deformed potential of Capote, Soukhovitskii from JENDL4 5 coupl. levels, β2=0.213, β4=0.066, β6=0.0015 ENDF/B-VII JEFF3.1 JENDL4, JENDL/AC

234U(n,tot)

TOTAL CROSS SECTION (B) En (MeV)

10

• 3

10

• 2

10

• 1

10 10

1

5 10 15 20

present calculation JENDL4, JENDL/AC ENDF/B-VII

234U(n,n)

Elastic cross section (b) En (MeV)

CC calculations (ECIS) deformed optical potential

• f Capote-Soukhovitsky

(given in JENDL4) Coupled levels 0+, 2+, 4+, 6+, 8+ β2, β4, β6 values given in the figure

• A.Tudora ERINDA meeting Prague 2012

WONDER-2012

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 10 10

1

10

2

10

3

10

4

a=28.197 (Mughabghab <D0>=3.5 eV) T=0.4016, Er=4.3503, E0=-0.1884, NL=15 238U

Experimental level scheme (RIPL3)

Cumulative number of levels E* (MeV)

10 10

1

10

2

10

3

10

4

10

5

a=30.581 (Mughabghab <D0>=20.26eV) T=0.3827,Er=3.9176, E0=-0.6723, NL=18 239U

Experimental level scheme (RIPL3)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 10 10

1

10

2

10

3

10

4

10

5

a=28.997 A T=0.435, Erac=4.7675, E0=-1.1813, KA=1.043, NL=30 B T=0.440, Erac=4.8799, E0=-1.2584, KB=2.114, NL=40

U-235

Discrete trans.states build up to Jmax=10.5

• n the band heads K

π=0.5+,0.5-,1.5+,1.5-,3.5+,3.5-

barrier A barrier B

Cumulative number of levels E*(MeV)

A.Tudora ERINDA meeting Prague 2012 WONDER-2012

10

• 3

10

• 2

10

• 1

10 10

• 3

10

• 2

10

• 1

10

2011 (STATIS) ENDF/B-VII JENDL4(Ac) 234U(n,f)

given in EXFOR as ratio to 235U Behrenz 77 USALRL Meadows 78 USAANL , Goverdovski 87 RUSFEI Kanda 86 JPNTOH Fursov 91 RUSFEI given in EXFOR as ratio to 235U , White 65 UKALD , , Lamphere 62 USAORL Fumitoshi 88 JPNTOH Lisowski 91 USALAS given in EXFOR as absolute data James 77 USAORL Lowry 54 USALAS Lamphere 53 USAORL Paradela 2006 IN2P3/IPN

Fission cross section (b) En (MeV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 0.0 0.5 1.0 1.5 2.0

2011 (STATIS) ENDF/B-VII JENDL4(Ac) 234U(n,f)

given in EXFOR as ratio to 235U Behrenz 77 USALRL Meadows 78 USAANL , Goverdovski 87 RUSFEI Kanda 86 JPNTOH Fursov 91 RUSFEI given in EXFOR as ratio to 235U , White 65 UKALD , , Lamphere 62 USAORL Fumitoshi 88 JPNTOH Lisowski 91 USALAS given in EXFOR as absolute data James 77 USAORL Lowry 54 USALAS Lamphere 53 USAORL Paradela 2006 IN2P3/IPN

Fission cross section (b) En (MeV)

Inner barrier (SS) 4.90 0.80 Isomertic well 2.00 1.00 Outer barrier (SA) 5.855 0.45 Obs: ENDF/B-VII and JENDL4 are not pure calculations (they are fits of experimental data) Curvature values close to RIPL3 (0.8, 0.5). Heights differ from RIPL3 (5.25, 6.)

A.Tudora ERINDA meeting Prague 2012 WONDER-2012

• III. Prompt neutron emission calculation
• III. Prompt neutron emission calculation

PbP model provides as primary results the multi-parametric

matrixes ν(Z,A,TKE), N(Z,A,TKE), ε(Z,A,TKE), Eγ(Z,A,TKE) and so on. FF range: the entire FF mass range covered by a mass distribution with a step of 1 mass unit. For each A two or four Z are taken as the nearest integer values above and below the most probable charge (taken as UCD corrected with a charge polarization) Average quantities are obtained by averaging the corresponding multi-parametric matrix quantity(Z,A,TKE) over FF distributions: P(Z) (taken as a narrow gaussian) Y(A, TKE) usually experimental data (or models TKE(A), simulations Y(A)) Most probable fragmentation approach (improved LA) – using average model parameter values (depending on En / E*) obtained from the PbP treatment used for the improvement and validation

• f the systematic of LA parameters, 2009)

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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

PbP calculation Tudora et al. (NPA 2004) using param. from the systematic (Tudora ANE 2009) using the fit of average parameters from the PbP treatment 238U(n,f)

data without renormalization Batchelor 65 UKALD Savin 72 CCPKUR Vorob'jova 74 CCPFEI BaoZongyu 75 CPRAEP data renormalized to

252Cf(SF) or 235U(nth,f)

Asplund-Nilsson 64 SWDFOA Mather 65 UKALD Nurpeisov 75 CCPFEI Malynovsky 83 CCPFEI Frehaut 80 BRC Fr

• ther data sets from EXFOR
• ther data requiring renorm

Manero and Konshin 72 eval.

PFNM En (MeV) The present PbP calculations as well as the most probable fragm. approach with average param. from the PbP treatment confirmed the following predictions

Tudora et al., Nucl.Phys.A 890-891 (2012) 77

: previous calculations reported in 2004 and model parameter values provided by the systematic (2009)

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.4 0.6 0.8 1.0 1.2

TM = 1.32 MeV , Baba JPNKTO 1989 PbP calc. with σc(ε) Becchetti-Greenless

E (MeV)

0.4 0.6 0.8 1.0 1.2

En = 2 MeV

238U(n,f) TM=1.3724 MeV , Baba JPNKTO 1989 PbP calc. with σc(ε) Koning-Delaroche

Ratio to Maxwellian

0.1 1 10 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

238U(n,f)

En = 3 MeV

Bojkov En = 2.9 MeV PbP calculation with σc(ε) Becchetti-Greenless

Ratio to Maxwellian TM = 1.32 MeV E (MeV)

Consistency of PbP calculation:

All prompt emission quantities

• btained concomitantly (in the

same run) are in good agreement with existing experimental data.

Tudora et al., Nucl.Phys.A 890-891 (2012) 77 WONDER-2012

130 140 150 160 170 180 190 200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

234U(n,f)

Most probable fragmentation En = 0.5 MeV En = 3. MeV En = 5. MeV PbP calculations En = 0.5 MeV En = 3. MeV En = 5. MeV

<ν>(TKE)

TKE(MeV)

130 140 150 160 170 180 190 200 0.0 0.5 1.0 1.5 2.0 2.5

234U(n,f)

Most probable fragmentation En = 0.5 MeV En = 3. MeV En = 5. MeV PbP calculations En = 0.5 MeV En = 3. MeV En = 5. MeV

Average prompt neutron energy <ε> in SCM (MeV) TKE (MeV)

A.Tudora Report ERINDA (IRMM) August 2012

• The slope dTKE/dν does not

vary with En

• The decrease or flat behaviour
• f <ν> at low TKE values

diminishes with the En increase <ν>(TKE) and <ε>(TKE) are

• btained by averaging the

PbP matrixes ν(Z,A,TKE) and ε(Z,A,TKE) over P(Z) and

• ver the experimental Y(A,TKE)

recently measured at IRMM.

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80 90 100 110 120 130 140 150 160 10

• 9

10

• 7

10

• 5

10

• 3

10

• 1

10

1

234U(n,f) En = 0.5 MeV

TKE 150 MeV 160 MeV 170 MeV 180 MeV 190 MeV 200 MeV

Y(A,TKE) A

130 140 150 160 170 180 190 200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

234U(n,f)

exp.IRMM En = 0.5 MeV from reconstructed Y(A,TKE)

Y(TKE) TKE (MeV)

We have used the double distrib. Y(A,TKE) reconstructed from the experimental single distributions

Y(A), TKE(A), σTKE(A)

recently measured at IRMM at 14 incident energy values covering the range 0.2 MeV – 5 MeV.

• A.Tudora Report ERINDA (IRMM) August 2012

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − =

2 2

)) ( ( 2 )) ( ( exp ) ( 2 1 ) ( ) , ( A A TKE TKE A A Y TKE A Y

TKE TKE

σ σ π

∑ ∑

=

A A

A Y TKE A Y TKE Y ) ( ) , ( ) ( Verification: Y(TKE) obtained by using the reconstructed Y(A,TKE) in excellent agreement with the measured Y(TKE)

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• The correlation between the sub-barrier resonant behaviour of σ(n,f)
• f fertile actinides (pre-scission) and the visible fluctuations of their

fragment and prompt neutron data (post-scission) around En of sub- barrier resonances is outlined and supported by quantitative results in the cases 238U(n,f) and 234U(n,f).

Through the PbP treatment of prompt emission and the multi-modal fission concept (also included in the statistical model with sub-barrier effects for nuclear reactions) we arrived at a quantitative explanation of the observed fluctuations.

• New calculations of neutron induced xs of 238,234U using recent CC deform.
• ptical model parameteriz., recent values of s-wave resonance data, the

refined statistical model for fission. The consistency of present calc. is proven by all integral and differential xs in good agreement with experimental data

• PbP model used with experimental Y(A,TKE) to provide average quantities

characterizing the fission fragments and the prompt neutron emission, allow a) the quantitative support of the correlation mentioned above b) to validate the prediction of previous calculations and systematics in the case of 238U(n,f)

CONCLUSIONS CONCLUSIONS

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