IAEA Research Contract No. 15805Prompt fission neutron spectrum

calculations in the frame of extended Los Alamos and Point by Point models

First yearApplication on 233,232U(n,f) and 239Pu(n,f)

Preliminary results

Professor Dr. Anabella TUDORABucharest 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. 239Pu(n,f), 233U(n,f), 232U(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), < ε >(A), <ν>(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 compoundnucleus cross-section of the inverse process σc(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 thatcan be used (as fission c.s. ratios) to calculate PFNM and PFNS atincident energies where multiple fission chances are involved

Content of the presentation

Basic features of models based on neutron evaporation fromfully-accelerated fission fragments (Los Alamos type models)

SCM, one fragment

Tm

fm

fcfc dTTk

T 02 )exp()(

)(2),(

1

0

)/exp()()(

dTTk cff

m

mm

TT

TTTTTP

0

2)( 2

SCM, one fragmentation, “most probable fragmentation” approach. :

),(),(21)( HcLc

0 0

22

12 )/exp()()(1

mT

ffcfm

dTTTTkdT

2

2

)(

)( 02

)/exp()()(2

1),,(f

f

mEE

EE

T

fcffm

cff dTTTTkdET

EEN

LS, one fragment

),,(),,(21)( cH

HfcL

Lf EENEENEN

Obs.:Most prob.fragmentation around AH=140 where νH = νL, factobserved for all fissioning systems with experimental sawtooth data.Madland & Nix assumption (Nucl.Sci.Eng.81(1982)213) is correct.

ESnTKEExEr p )(

CN cross-section of the inverse process: DI mechanism, SCAT2 codewith optical model parameterizations appropriate for FF nuclei region:Becchetti-Greenless, Wilmore-Hodgson, Koning-Delaroche, as well as the simplified σc form proposed by Iwamoto.

Total spectrum

New form of FF residual nuclear temperature distribution (Vladuca and Tudora, Ann.Nucl.Energy 32 (2005) 1032-1046)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0

1.5

2.0

Tm

P(T) of Madland and Nix new P(T) for s=1.2

P(T

)

T

bTT

TTTP

12

02

)(

With conditions:- continuity in T=α- P(T=β)=0- normalization on 1- <T>=2Tm/3

1 swiths

parameterization in thecomputer code:

12

12

21

)1(212

120

4)1(2

)(

2

2

2

ssTT

sTTT

ss

ss

T

sTTT

ss

TTPmm

mm

m

m

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 isalso possible, leading to a non-isotropic spectrum in CMS. Another sourceof non-isotropic neutrons can be the emission at the scission moment (scission-neutrons). According to Terrel the anisotropy of neutronemission if present is symmetrical about 90o and the SCM spectrum could be described by:

3/1cos1

)(),(2

bb cm

cm

b = anisotropy parameter

sa

amf

ma

f

dTTTTs

sTks

ssT

adTTTsTksI

)/exp(2

1)()1(2

11

2)/exp()1()(

41

)( 0

2

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

dIbEEEb

b

ETEEN

f

f

EE

EEcf

fmcff

f

f

)()3/1(4

)(3/1

1

)(2

1),,(

2

)(

)(2

2

2

In the case where only one fissioning nucleus is involved: SF and neutron induced fission in En range of the first chancea) “Most probable fragmentation approach” with average values ofmodel parameters (<Er>, <TKE>, <Sn>, <Eγ>, <C>=Ac/<a>)b) “Multi-modal” fission concept: total PFNM and PFNS calculatedas superposition of the multiplicity and spectrum of each mode weighted with the modal branching ratios. Average model parametersare determined for each mode.c) Point by Point (PbP) model: the entire FF range covered by theY(A,TKE) distribution is taken into account. Total PFNM and PFNSare 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 accountthe 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.

NnBnExEx

BnEnEx

nevnnn ,...2 111

11

Fissioning nuclei of the main chain (formed by neutron evaporation from the precursor) – LA classical:

N

nnpntotp nRF

1

1

N

n

n

jnnpj

totp

ntot ENE

RFEN

1

1

1

)()()(

),(),()(

FnxnfnRF

totf

nf

n

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 byGNASH-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 chainsformed 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. emission4) Deuterons way (fiss. nuclei formed by d. emission from the nuclei of the main chain5) Alpha way (fiss. nuclei formed by alpha emission form the nuclei of the main chain6) Neutrons via alpha way (fiss. nuclei formed by n. evaporation from the nucleiformed by alpha emission

)()1()1()( ,...1 kikeviki

ki NiSExEx

)(

)1()1(

ci

ikiik a

SEx

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)

)(1

)1(1

)1(1

)( ,...2 kikeviki

ki NiSExEx

Paths: k=4 (d)

)1,...(1 )()(

1

)1()1(

kII

i

ikiik Ni

aSEx

Sk p or α separation energy from “i” precursor of main ch.

Paths: k=3 (nvp) and k=6 (nvα)

)1(1

)(1

)()(1

)(1

)(1

)( ,...2

kk

kkiev

ki

ki

ki

ExEx

NiBnExEx

)1,...(1 )()(1

)()()(

kc

i

ki

kik

i Nia

BnEx

Total and partial fission cross-section ratios

totf

ifiRF

)1(

)1( totf

IIifII

iRF )(

)( totf

IIIifIII

iRF )(

)(

)(4

2''

)( IIj

kjk

jkkj RFRF

)(6

5''

)( IIIj

kjk

jkkj RFRF

production cross sections of the j-th secondary nucleus by proton (σ2 j), neutron (σ3 j) and deuteron (σ4 j) emission and respectively by alpha and neutron via alpha emission

6

1

)(

k

ktottotal Prompt neutron multiplicity:

)(

)1( )()()(kN

ni

ki

ki

ktot iRF

)(

)()()(kN

ni

ki

ki

ktot RF

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)

)( 1

1

)()()()(

)()( )()()(

kN

ni

i

j

ki

ki

kjk

tot

kik

tot ENERF

EN

Total prompt neutron spectrum for k=2(p), 4(d) and 5(α)

)(

)()( )()()(

)()(

kN

ni

ki

kik

tot

kik

tot ENRFEN

)()( EN ki

)()( Ekj

the individual PFNS of the i-th fissioning nucleus of the k way

the evaporation spectrum of neutron emitted prior to the scissionfor 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) 221-238)Program Library of CPC id. ADLH (2000)- Most prob. fragm, σc=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 spectraof 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 chainsand ways (paths) formed by charged particle emission (high En)All versions allow also the options: σc=const and σc=the simplified formof Iwamoto

1)( 0c

4. SPECTRUM with multiple fragmentations (2002)Including 2 options:

A. Multi-modal fission approachB. Point by Point approach

Dimensioned for 300 pairs (meaning 600 fragments)

Auxiliary input files for all versions:• σc 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 modelFF pair range: all mass pairs {AL, AH} 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 chargenumber 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 LFi, HFi) quantities as: number ofprompt 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), νpair(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 < νp> , N(E), < νp>(TKE), <ε>(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) : 252Cf(SF), 248,244Cm(SF), 240,242Pu(SF), 235U(nth,f) and 239Pu(nth,f) Tudora, Ann.Nucl.Energy 37 (4) (2010) 492-497 ( for 252Cf, 248,244Cm(SF)) Tudora, Hambsch Ann.Nucl.Energy (2010) in press (7 fissioning systems)•PbP describes very well experimental < νp>(TKE) data too: 252Cf(SF), 248,244Cm(SF), 233,235U(nth,f) Tudora, Ann.Nucl.Energy 35 (2008) 1-10

Because at this meeting many results concerning 235U(nth,f) and 252Cf(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

Nper

iii

Nper

iipii

totp

pzY

pzY

1

1

Nper

iiiip

Nper

iiiiip

tot

pzY

ENpzYEN

1

1

)()(

ii

iiiip Sn

ETKEBnEnEr

)(1

1)(1

)( ENr

ENr

rEN H

ii

Li

i

ii

Hip

Lip

ir

)121(2 with

)(exp1)( 2

2

c

cZZ

cZpz p

Tudora, Morillon, Vladuca, Hambsch…Nucl.Phys.A 756 (2005) 176-191

PbP model parameters and average parameter values

Nper

iii

Nper

iiii

Ypz

paramYpzparam

1

1

parami: Eri, TKEi, Sni, Ci

Hi

Lii aaa

)1(),(1~),,( Ue

UAZWaUAZa

Nper

iii

Nper

iiii

Ypz

aYpza

1

1

aA

C CN

Level density parameter of each FF Super-fluid model (Ignatiuk)

),(* AZEU 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

80 90 100 110 120 130 140 150 1604

6

8

10

12

14

16

A/10

A/11

PbP: 1Z/A, Z=0 TKE(A) Wagemans

239Pu(nth,f)

E*L/E*H = L/H <C>=10.90 MeVE*L/E*H = aL/aH <C>=10.92 MeV

a of

FF

(1/M

eV)

A of FF

80 90 100 110 120 130 140 150 1604

6

8

10

12

14

16

A/11

PbP: 1Z/A, Z=0.5 TKE(A) Nishio

233U(nth,f)

E*L/E*H = L/H <C>=11.36 MeVE*L/E*H = aL/aH <C>=11.23 MeV

a of

FF

(1/M

eV)

A of FF

TXE partition between the two fragments of the pair

Lemaire,Talou, Madland (Los Alamos)

)*()*( iH

iLi EETXE

)(

)()(* 1 i

L

iH

ii

L aaTXEE

)(

)()(* 1 i

H

iL

ii

H aaTXEE

aL, aH super-fluid model, iterative procedureThe two FF have the same Tm (thermodynamic equilibrium)

Tudora (Bucharest))(

)(

)(*

)*(

iH

iL

iH

iL

EE

aL, aH super-fluid model. νH/(νL+ νH) 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) 024601

Tudora Ann.Nucl.Energy 33 (2006) 1030-1038

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 234U electromagnetic induced fission(Schmidt et al., Nucl.Phys.A 665 (2000) 221-267) PbP treatment to obtain Y(A) of FF for 233U(n,f)

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

Experimental P(Z) of post-n FF for 239Pu(nth,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 239Pu(nth,f)

Exp.P(Z) of 233U electrmg.ind.fiss. and of 232U(nth,f) used to obtain Y(A) of FF PbP model to calculate prompt neutron emission data for 232U(n,f)

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

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

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

PROMPT NEUTRON EMISSION DATA FOR

239Pu(n,f), 233U(n,f), 232U(n,f)PRELIMINARY / PARTIAL RESULTS

239Pu(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 <TKE> as a function of En andrenormalization 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: νH/(νL+ νH) parameterization (Tudora, 2006) Iterative procedure of Lemaire et al., 2005

239Pu(nth,f) multi-parametric representation of the PbP calculated matrix ν(A,TKE)

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

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

PbP calculations at En=th: all experimental FF distributions wereused, 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 <νp>thENDF/B-VII2.87245

TKE(A) IRMM, opt.K-D, TXE Tudora 2.87678 0.151 %TKE(A) IRMM, opt.K-D, TXE Lemaire et al 2.87607 0.126 %TKE(A) IRMM, opt.B-G, TXE Tudora 2.88279 0.360 %TKE(A) Wagemans, opt.B-G, TXE Tudora 2.86931 0.109 %

PbP calculation at other En: - σc(ε) Becchetti-Greenless parameterization- TXE partition – the iterative procedure Lemaire et al., 2005

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

PbP 1Z/A, Z=0, TKE(A) Wagemans opt B-G, TXE Tudora

<p>=2.8693

ENDF/B-VII<p>=2.87245

PbP 1Z/A, Z=0, Y(A,TKE) IRMM opt K-D, TXE Tudora <p>=2.8768 opt K-D, TXE Lemaire <p>=2.8761

239Pu(nth,f)

Werle GERKFK 84Lajtay HUNKFI 87Bojcov CCPNIR 86Nefedov RUSNIR 83Starostov RUSNIR 83

Nefedov (ratio 252Cf(SF))

Nefedov (ratio 252Cf(SF))

Starostov (ratio 252Cf(SF))Belov CCPRI 68Batenkov RUSRI 2004

Rat

io to

Max

wel

lian

TM=1

.42

MeV

E(MeV)

0 2 4 6 8 10 12 14 16 18 2010-6

10-5

10-4

10-3

10-2

10-1

100

En = 1.72 MeV PbP calculation

exp.Y(A) Akimov

239Pu(n,f)

Staples 1995 USALTI (En = 1.5 MeV)N(E

) (1/

MeV

)

E(MeV)

10-5

10-4

10-3

10-2

10-1

100

PbP calc., exp.Y(A) Akimov calc. at En = 0.72 MeV calc. at En = 0.5 MeV

239Pu(n,f)

Staples 1995 USALTI (En = 0.5 MeV)

N(E

) (1/

MeV

)

0 2 4 6 8 10 12 14 16 18 2010-6

10-5

10-4

10-3

10-2

10-1

100

En = 4.48 MeV

PbP calc.,exp.Y(A) Akimov

239Pu(n,f)

Staples 1995 USALTI (En = 3.5 MeV)

N(E

) (1/

MeV

)

E(MeV)

10-5

10-4

10-3

10-2

10-1

100

En = 2.72 MeV

PbP calc.,exp.Y(A) Akimov

239Pu(n,f)

Staples 1995 USALTI (En = 2.5 MeV)

N(E

) (1/

MeV

)

En (MeV) <Er>(MeV) <TKE>(MeV) <Sn>(MeV) <C>(MeV)

th (Wagem)th (IRMM)

197.650197.648

177.932177.811

5.52735.5273

10.8985 (Tudora)

10.8936 (Tudora)

10.9138 (Lemaire)

0.72 196.961 177.428 5.4823 10.8168

1.72 196.949 177.290 5.4950 10.8201

2.72 196.821 176.979 5.4923 10.8153

4.48 196.779 176.142 5.5147 10.7713

239Pu(n,f) average model parameter values obtained from PbP treatment

239Pu(n,f) MOST PROBABLE FRAGMENTATION APPROACH

Using average model parameter values obtained by PbP treatment

1)( 0c Iwamoto spectrum shape close to the case σc=const

Most probable fragmentation approach – calculation at En wheremore fission chances are involved (up to En = 20 MeV, only thefission 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+239Pu, 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.

),(),(

, FnxnfnRF xnfn

provided by BRC are preferable.

Previous calculations using RF of BRC evaluation, 30 MeV

0 5 10 15 20 25 302.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

Tudora, 2006

ENDF/B-VII JENDL/AC

Exp.data renormalized to 256Cf(SF) NUP=3.756 (Manero)

239Pu(n,f)

Tudora, Vladuca, Morillon calc.2002 JEFF3.1

Hopkins USALAS 63/84Leroy FRSAC 80,Smirenkin,JohnslomLiu Zu-Hua CPRAEP84Manero IAE 80Frehaut BRC 80Other (En=th)

Gwin ORNL 84Nurpeisov CCPFEI 85, , Mather UKALD 84,85 , Gwin USAORL 87,86, Frehaut BRC 80,73/03Zang CPRAER 80,85, Volodin CCPFEI 73/85Boldeman AULAUA 71/04Soleihac,Frehaut BRC 84Nesterov RUSFEI 70/02Conde SWDFOA 68/83

PFN

M

En (MeV)

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

0 5 10 15 202.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Tudora, 2006

ENDF/B-VII JENDL/AC

Exp.data renormalized to 256Cf(SF) NUP=3.756 (Manero)

239Pu(n,f)

Tudora, Vladuca, Morillon calc.2002 JEFF3.1

Hopkins USALAS 63/84Leroy FRSAC 80,Smirenkin,JohnslomLiu Zu-Hua CPRAEP84Manero IAE 80Frehaut BRC 80Other (En=th)

Gwin ORNL 84Nurpeisov CCPFEI 85, , Mather UKALD 84,85 , Gwin USAORL 87,86, Frehaut BRC 80,73/03Zang CPRAER 80,85, Volodin CCPFEI 73/85Boldeman AULAUA 71/04Soleihac,Frehaut BRC 84Nesterov RUSFEI 70/02Conde SWDFOA 68/83

PFN

M

En (MeV)

233U(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: νH/νpair parameterizations of Tudora done in 2006 (Ann.Nucl.Energy 33, 1030-1038) and new parameteriz. (February 2010) Lemaire, Talou et al. method (equal residual nuclear temperature of FF forming a pair).

PbP calc. ΔZ=0.5Y(A,TKE) Nishio

<νp>th Dev.ENDF/B-VII 2.4894

Optical pot.B-G, TXE Tudora 2006 2.4871 0.092 %

Optical pot.B-G, TXE Tudora 2010 2.4853 0.165 %

Optical pot.B-G, TXE Lemaire 2005 2.4880 0.056 %

Optical pot.K-D, TXE Tudora 2010 2.4745 0.599 %

Optical pot.B-G, TXE Tudora 2010Y(A,TKE) of Surin

2.4027 3.48 %

Prompt neutron multiplicity resuts at thermal En:

Tudora, Ann.Nucl.Energy 33 (2006) 1030-1038

Most probable fragmentation approach calculations

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

A. Tudora, Annals of Nuclear Energy 37(1) (2010) 43-51Fig.9: 232U(nth,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) 43-51Fig.10: 232U(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.