94-Pu-236 JAEA+ EVAL-FEB10 O.Iwamoto, T.Nakagawa, et al.
DIST-MAY10 20100318
----JENDL-4.0 MATERIAL 9428
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
History
06-04 Resonance parameters and fission cross section were revised.
07-02 Theoretical calculation was made with CCONE code.
07-05 Re-calculation with CCONE code was made.
Data were compiled as JENDL/AC-2008/1/.
09-02 (1,452), (1,455) and (1,456) were revised.
10-02 Data of prompt gamma rays due to fission were given.
10-03 Covariance data were given.
MF= 1 General information
MT=452 Number of Neutrons per fission
Sum of MT's = 455 and 456.
MT=455 Delayed neutron data
Average values of systematics by Tuttle/2/, Benedetti et al.
/3/ and Waldo et al./4/, and partial fission cross sections
calculated with CCONE code/5/
Decay constants were assumed to be the same as those of Pu-238
calculated by Brady and England/6/.
MT=456 Number of prompt neutrons per fission
Based on systematics by Ohsawa/7/.
MF= 2 Resonance parameters
MT=151
Resolved resonance parameters (below 10 eV)
The resonance parameters of ENDF/B-VI were adopted and those
of a negative resonance were modified to reproduce the thermal
fission cross section of 141+-15 b which were derived from the
experimental data of Gindler et al./8/, Hulet et al./9/,
Belyaev et al./10/
Unresolved resonance parameters (10 eV - 40 keV)
Parameters were determined with ASREP code/11/ to reproduce
the fission cross section determined from the experimental
data/12,13/, and total and capture cross sections calculated
with CCONE code/5/. The parameters are used only for self-
shielding calculations.
Thermal cross sections and resonance integrals (at 300K)
-------------------------------------------------------
0.0253 eV reson. integ.(*)
(barns) (barns)
-------------------------------------------------------
total 176.72
elastic 9.20
fission 139.96 971
capture 27.56 248
-------------------------------------------------------
(*) In the energy range from 0.5 eV to 10 MeV.
MF= 3 Neutron cross sections
Cross sections above the resolved resonance region except for
the elastic scattering (MT=2) and fission cross sections (MT=18,
19, 20, 21, 38) were calculated with CCONE code/5/.
MT= 1 Total cross section
The cross section was calculated with CC OMP of Soukhovitskii
et al./14/
MT=2 Elastic scattering cross section
Calculated as total - non-elstic scattering cross sections
MT=18 Fission cross section
The following experimental data were analyzed in the energy
range from 100 eV to 4 MeV with the GMA code/15/:
Authors Energy range Data points Reference
Gromova+ 7.14 eV - 5.78 MeV 106 /12/
Gerasimov+ 15.8 eV - 34 keV 9 /13/
Below 80 eV, resonance structure was reproduced by eye-
guiding. Avove 5.5 MeV, cross sections calculated with CCONE
code were adopted.
The simulated (n,f) cross sections of Britt and Wilhelmy/16/,
and the experimental data of Gromova et al./12/, Gerasimov et
al./13/ and Vorotnikov et al./17/ were used to determine
the parameters in the CCONE calculation.
MT=19, 20, 21, 38 Multi-chance fission cross sections
Calculated with CCONE code, and renormalized to the total
fission cross section (MT=18).
MF= 4 Angular distributions of secondary neutrons
MT=2 Elastic scattering
Calculated with CCONE code.
MT=18 Fission
Isotropic distributions in the laboratory system were assumed.
MF= 5 Energy distributions of secondary neutrons
MT=18 Prompt fission neutrons
Calculated with CCONE code.
MF= 6 Energy-angle distributions
Calculated with CCONE code.
Distributions from fission (MT=18) are not included.
MF=12 Photon production multiplicities
MT=18 Fission
Calculated from the total energy released by the prompt
gamma-rays due to fission which was estimated from its
systematics, and the average energy of gamma-rays.
MF=14 Photon angular distributions
MT=18 Fission
Isotoropic distributions were assumed.
MF=15 Continuous photon energy spectra
MT=18 Fission
Experimental data measured by Verbinski et al./18/ for
Pu-239 thermal fission were adopted.
MF=31 Covariances of average number of neutrons per fission
MT=452 Number of neutrons per fission
Sum of covariances for MT=455 and MT=456.
MT=455
Error of 15% was assumed.
MT=456
Covariance was obtained by fitting a linear function to the
data at 0.0 and 5.0 MeV with an uncertainty of 5%.
MF=32 Covariances of resonance parameters
MT=151 Resolved resonance parameterss
Format of LCOMP=0 was adopted.
Uncertainties of parameters were assumed as follows:
Resonance energy 0.1 %
Neutron width 10 %
Capture width 50 %
Fission width 20 %
They were further modified by considering experimental data
of the fission cross section at the thermal neutron energy.
MF=33 Covariances of neutron cross sections
Covariances were given to all the cross sections by using
KALMAN code/19/ and the covariances of model parameters
used in the cross-section calculations.
For the fission cross section, covariances obtained with the
GMA analysis were adopted. Standard deviations (SD) were
multiplied by a factor of 1.5. SD's of 15% were assumed in the
energy region below 86 eV and above 4 MeV.
In the resolved resonance region, the following standard
deviations were added to the contributions from resonance
parameters:
Total 2 b
Elastic scattering 20 %
MF=34 Covariances for Angular Distributions
MT=2 Elastic scattering
Covariances were given only to P1 components.
MF=35 Covariances for Energy Distributions
MT=18 Fission spectra
Estimated with CCONE and KALMAN codes.
*****************************************************************
Calculation with CCONE code
*****************************************************************
Models and parameters used in the CCONE/5/ calculation
1) Coupled channel optical model
Levels in the rotational band were included. Optical model
potential and coupled levels are shown in Table 1.
2) Two-component exciton model/20/
* Global parametrization of Koning-Duijvestijn/21/
was used.
* Gamma emission channel/22/ was added to simulate direct
and semi-direct capture reaction.
3) Hauser-Feshbach statistical model
* Moldauer width fluctuation correction/23/ was included.
* Neutron, gamma and fission decay channel were included.
* Transmission coefficients of neutrons were taken from
coupled channel calculation in Table 1.
* The level scheme of the target is shown in Table 2.
* Level density formula of constant temperature and Fermi-gas
model were used with shell energy correction and collective
enhancement factor. Parameters are shown in Table 3.
* Fission channel:
Double humped fission barriers were assumed.
Fission barrier penetrabilities were calculated with
Hill-Wheler formula/24/. Fission barrier parameters were
shown in Table 4. Transition state model was used and
continuum levels are assumed above the saddles. The level
density parameters for inner and outer saddles are shown in
Tables 5 and 6, respectively.
* Gamma-ray strength function of Kopecky et al/25/,/26/
was used. The prameters are shown in Table 7.
------------------------------------------------------------------
Tables
------------------------------------------------------------------
Table 1. Coupled channel calculation
--------------------------------------------------
* rigid rotor model was applied
* coupled levels = 0,1,2,3,4 (see Table 2)
* optical potential parameters /14/
Volume:
V_0 = 49.97 MeV
lambda_HF = 0.01004 1/MeV
C_viso = 15.9 MeV
A_v = 12.04 MeV
B_v = 81.36 MeV
E_a = 385 MeV
r_v = 1.2568 fm
a_v = 0.633 fm
Surface:
W_0 = 17.2 MeV
B_s = 11.19 MeV
C_s = 0.01361 1/MeV
C_wiso = 23.5 MeV
r_s = 1.1803 fm
a_s = 0.601 fm
Spin-orbit:
V_so = 5.75 MeV
lambda_so = 0.005 1/MeV
W_so = -3.1 MeV
B_so = 160 MeV
r_so = 1.1214 fm
a_so = 0.59 fm
Coulomb:
C_coul = 1.3
r_c = 1.2452 fm
a_c = 0.545 fm
Deformation:
beta_2 = 0.21978
beta_4 = 0.07414
beta_6 = -0.00968
* Calculated strength function
S0= 1.11e-4 S1= 2.50e-4 R'= 9.45 fm (En=1 keV)
--------------------------------------------------
Table 2. Level Scheme of Pu-236
-------------------
No. Ex(MeV) J PI
-------------------
0 0.00000 0 + *
1 0.04463 2 + *
2 0.14745 4 + *
3 0.30580 6 + *
4 0.51570 8 + *
5 0.77350 10 +
-------------------
*) Coupled levels in CC calculation
Table 3. Level density parameters
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Pu-237 18.3022 0.7795 1.8799 0.3586 -0.5090 2.5865
Pu-236 18.2358 1.5623 1.9752 0.3737 0.1216 3.5619
Pu-235 18.1694 0.7828 1.9791 0.3502 -0.4208 2.4828
Pu-234 18.1029 1.5689 2.1707 0.3732 0.1282 3.5689
--------------------------------------------------------
Table 4. Fission barrier parameters
----------------------------------------
Nuclide V_A hw_A V_B hw_B
MeV MeV MeV MeV
----------------------------------------
Pu-237 5.800 0.800 5.800 0.520
Pu-236 6.000 1.040 5.000 0.600
Pu-235 6.000 0.800 5.000 0.520
Pu-234 5.600 1.040 4.600 0.600
----------------------------------------
Table 5. Level density above inner saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Pu-237 20.1324 0.9094 2.6000 0.3320 -1.5137 2.9094
Pu-236 20.0594 1.8226 2.6000 0.3326 -0.6004 3.8226
Pu-235 19.9863 0.9133 2.6000 0.3333 -1.5098 2.9133
Pu-234 19.9132 1.8304 2.6000 0.3339 -0.5927 3.8304
--------------------------------------------------------
Table 6. Level density above outer saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Pu-237 20.1324 0.9094 0.3000 0.3706 -0.7963 2.9094
Pu-236 20.0594 1.8226 0.2600 0.3719 0.1175 3.8226
Pu-235 19.9863 0.9133 0.2200 0.3732 -0.7913 2.9133
Pu-234 19.9132 1.8304 0.1800 0.3744 0.1264 3.8304
--------------------------------------------------------
Table 7. Gamma-ray strength function for Pu-237
--------------------------------------------------------
K0 = 1.501 E0 = 4.500 (MeV)
* E1: ER = 10.90 (MeV) EG = 2.50 (MeV) SIG = 300.00 (mb)
ER = 13.80 (MeV) EG = 4.70 (MeV) SIG = 450.00 (mb)
* M1: ER = 6.63 (MeV) EG = 4.00 (MeV) SIG = 2.67 (mb)
* E2: ER = 10.18 (MeV) EG = 3.27 (MeV) SIG = 6.80 (mb)
--------------------------------------------------------
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