92-U -236 JAEA+ EVAL-JAN10 O.Iwamoto, T.Nakagawa, et al.
DIST-MAY10 20100302
----JENDL-4.0 MATERIAL 9231
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
History
05-10 Fission cross section was evaluated with GMA code.
06-06 Resonance parameters were modified.
07-05 Theoretical calculation was made with CCONE code.
07-12 Resonance parameters were modified.
Data were compiled as JENDL/AC-2008/1/.
09-03 (MF1,MT455) was modified.
09-08 (MF1,MT458) was evaluated.
09-11 (MF1,MT455) was modified.
New theoretical calculation was made with CCONE code.
10-01 Data of prompt gamma rays due to fission were given.
10-02 Covariance data were given.
MF=1 General Information
MT=452 Total number of neutrons per fission
Sum of MT's 455 and 456.
MT=455 Delayed neutrons per fission
Determined from nu-d of the following three nuclides and
partial fission cross sections calculated with CCONE code/2/.
U -237 = 0.02250
U -236 = 0.007
U -235 = 0.004
The data for U-237 is average of experimental data
of Roschenko et al./3/
For the other nuclide, estimated so as to reproduce
the data of Bobkov et al./4/ at 14.7 MeV.
Six group decay constants were adopted from Brady and England
/5/.
MT=456 Prompt neutrons per fission
(same as JENDL-3.3)
Taken from Malinovskii's paper/6/. Above 5.9 MeV, their
recommendation was extrapolated.
MT=458 Components of energy release due to fission
Total energy and prompt energy were calculated from mass
balance using JENDL-4 fission yields data and mass excess
evaluation. Mass excess values were from Audi's 2009
evaluation/7/. Delayed energy values were calculated from
the energy release for infinite irradiation using JENDL FP
Decay Data File 2000 and JENDL-4 yields data. For delayed
neutron energy, as the JENDL FP Decay Data File 2000/8/ does
not include average neutron energy values, the average values
were calculated using the formula shown in the report by
T.R. England/9/. The fractions of prompt energy were
calculated using the fractions of Sher's evaluation/10/ when
they were provided. When the fractions were not given by Sher,
averaged fractions were used.
MF= 2 Resonance parameters
MT=151
Resolved resonance parameters (MLBW: 1.0-5 eV - 4.0 keV)
Parameters were based on the data of Macklin and
Alexander/11/, Parker et al./12/, and recommendation of
Mughabghab/13/:
Parameters above 20 eV: Macklin and Alexander
5.45-eV resonancd: Mughabghab
Fission widths: Parker et al.
The parameters of 5.45-eV resonance were adjusted so as to
reproduce the fission cross section measured by Wagemans et
al./14/ and capture resonance integral of about 350 b/15,16,
17/
P-wave resonances were assigned according to Carraro and
Brusegan/18/. Capture widths were adjusted so as to reproduce
well the capture cross sections measured by Adamchuk et
al./19/ and Muradian et al./20/.
A negative resonance was assumed at -9.7eV/13/. Its
parameters were adjusted to the thermal cross sections.
The thermal cross sections to be reproduced:
Fission = 0.00022 +- 0.00002 b
Wagemans et al./14/
Capture = 5.12 +- 0.09 b
Davletshin et al./21/, Vorona et al./22/, Carlson /23/,
Schuman et al./16/ etc.
Elastic scattering = 10.6 +- 0.7 b
Mc Callum /24/
Total = 16.0 +- 0.1 b
Vorona et al./22/
Unresolved resonance parameters (4 keV - 100 keV)
Determined to reproduce the total and capture cross sections
with ASREP code/25/. 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 15.95
elastic 10.83
fission 0.00026 2.22
capture 5.122 353
-------------------------------------------------------
(*) 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/2/.
MT= 1 Total cross section
The cross section was calculated with CC OMP of Soukhovitskii
et al./26/
MT=2 Elastic scattering cross section
Calculated as total - non-elstic scattering cross sections.
MT=18 Fission cross section
Above 300keV, the following experimental data were analyzed
with the GMA code/27/:
Authors Energy range Data points Reference
Behrens+ 0.172 - 20.0 MeV 129 /28/(*1)
Meadows 0.596 - 9.91 MeV 57 /29/(*1)
Nordborg+ 3.21 - 8.62 MeV 40 /30/(*1)
Goverdovskii+ 4.24 - 10.7 MeV 39 /31/(*1)
Fursov+ 1.48 - 7.4 MeV 70 /32/(*1)
Goverdovskii+ 15.1 - 16.4 MeV 2 /33/(*1)
Terayama+ 0.99 - 6.99 MeV 27 /34/(*1)
Meadows 14.7 MeV 1 /35/(*1)
Shpak+ 0.5 - 3.72 MeV 77 /36/(*1)
(*1) Relative to U-235 fission. Data were converted to
cross sections using JENDL-3.3 data.
The results of GMA were used to determine the parameters in
the CCONE calculation.
Between 4 and 300 keV, the data in the resolved resonance
region and those above 300 keV were connected by eye-guiding.
MT=19, 20, 21, 38 Multi-chance fission cross sections
Calculated with CCONE code, and renormalized to the total
fission cross section (MT=18).
MT=102 Capture cross section
Calculated with CCONE code. The experimental data of Bergman
et al./37/, Adamchuk et al./19/, Kazakov et al./38/, and
Buleeva et al./39/ were considered to determine the model
parameters for CCONE calculation.
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 neutron spectra
Calculated with CCONE code.
MT=455 Delayed neutron spectra
(same as JENDL-3.3)
Summation calculation made by Brady and England /5/ was
adopted.
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 given in MF=1/MT=458 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./40/ for
U-235 thermal fission were adopted.
MF=31 Covariances of average number of neutrons per fission
MT=452 Number of neutrons per fission
Combination of covariances for MT=455 and MT=456.
MT=455
Assumed uncertainties:
En < 5 MeV 5% /3/
5 MeV < En < 7 MeV 15%
7 MeV < En < 20 MeV 20%
MT=456
Covariance was obtained by fitting a stlight line to data
measured by Malinovskii et al./6/
MF=32 Covariances of resonance parameters
Format of LCOMP=0 was adopted.
Errors of neutron and capture widths for the levels above 29
eV were based on the data of Macklin and Alexander/11/.
Those of fission widths were taken from Ref./12/
Error of the 5.456-eV level capture width was recommendation
of Mughabghab/13/. For the neutron and capture widths,
error of 5 % was assumed.
Error of resonance energies was assumed to be 0.02%/11/.
Addtional error of 90 % was given to fission cross section
below above 10 eV in MF=33. The parameters of 5.45-eV
resonance were determined so that the fission cross section
measured by Wagemans et al./14/ were reproduced well.
Therefore the cross section around this resonance was well
determined. Additional error of 8% was assumed below 1 eV.
For the capture cross section, contributions of resonance
parameter errors to the cross section are only a few %.
Since it seemes to be too small, uncertainties of 5% were
added in the energy range from 50 eV to 4 keV.
For the total and elastic scttering cross sections, error of
5% was added.
MF=33 Covariances of neutron cross sections
Covariances were given to all the cross sections by using
KALMAN code/41/ and the covariances of model parameters
used in the theoretical calculations.
For the following cross sections, covariances were determined
by different methods.
MT=18 Fission cross section
Evaluated with GMA code/27/.
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/2/ 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/42/
* Global parametrization of Koning-Duijvestijn/43/
was used.
* Gamma emission channel/44/ was added to simulate direct
and semi-direct capture reaction.
3) Hauser-Feshbach statistical model
* Moldauer width fluctuation correction/45/ 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/46/. 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/47/,/48/
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 /26/
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 = 0.213213
beta_4 = 0.066
beta_6 = 0.0015
* Calculated strength function
S0= 0.89e-4 S1= 2.40e-4 R'= 9.52 fm (En=1 keV)
--------------------------------------------------
Table 2. Level Scheme of U-236
-------------------
No. Ex(MeV) J PI
-------------------
0 0.00000 0 + *
1 0.04524 2 + *
2 0.14948 4 + *
3 0.30978 6 + *
4 0.52224 8 + *
5 0.68760 1 -
6 0.74415 3 -
7 0.78230 10 +
8 0.84830 5 -
9 0.91921 0 +
10 0.95799 2 +
11 0.96030 2 +
12 0.96663 1 -
13 0.98767 2 -
14 0.99980 7 -
15 1.00150 3 +
16 1.03560 3 -
17 1.05085 4 +
18 1.05289 4 -
19 1.05861 4 +
20 1.06610 3 +
21 1.07000 4 -
22 1.08530 12 +
23 1.09380 2 +
24 1.10440 5 -
25 1.11067 2 -
26 1.12690 5 +
27 1.14700 4 +
28 1.14940 3 -
29 1.16400 5 -
-------------------
*) Coupled levels in CC calculation
Table 3. Level density parameters
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
U-237 18.3937 0.7795 2.7455 0.3633 -0.6631 2.7715
U-236 18.6005 1.5623 2.7551 0.3859 -0.1547 3.8920
U-235 18.4419 0.7828 2.6265 0.3721 -0.7434 2.8828
U-234 18.4650 1.5689 2.5578 0.3902 -0.1511 3.9087
U-233 18.3972 0.7861 2.4694 0.3708 -0.6995 2.8410
--------------------------------------------------------
Table 4. Fission barrier parameters
----------------------------------------
Nuclide V_A hw_A V_B hw_B
MeV MeV MeV MeV
----------------------------------------
U-237 6.100 0.600 5.900 0.600
U-236 6.500 1.100 5.230 0.600
U-235 5.790 0.400 5.470 0.300
U-234 6.180 1.040 5.080 0.600
U-233 5.970 0.800 5.450 0.520
----------------------------------------
Table 5. Level density above inner saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
U-237 20.4984 0.9094 2.6000 0.3286 -1.5020 2.9094
U-236 21.8830 1.8226 2.6000 0.3308 -0.7586 4.0226
U-235 18.1694 0.9133 2.6000 0.3671 -1.7919 3.1133
U-234 20.2753 1.8304 2.6000 0.3306 -0.5810 3.8304
U-233 20.2008 0.9172 2.6000 0.3312 -1.4942 2.9172
--------------------------------------------------------
Table 6. Level density above outer saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
U-237 21.9626 0.9094 0.1800 0.3813 -1.1131 3.3094
U-236 20.4241 1.8226 0.1400 0.4250 -0.5513 4.6226
U-235 18.1694 0.9133 0.1000 0.4121 -0.9812 3.1133
U-234 20.2753 1.8304 0.0600 0.3719 0.1310 3.8304
U-233 20.2008 0.9172 0.0200 0.3732 -0.7817 2.9172
--------------------------------------------------------
Table 7. Gamma-ray strength function for U-237
--------------------------------------------------------
K0 = 1.650 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 = 2.86 (mb)
* E2: ER = 10.18 (MeV) EG = 3.27 (MeV) SIG = 6.51 (mb)
--------------------------------------------------------
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