94-Pu-238 JAEA+ EVAL-JAN10 O.Iwamoto,T.Nakagawa +
DIST-MAY10 20100303
----JENDL-4.0 MATERIAL 9434
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
History
06-02 Fission cross section was revised.
06-07 Resolved resonance parameters were revised.
07-05 Theoretical calculation was made with CCONE code.
Data were compiled as JENDL/AC-2008/1/.
09-08 (MF1,MT458) was evaluated.
09-12 New theoretical calculation was made with CCONE code.
10-01 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
Determined from nu-d of the following three nuclides and
partial fission cross sections calculated with CCONE code/2/.
Pu-239 = 0.004710
Pu-238 = 0.0026
Pu-237 = 0.0018
The value of Pu-239 are averages of systematics
by Tuttle/3/, Benedetti et al./4/ and
Waldo et al./5/ Other two are 20% decreased
from the systematics.
Decay constants calculated by Brady and England./6/ were
adopted.
MT=456 Number of prompt neutrons per fission
Based on the systematics recommended by Ohsawa/7/.
The result is in very good agreement with experimental data
of Kroshin and Zamjatnin/8/, and Jaffy and Lerner/9/.
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/10/. 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 2000/11/ does
not include average neutron energy values, the average values
were calculated using the formula shown in the report by
T.R. England/12/. The fractions of prompt energy were
calculated using the fractions of Sher's evaluation/13/ 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 (below 500 eV)
Based on the resonance parameters reported by Young et
al./14/, Silbert et al. /15/ and Alam et al./16/.
These parameters were adjusted to the thermal cross
sections:
Total = 588 b /14/
Fission = 17.7 b /17,18,19,20/
Capture = 412 b /21/
Unresolved resonance parameters (500 eV - 60 keV)
Parameters were determined with ASREP code /22/ to reproduce
the total, fission and capture cross sections described below
Since the fission cross section in this energy region had
resonance structure, average cross sections were used in the
fitting. 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 585.18
elastic 154.56
fission 17.77 27.6
capture 412.85 146
-------------------------------------------------------
(*) 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 total (MT=1), 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
Below 10 keV, total cross section was calculated as a sum of
elastic scattering and capture cross sections calculated with
CCONE code /2/ and fission cross section determined from
expeimental data (see MT=18). Above 10 keV, the cross-section
data calculated with CCONE code were adopted. The calculation
was made with CC OMP of Soukhovitskii et al./23/.
MT=2 Elastic scattering cross section
Below 10 keV, the elastic scattering cross section was calcu-
lated with CCONE code. Above 10 keV, it was obtained as (total
cross section) - (partial cross sections).
MT=18 Fission cross section
The following experimental data were analyzed in the energy
range above 450 eV with the GMA code/24/:
Authors Energy range Data points Reference
Fumushkin+ 0.44 - 3.62 MeV 14 /25/(*1)
Drake+ 450 eV - 2.58 MeV 774 /26/
Silbert+ 451 eV - 2.97 MeV 4228 /15/
Knitter+ 0.146 - 9.94 MeV 89 /27/(*1)
Budtz-Jorgensen+
0.45 - 265 keV 602 /28/
Aleksandrov+ 2.9 MeV 1 /29/
Fursov+ 0.149 - 14.7 MeV 71 /30/(*2)
(*1) Ratio to U-235 fission, (*2) Ratio to Pu-239 fission.
JENDL-3.3 data was used to convert them to cross sections.
The results of GMA were used to determine the parameters in
the CCONE calculation.
Above 10 MeV, the cross section was determined with 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 Silbert
et al./15/ were used to determine the model parameters of
CCONE code.
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.
MT=455 Delayed neutron spectra
Summation calculation by Brady and England /6/ 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./31/ for
Pu-239 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
Error of 15% was assumed below 5 MeV and above 5 MeV,
respectively.
MT=456
Covariance was obtained by fitting a linear function to the
data at the thermal energy and 5 MeV assuming errors of 3%
and 5%, respectively. The error at the thermal energy was
estimated from experimental data/8,9/
MF=32 Covariances of resonance parameters
Format of LCOMP=0 was adopted.
Standard deviations were adopted from the data of Silbert et
al./15/ Error of the capture width was assumed to be 18%.
Error of 0.1% was given to the resonance energies.
MF=33 Covariances of neutron cross sections
Covariances were given to all the cross sections by using
KALMAN code/32/ and the covariances of model parameters
used in the theoretical calculations.
For the following cross sections, covariances were determined
by different methods.
MT=1 Total cross section
In the energy region from 1 to 500eV, uncertainty of 10 %
was added.
MT=2 Elastic scattering cross sections
In the resonance region (below 500eV), uncertainty of 10 %
was added.
MT=18 Fission cross section
Above the resonance region, cross section was evaluated with
GMA code/24/. Standard deviations obtained were multiplied
by a factor of 2.0. Above 12 MeV, they were assumed to be 20%.
MT=102 Capture cross section
In the resonance region, addtional error of 10 % was given.
Above 400 eV, covariance matrix was obtained with CCONE and
KALMAN codes/32/.
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/33/
* Global parametrization of Koning-Duijvestijn/34/
was used.
* Gamma emission channel/35/ was added to simulate direct
and semi-direct capture reaction.
3) Hauser-Feshbach statistical model
* Moldauer width fluctuation correction/36/ 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/37/. 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/38/,/39/
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 /23/
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 = 0.22495
beta_4 = 0.07282
beta_6 = -0.01518
* Calculated strength function
S0= 1.11e-4 S1= 2.54e-4 R'= 9.40 fm (En=1 keV)
--------------------------------------------------
Table 2. Level Scheme of Pu-238
-------------------
No. Ex(MeV) J PI
-------------------
0 0.00000 0 + *
1 0.04408 2 + *
2 0.14595 4 + *
3 0.30338 6 + *
4 0.51358 8 + *
5 0.60514 1 -
6 0.66140 3 -
7 0.76324 5 -
8 0.77348 10 +
9 0.94146 0 +
10 0.96278 1 -
11 0.96820 2 -
12 0.98309 2 +
13 0.98545 2 -
14 1.01860 3 +
15 1.02854 2 +
16 1.06994 3 +
17 1.08010 12 +
18 1.08256 4 -
19 1.12576 4 +
20 1.13400 0 +
21 1.17440 2 +
22 1.20246 3 -
23 1.22865 0 +
24 1.25200 7 -
-------------------
*) 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-239 18.4349 0.7762 1.8503 0.3560 -0.5001 2.5655
Pu-238 18.3685 1.5557 1.9652 0.3804 0.0287 3.6608
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
--------------------------------------------------------
Table 4. Fission barrier parameters
----------------------------------------
Nuclide V_A hw_A V_B hw_B
MeV MeV MeV MeV
----------------------------------------
Pu-239 6.050 0.700 5.700 0.600
Pu-238 5.500 0.600 4.800 0.600
Pu-237 5.800 0.800 5.800 0.520
Pu-236 6.000 1.040 5.000 0.600
----------------------------------------
Table 5. Level density above inner saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Pu-239 20.2784 0.9056 2.6000 0.3523 -1.8394 3.2056
Pu-238 20.2054 1.8150 2.6000 0.3668 -1.1448 4.3150
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
--------------------------------------------------------
Table 6. Level density above outer saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Pu-239 20.2784 0.9056 0.3800 0.3901 -1.0534 3.2056
Pu-238 20.2054 1.8150 0.3400 0.4053 -0.3124 4.3150
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
--------------------------------------------------------
Table 7. Gamma-ray strength function for Pu-239
--------------------------------------------------------
K0 = 1.800 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 = 6.61 (MeV) EG = 4.00 (MeV) SIG = 3.04 (mb)
* E2: ER = 10.15 (MeV) EG = 3.24 (MeV) SIG = 6.79 (mb)
--------------------------------------------------------
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