91-Pa-231 JAEA+ EVAL-JAN10 O.Iwamoto, T.Nakagawa, et al.
DIST-MAY10 20100323
----JENDL-4.0 MATERIAL 9131
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
History
05-11 Fission cross section was evaluated with GMA code.
06-08 Resonance parameters were revised.
07-10 Theoretical calculation was performed with CCONE code.
Data were compiled as JENDL/AC-2008/1/.
09-04 MF01 was revised.
09-08 (MF1,MT458) was evaluated.
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 fissioning
nuclides and partial fission cross sections calculated with
CCONE code/2/.
Pa-232 = 0.01083
Pa-231 = 0.007461
Pa-230 = 0.005154
They are averages of systematics by Tuttle/3/,
Benedetti et al./4/ and Waldo et al./5/
Decay constants were evaluated by Brady and England/6/.
MT=456 Number of prompt neutrons per fission
Estimated from Ohsawa's systematics/7/.
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/8/. 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 2000/9/ does
not include average neutron energy values, the average values
were calculated using the formula shown in the report by
T.R. England/10/. The fractions of prompt energy were
calculated using the fractions of Sher's evaluation/11/ 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; below 115 eV)
The resonance parameters of JENDL-3.3 were based on the
following data:
Resonance energies, neutron and gamma widths:
Hussein et al./12/
Fission area: Plattard et al./13/
Parameters of resonances below 1.24 eV: Mughabghab/14/
Those data were revised by comparing with the total cross
section of Simpson et al./15/ and the fission cross section
of Kobayashi et al./16/
The resonance formula was changed to MLBW. Total spin of each
level was assumed with JCONV code/17/.
Thermal cross section and resonance integral calculated from
the present resonance parameters are given in the following
table. The thermal cross sections to be reproduced were
determined from experimental data:
Total = 211.0+-3.1 b
Simpson et al./15/
Fission = 0.0239+-0.0007 b
Wagemans et al./18,19/, Kobayashi et al./20/
Capture = 202.2+-5.3 b
Smith et al./21/, Aleksandrov et al./22/,
Gryntakis et al./23/, Kobayashi/24/
The capture resonance integrals reported by Jurova et al./25/
and Aleksandrov et al./22/ were 1044b and 1180b, respectively.
Unresolved resonance parameters (115 eV - 10 keV)
Cross sections were reproduced with average resonance
parameters determined by ASREP code/26/. These parameters
are used only for self-shielding effects.
Thermal cross sections and resonance integrals (at 300K)
-------------------------------------------------------
0.0253 eV reson. integ.(*)
(barns) (barns)
-------------------------------------------------------
total 212.32
elastic 10.59
fission 0.0236 3.24
capture 201.71 542
-------------------------------------------------------
(*) 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
elastic scattering and fission cross sections (MT's =2, 18-21,
38) were calculated with CCONE code/2/.
MT= 1 Total cross section
The cross section was calculated with CC OMP of Soukhovitskii
et al./27/ with modification of the quadrupole deformation
parameter.
MT=2 Elastic scattering cross section
Calculated as total - non-elstic scattering cross sections
MT=18 Fission cross section (Above 115 eV)
The following experimental data were analyzed in the energy
ranges from 115 eV to 12 keV, and from 110 keV to 12 MeV with
the GMA code/28/:
Authors Energy range Data points Reference
Plattard+ 0.112 - 16.9 MeV 4120 /29/
Fursov+ 0.135 - 7.4 MeV 69 /30/(*1)
Kobayashi+ 0.089 - 12.6 keV 44 /16/
Oberstedt+ 0.76 - 3.46 MeV 15 /31/
(*1) The data were measured relatively to Pu-239 fission.
They were converted to Pa-231 fission by using JENDL-
3.3 data.
The results of the analysis were adopted in the energy ranges
from 115 eV to 10 keV and from 120 keV to 9.5 MeV.
CCONE calculation was adopted in the energy ranges from 10 to
120 keV and above 9.5 MeV.
The results of GMA below 10 MeV, the preliminary experimental
data of IRMM/32/ above 15 MeV, and the experimental data of
Birgul and Lyle/33/ at 15 MeV 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/2/.
MT=18 Fission
Isotropic distributions in the laboratory system were assumed.
MF= 5 Energy distributions of secondary neutrons
MT=18 Prompt neutrons
Calculated with CCONE code/2/.
MT=455 Delayed neutrons
Calculated by Brady and England/6/.
MF= 6 Energy-angle distributions
Calculated with CCONE code/2/.
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./34/ for
U-235 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 taken from Mughabghab /35/.
For the parameters without any information on uncertainty,
the following uncertainties were assumed:
Resonance energy 0.1 %
Neutron width 10 %
Capture width 20 %
Fission width 20 %
They were further modified by considering experimental data
of the fission and capture cross sections at the thermal
neutron energy.
MF=33 Covariances of neutron cross sections
Covariances were given to all the cross sections by using
KALMAN code/36/ and the covariances of model parameters
used in the cross-section calculations.
Covariances of the total, elastic-scattering and capture cross
sections were determined by considering the experimental data
(see MF=3).
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 of 18% was assumed in the
energy region above 13 MeV.
In the resolved resonance region, the following standard
deviations were added to the contributions from resonance
parameters:
Total 2 b
Elastic scattering 10 %
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/37/
* Global parametrization of Koning-Duijvestijn/38/
was used.
* Gamma emission channel/39/ was added to simulate direct
and semi-direct capture reaction.
3) Hauser-Feshbach statistical model
* Moldauer width fluctuation correction/40/ 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/41/. 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/42/,/43/
was used. The prameters are shown in Table 7.
------------------------------------------------------------------
Tables
------------------------------------------------------------------
Table 1. Coupled channel calculation
--------------------------------------------------
* rigid rotor model was applied
* coupled levels = 0,1,2,3,9,14 (see Table 2)
* optical potential parameters /27/
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 = 0.19
beta_4 = 0.066
beta_6 = 0.0015
* Calculated strength function
S0= 0.81e-4 S1= 2.50e-4 R'= 9.64 fm (En=1 keV)
--------------------------------------------------
Table 2. Level Scheme of Pa-231
-------------------
No. Ex(MeV) J PI
-------------------
0 0.00000 3/2 - *
1 0.00921 1/2 - *
2 0.05857 7/2 - *
3 0.07769 5/2 - *
4 0.08421 5/2 +
5 0.10141 7/2 +
6 0.10227 3/2 +
7 0.11165 9/2 +
8 0.13400 11/2 +
9 0.16860 11/2 - *
10 0.17150 11/2 +
11 0.17416 5/2 -
12 0.18350 5/2 +
13 0.18890 13/2 +
14 0.19350 9/2 - *
15 0.21824 7/2 -
16 0.24732 7/2 +
17 0.27200 9/2 -
18 0.27380 1/2 +
19 0.29660 17/2 +
20 0.30070 15/2 +
21 0.30400 9/2 +
22 0.31150 5/2 +
23 0.31680 17/2 +
24 0.31795 3/2 +
25 0.32021 3/2 -
26 0.32870 15/2 -
27 0.34000 11/2 -
28 0.35150 13/2 -
29 0.35184 5/2 -
30 0.38500 23/2 +
-------------------
*) Coupled levels in CC calculation
Table 3. Level density parameters
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Pa-232 17.9699 0.0000 2.9784 0.2779 -0.6740 1.0000
Pa-231 17.9034 0.7895 3.1164 0.4176 -1.2470 3.5007
Pa-230 17.8368 0.0000 2.9470 0.2794 -0.6728 1.0000
Pa-229 17.7702 0.7930 3.0707 0.3881 -0.8689 3.0597
Pa-228 17.7035 0.0000 2.9095 0.2810 -0.6716 1.0000
--------------------------------------------------------
Table 4. Fission barrier parameters
----------------------------------------
Nuclide V_A hw_A V_B hw_B
MeV MeV MeV MeV
----------------------------------------
Pa-232 5.800 0.800 6.180 0.400
Pa-231 6.000 0.800 5.750 0.520
Pa-230 5.800 0.800 6.180 0.400
Pa-229 6.000 0.800 5.800 0.520
Pa-228 5.800 0.800 6.180 0.400
----------------------------------------
Table 5. Level density above inner saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Pa-232 20.6654 0.0000 2.6000 0.3415 -2.6081 2.2000
Pa-231 20.5889 0.9211 2.6000 0.3276 -1.4734 2.9211
Pa-230 20.5123 0.0000 2.6000 0.3428 -2.6080 2.2000
Pa-229 20.4357 0.9251 2.6000 0.3435 -1.6829 3.1251
Pa-228 20.3591 0.0000 2.6000 0.3442 -2.6080 2.2000
--------------------------------------------------------
Table 6. Level density above outer saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Pa-232 20.6654 0.0000 -0.0800 0.4050 -2.1087 2.5000
Pa-231 20.5889 0.9211 -0.1200 0.3706 -0.7702 2.9211
Pa-230 20.5123 0.0000 -0.1600 0.3867 -1.8562 2.2000
Pa-229 20.4357 0.9251 -0.2000 0.3880 -0.9302 3.1251
Pa-228 20.3591 0.0000 -0.2400 0.3894 -1.8544 2.2000
--------------------------------------------------------
Table 7. Gamma-ray strength function for Pa-232
--------------------------------------------------------
K0 = 1.502 E0 = 4.500 (MeV)
* E1: ER = 11.03 (MeV) EG = 2.71 (MeV) SIG = 302.00 (mb)
ER = 13.87 (MeV) EG = 4.77 (MeV) SIG = 449.00 (mb)
* M1: ER = 6.67 (MeV) EG = 4.00 (MeV) SIG = 2.79 (mb)
* E2: ER = 10.25 (MeV) EG = 3.33 (MeV) SIG = 6.39 (mb)
--------------------------------------------------------
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