92-U -237 JAEA+ EVAL-JAN10 O.Iwamoto, T.Nakagawa, et al.
DIST-MAY10 20100318
----JENDL-4.0 MATERIAL 9234
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
History
06-08 Fission cross section was modified.
07-05 New calculation was performed with CCONE code.
Data were compiled as JENDL/AC-2008/1/.
09-02 (MF1,MT452,MT455,MT456) were revised.
09-08 (MF1,MT458) was evaluated.
09-11 (3,18) was revised.
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=455 and 456.
MT=455 Delayed neutron data
Determined from 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 taken from the evaluation of Brady and
England/6/.
MT=456 Number of prompt neutrons per fission
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: 1.0E-5 - 200 eV)
(same as JENDL-3.3)
Below 45 eV, hypothetical resonances were generated from
fission width of 0.004 eV, S0 of 1.0E-4 and level spacing of
3.5 eV, and adjusted to reproduce thermal cross sections.
Above 46 eV, parameters were estimated from fission-area data
measured by McNally et al./12/
Unresolved resonance parameters (200 eV- 40 keV)
Parameters were determined with ASREP code/13/ so as to
repruduce the cross sections in this region. 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 478.46
elastic 24.44
fission 1.70 45.1
capture 452.32 1080
-------------------------------------------------------
(*) 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
Below about 1 MeV, a smooth curve was determined by eye-
guiding.
Above 1 MeV, the experimental data of Burke et al./15/ were
analyzed with GMA code /16/. They measured the fission cross
section with a surrogate ratio method in the energy region
from 493 keV to 24.9 MeV. The results of GMA 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 neutron spectra
Calculated with CCONE code.
MT=455 Delayed neutron spectra
(same as JENDL-3.3)
The spectra adopted were calculated by Brady and England/6/.
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./17/ 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 /18/.
Those of neutron widths were due to the uncertainties of the
fission area. For the parameters without any information on
uncertainty, the following uncertainties were assumed:
Resonance energy 0.1 %
Neutron width 20 %
Capture width 50 %
Fission width 50 %
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.
In the resolved resonance region, the following standard
deviations were added to the contributions from resonance
parameters:
Total 30 %
Elastic scattering 20 %
Capture 30 %
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 = 0,1,2,3,5 (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 = 0.213
beta_4 = 0.066
beta_6 = 0.0015
* Calculated strength function
S0= 0.76e-4 S1= 1.99e-4 R'= 9.48 fm (En=1 keV)
--------------------------------------------------
Table 2. Level Scheme of U-237
-------------------
No. Ex(MeV) J PI
-------------------
0 0.00000 1/2 + *
1 0.01139 3/2 + *
2 0.05630 5/2 + *
3 0.08286 7/2 + *
4 0.15996 5/2 +
5 0.16300 9/2 + *
6 0.20419 7/2 +
7 0.20500 11/2 +
8 0.26095 9/2 +
9 0.27400 7/2 -
10 0.31600 9/2 -
11 0.32700 11/2 +
12 0.36700 11/2 -
13 0.42615 7/2 +
14 0.43200 13/2 -
15 0.43200 13/2 +
16 0.48200 9/2 +
17 0.48400 7/2 +
18 0.50600 15/2 -
19 0.53000 13/2 -
20 0.54062 1/2 -
21 0.54500 11/2 -
22 0.55100 11/2 +
23 0.55498 3/2 -
24 0.57500 21/2 +
-------------------
*) Coupled levels in CC calculation
Table 3. Level density parameters
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
U-238 18.7359 1.5557 3.0121 0.3767 -0.1089 3.8153
U-237 18.6682 0.7795 2.7455 0.3584 -0.6445 2.7495
U-236 18.6005 1.5623 2.7551 0.3859 -0.1547 3.8920
U-235 18.5328 0.7828 2.6265 0.3874 -0.9246 3.1046
U-234 18.4650 1.5689 2.5578 0.3902 -0.1511 3.9087
--------------------------------------------------------
Table 4. Fission barrier parameters
----------------------------------------
Nuclide V_A hw_A V_B hw_B
MeV MeV MeV MeV
----------------------------------------
U-238 6.320 0.800 5.200 0.600
U-237 6.150 0.650 5.750 0.500
U-236 6.400 1.040 5.050 0.550
U-235 5.790 0.400 5.470 0.300
U-234 6.180 1.040 5.080 0.600
----------------------------------------
Table 5. Level density above inner saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
U-238 20.5728 1.8150 2.6000 0.3280 -0.5964 3.8150
U-237 20.4984 0.9094 2.6000 0.3431 -1.7162 3.1094
U-236 20.0594 1.8226 2.6000 0.3473 -0.8150 4.0226
U-235 20.3497 0.9133 2.6000 0.3299 -1.4981 2.9133
U-234 20.2753 1.8304 2.6000 0.3306 -0.5810 3.8304
--------------------------------------------------------
Table 6. Level density above outer saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
U-238 21.1238 1.8150 0.2200 0.3757 -0.0486 4.0150
U-237 20.4984 0.9094 0.1800 0.3828 -0.9590 3.1094
U-236 20.0594 1.8226 0.1400 0.3882 -0.0489 4.0226
U-235 20.3497 0.9133 0.1000 0.3706 -0.7868 2.9133
U-234 20.2753 1.8304 0.0600 0.3719 0.1310 3.8304
--------------------------------------------------------
Table 7. Gamma-ray strength function for U-238
--------------------------------------------------------
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 = 6.62 (MeV) EG = 4.00 (MeV) SIG = 2.66 (mb)
* E2: ER = 10.17 (MeV) EG = 3.25 (MeV) SIG = 6.51 (mb)
--------------------------------------------------------
References
1) O.Iwamoto et al.: J. Nucl. Sci. Technol., 46, 510 (2009).
2) R.J.Tuttle: INDC(NDS)-107/G+Special, p.29 (1979).
3) G.Benedetti et al.: Nucl. Sci. Eng., 80, 379 (1982).
4) R.Waldo et al.: Phys. Rev., C23, 1113 (1981).
5) O.Iwamoto: J. Nucl. Sci. Technol., 44, 687 (2007).
6) M.C.Brady, T.R.England: Nucl. Sci. Eng., 103, 129 (1989).
7) T.Ohsawa: J.Nucl. Radiochem. Sci., 9, 19 (2008).
8) G.Audi: Private communication (April 2009).
9) J.Katakura et al.: JAERI 1343 (2001).
10) T.R.England et al.: LA-11151-MS (1988).
11) R.Sher, C.Beck: EPRI NP-1771 (1981).
12) J.H.McNally et al.: Phys. Rev., C9, 717 (1974).
13) Y.Kikuchi et al.: JAERI-Data/Code 99-025 (1999) in Japanese.
14) E.Sh.Soukhovitskii et al.: Phys. Rev. C72, 024604 (2005).
15) J.T.Burke et al.: Phys. Rev. C73, 054604 (2006).
16) W.P.Poenitz: BNL-NCS-51363, Vol.I, p.249 (1981).
S.Chiba, D.L.Smith: ANL/NDM-121 (1991).
17) V.V.Verbinski et al.: Phys. Rev., C7, 1173 (1973).
18) S.F.Mughabghab: "Atlas of Neutron Resonances," Elsevier
(2006).
19) T.Kawano, K.Shibata, JAERI-Data/Code 97-037 (1997) in
Japanese.
20) C.Kalbach: Phys. Rev. C33, 818 (1986).
21) A.J.Koning, M.C.Duijvestijn: Nucl. Phys. A744, 15 (2004).
22) J.M.Akkermans, H.Gruppelaar: Phys. Lett. 157B, 95 (1985).
23) P.A.Moldauer: Nucl. Phys. A344, 185 (1980).
24) D.L.Hill, J.A.Wheeler: Phys. Rev. 89, 1102 (1953).
25) J.Kopecky, M.Uhl: Phys. Rev. C41, 1941 (1990).
26) J.Kopecky, M.Uhl, R.E.Chrien: Phys. Rev. C47, 312 (1990).