90-Th-231 JAEA+ EVAL-FEB10 O.Iwamoto, T.Nakagawa, et al.
DIST-MAY10 20100303
----JENDL-4.0 MATERIAL 9037
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
History
07-10 Theoretical calculation was performed with CCONE code.
07-11 Data were compiled as JENDL/AC-2008/1/.
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
Estimated from systematics by Tuttle/2/, Benedetti et al./3/
and Waldo et al./4/
MT=456 Number of prompt neutrons per fission
Estimated from Howerton's systematics/5/.
MF= 2 Resonance parameters
MT=151
No resonance parameters are given.
Thermal cross sections and resonance integrals (at 300K)
-------------------------------------------------------
0.0253 eV reson. integ.(*)
(barns) (barns)
-------------------------------------------------------
total 1683.2
elastic 12.03
fission 40.01 282
capture 1630.8 725
-------------------------------------------------------
(*) In the energy range from 0.5 eV to 10 MeV.
MF= 3 Neutron cross sections
Below 0.33 eV:
* Elastic scattering cross section is 12.0 b calculated from
scattering radius of 9.779 fm/6/.
* Fission cross section is in the 1/v shape.
Cross section of 40 b at 0.0253 eV was assumed from
systematics.
* Capture cross section is in the 1/v shape.
CCONE calculation was extrapolated to 1.0e-5 eV.
Cross section at 0.0253 eV is 1630 b.
Above 0.33 eV:
Cross sections calculated with CCONE code/6/ were adopted.
MT= 1 Total cross section
The cross section was calculated with CC OMP of Soukhovitskii
et al./7/.
MF= 4 Angular distributions of secondary neutrons
MT=2 Elastic scattering
Calculated with CCONE code/6/.
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/6/.
MF= 6 Energy-angle distributions
Calculated with CCONE code/6/.
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./8/ 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
at 0.0 and 5.0 MeV with an uncertainty of 5%.
MF=33 Covariances of neutron cross sections
Covariances were given to all the cross sections by using
KALMAN code/9/ and the covariances of model parameters
used in the cross-section calculations.
For the following cross sections, standard deviations in the
energy region below 0.3 eV were assumed as follows:
Total 87 %
Elastic scattering 90 %
Fission 90 %
Capture 90 %
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/6/ 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/10/
* Global parametrization of Koning-Duijvestijn/11/
was used.
* Gamma emission channel/12/ was added to simulate direct
and semi-direct capture reaction.
3) Hauser-Feshbach statistical model
* Moldauer width fluctuation correction/13/ 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/14/. 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/15/,/16/
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 (see Table 2)
* optical potential parameters /7/
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= 0.87e-4 S1= 2.05e-4 R'= 9.78 fm (En=1 keV)
--------------------------------------------------
Table 2. Level Scheme of Th-231
-------------------
No. Ex(MeV) J PI
-------------------
0 0.00000 5/2 + *
1 0.04195 7/2 + *
2 0.09613 9/2 + *
3 0.16194 11/2 + *
4 0.18571 5/2 -
5 0.20531 7/2 -
6 0.22140 3/2 +
7 0.23689 9/2 -
8 0.24088 5/2 +
9 0.24758 1/2 +
10 0.27218 3/2 +
11 0.27542 7/2 +
12 0.27780 11/2 -
13 0.30174 5/2 +
14 0.31708 5/2 +
15 0.32491 9/2 +
16 0.33400 13/2 -
17 0.35151 7/2 +
18 0.37758 7/2 +
19 0.38569 11/2 +
20 0.38783 7/2 -
-------------------
*) Coupled levels in CC calculation
Table 3. Level density parameters
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Th-232 18.7786 1.5757 3.3953 0.3835 -0.2200 3.9949
Th-231 18.7090 0.7895 3.3191 0.3770 -0.9082 3.0943
Th-230 18.6395 1.5825 3.2401 0.4059 -0.4442 4.2813
Th-229 17.7702 0.7930 3.2566 0.4327 -1.4313 3.7239
Th-228 17.7035 1.5894 3.0590 0.3964 -0.1539 3.9563
--------------------------------------------------------
Table 4. Fission barrier parameters
----------------------------------------
Nuclide V_A hw_A V_B hw_B
MeV MeV MeV MeV
----------------------------------------
Th-232 5.800 1.040 5.950 0.500
Th-231 6.000 0.800 6.000 0.600
Th-230 5.500 1.040 5.950 0.600
Th-229 5.500 0.800 6.000 0.520
Th-228 3.900 1.040 6.400 0.600
----------------------------------------
Table 5. Level density above inner saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Th-232 20.1263 1.8383 2.6000 0.3319 -0.5731 3.8383
Th-231 19.6937 0.9211 2.6000 0.3507 -1.7165 3.1211
Th-230 19.9772 1.8463 2.6000 0.3332 -0.5651 3.8463
Th-229 19.9026 0.9251 2.6000 0.3339 -1.4862 2.9251
Th-228 19.8280 1.8543 2.6000 0.3346 -0.5570 3.8543
--------------------------------------------------------
Table 6. Level density above outer saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Th-232 20.5756 1.8383 -0.1400 0.3595 0.2690 3.6883
Th-231 19.6937 0.9211 -0.1800 0.3963 -0.9457 3.1211
Th-230 19.9772 1.8463 -0.2200 0.3786 0.1497 3.8463
Th-229 19.9026 0.9251 -0.2600 0.3799 -0.7708 2.9251
Th-228 19.8280 1.8543 -0.3000 0.3812 0.1590 3.8543
--------------------------------------------------------
Table 7. Gamma-ray strength function for Th-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 = 6.25 (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) R.J.Howerton: Nucl. Sci. Eng., 62, 438 (1977).
6) O.Iwamoto: J. Nucl. Sci. Technol., 44, 687 (2007).
7) E.Sh.Soukhovitskii et al.: Phys. Rev. C72, 024604 (2005).
8) V.V.Verbinski et al.: Phys. Rev., C7, 1173 (1973).
9) T.Kawano, K.Shibata, JAERI-Data/Code 97-037 (1997) in
Japanese.
10) C.Kalbach: Phys. Rev. C33, 818 (1986).
11) A.J.Koning, M.C.Duijvestijn: Nucl. Phys. A744, 15 (2004).
12) J.M.Akkermans, H.Gruppelaar: Phys. Lett. 157B, 95 (1985).
13) P.A.Moldauer: Nucl. Phys. A344, 185 (1980).
14) D.L.Hill, J.A.Wheeler: Phys. Rev. 89, 1102 (1953).
15) J.Kopecky, M.Uhl: Phys. Rev. C41, 1941 (1990).
16) J.Kopecky, M.Uhl, R.E.Chrien: Phys. Rev. C47, 312 (1990).