90-Th-232 JAEA+ EVAL-JAN10 O.Iwamoto,T.Nakagawa,et al.
DIST-DEC21 20100409
----JENDL-5 MATERIAL 9040
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
History
05-12 Fission cross section was evaluated with GMA code.
07-06 New theoretical calculation was made with CCONE code.
Data were compiled as JENDL/AC-2008/1/.
09-08 (MF1,MT458) was evaluated.
09-11 Nu-d was revised.
10-01 Data of prompt gamma rays due to fission were given.
10-03 Covariance data were given.
21-11 revised by O.Iwamoto
(MF3/MT19-21,38) deleted
(MF8/MT16-18,37,102) JENDL/AD-2017 adopted
(MF8/MT4) added
MF= 1
MT=452 Total neutron per fission
Sum of MT=455 and 456.
MT=455 Delayed neutrons
Nu-d was determined from nu-d of the following three nuclides
and partial fission cross sections calculated with CCONE
code/2/.
Th-233 = 0.0490
average value of experimental data of Masters et al./3/
and Dore et al./4/
Th-232 = 0.025
Th-231 = 0.020
assumed by considering the data of Masters et al. and
Dore et al.
Decay constants were taken from Brady and England/5/.
MT=456 Prompt neutrons per fission
Experimental data were fitted by a linear function.
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/6/. 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 2000/7/ does
not include average neutron energy values, the average values
were calculated using the formula shown in the report by
T.R. England/8/. The fractions of prompt energy were
calculated using the fractions of Sher's evaluation/9/ 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 (RM, 1.0e-5 - 4000 eV)
The parameters evaluated by Derrien et al./10/ were adopted.
Numerical data were taken from ENDF/B-VII.0/11/.
Fission widths were 0.0. The fission cross section was given
as background cross sections.
--> See Appendix A.1
Unresolved resonance parameters (4 keV - 100 keV)
Parameters were determined with ASREP code /12/ so as to
reproduce the cross sections. They are used only for self-
shielding calculations.
Thermal cross sections and resonance integrals (at 300K)
-------------------------------------------------------
0.0253 eV reson. integ.(*)
(barns) (barns)
-------------------------------------------------------
total 20.383
elastic 13.045
fission 5.4e-5 0.375
capture 7.338 84.3
-------------------------------------------------------
(*) 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./13/.
MT=2 Elastic scattering cross section
Calculated as total - non-elstic scattering cross sections
MT=16 (n,2n) cross section
The experimental of Karamanis et al./14/, Paics et al./15/ and
Filatenkov et al./16/ were used to determine the parameters
in the CCONE calculation.
MT=18 Fission cross section
Below 18 keV, the data measured by Nakagome et al. /17/ were
adopted.
Above 300 keV, the following experimental data were analyzed
with the GMA code /18/:
Authors Energy range Data points Reference
Muir+ 0.598 - 2.96 MeV 104 /19/
Casanova+ 4.48, 14.1 MeV 2 /20/
Blons+ 1.09 - 6.01 MeV 823 /21/
Nordborg+ 4.58 - 8.78 MeV 23 /22/
D'Hondt+ 2.44 MeV 1 /23/
Behrens+ 0.705 - 19.6 MeV 137 /24/
Meadows 1.27 - 9.9 MeV 70 /25/
Perez+ 0.15 - 1.55 MeV 15 /26/
Blons+ 1.1 - 4 MeV 1727 /27/
Garlea+ 14.75 MeV 1 /28/
Anand+ 1.38 - 1.95 MeV 7 /29/
Kanda+ 13.5 - 15 MeV 3 /30/
Goverdovskij+ 16.2 MeV 1 /31/
Goverdovskij+ 4.9 - 10.4 MeV 33 /32/
Kanda+ 1.5 - 6.8 MeV 17 /33/
Meadows 14.7 MeV 1 /34/
Fursov+ 0.13 - 7.4 MeV 67 /35/
Sastry+ 14 MeV 1 /36/
Garlea+ 14.8 MeV 1 /37/
Shcherbakov+ 0.577 - 19.4 MeV 115 /38/
The data measured relatively to U-235 fission were converted
to Th-232 fission by using JENDL-3.3 data.
Between the energies of 18 and 300 keV, the data at 18 and
300 keV were connected with a straight line.
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).
MT=102 Capture cross section
The experimental data of Aerts et al./39/ and Borella et
al./40/ were used to determine the parameters in the 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 neutrons
Calculated with CCONE code.
MT=455 Delayed neutrons
Taken from Brady and England /5/.
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./41/ 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
Error of 4% was assumed below 5 MeV and 12% above 5 MeV, by
comparing with experimental data/3,4/.
MT=456
Covariance was obtained by fitting a linear function to the
experimental data. Standard deviations were multiplied by a
factor of 4.0.
MF=33 Covariances of neutron cross sections
Covariances were given to all the cross sections by using
KALMAN code/42/ and the covariances of model parameters
used in the theoretical calculations.
For the following cross sections, covariances were determined
by different methods.
MT=1,2 Total and elastic scattering cross sections
In the resonance region up to 4 keV, uncertainties were
determined by comparing with experimental data.
MT=18 Fission cross section
In the resonance region, uncertainties were determined by
comparing with experimental data.
Above the resonance region, cross section was evaluated with
GMA code/18/.
MT=102 Capture cross section
In the resonance region, uncertainties were determined by
comparing with experimental data.
Above 4 keV, covariance matrix was obtained with CCONE and
KALMAN codes/42/.
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/43/
* Global parametrization of Koning-Duijvestijn/44/
was used.
* Gamma emission channel/45/ was added to simulate direct
and semi-direct capture reaction.
3) Hauser-Feshbach statistical model
* Moldauer width fluctuation correction/46/ 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/47/. 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/48/,/49/
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 /13/
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= 2.26e-4 R'= 9.75 fm (En=1 keV)
--------------------------------------------------
Table 2. Level Scheme of Th-232
-------------------
No. Ex(MeV) J PI
-------------------
0 0.00000 0 + *
1 0.04937 2 + *
2 0.16212 4 + *
3 0.33320 6 + *
4 0.55690 8 + *
5 0.71425 1 -
6 0.73035 0 +
7 0.77410 2 +
8 0.77440 3 -
9 0.78530 2 +
10 0.82700 10 +
11 0.82960 3 +
12 0.87300 4 +
13 0.88360 5 -
14 0.89010 4 +
15 0.96040 5 +
16 1.02310 6 +
17 1.04290 7 -
18 1.04990 6 +
19 1.05360 2 +
20 1.07290 2 +
21 1.07750 1 -
22 1.07870 0 +
23 1.09440 3 +
24 1.10570 3 -
25 1.12180 2 +
26 1.13710 12 +
27 1.14330 4 -
28 1.14600 7 +
29 1.14830 4 +
-------------------
*) 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-233 18.8481 0.7861 3.5545 0.3805 -1.0048 3.1955
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
--------------------------------------------------------
Table 4. Fission barrier parameters
----------------------------------------
Nuclide V_A hw_A V_B hw_B
MeV MeV MeV MeV
----------------------------------------
Th-233 5.820 1.000 6.150 0.530
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
----------------------------------------
Table 5. Level density above inner saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Th-233 20.2008 0.9172 2.6000 0.3312 -1.4942 2.9172
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
--------------------------------------------------------
Table 6. Level density above outer saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Th-233 20.7419 0.9172 -0.1000 0.3835 -0.9412 3.1172
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
--------------------------------------------------------
Table 7. Gamma-ray strength function for Th-233
--------------------------------------------------------
K0 = 1.700 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 = 6.66 (MeV) EG = 4.00 (MeV) SIG = 3.05 (mb)
* E2: ER = 10.24 (MeV) EG = 3.31 (MeV) SIG = 6.25 (mb)
--------------------------------------------------------
References
1) O.Iwamoto et al.: J. Nucl. Sci. Technol., 46, 510 (2009).
2) O.Iwamoto: J. Nucl. Sci. Technol., 44, 687 (2007).
3) C.F.Masters et al.: Nucl. Sci. Eng., 36, 202 (1969).
4) D.Dore et al.: 2007 Nice (ND2007), 383 (2007).
5) M.C.Brady, T.R.England: Nucl. Sci. Eng., 103, 129 (1989).
6) G.Audi: Private communication (April 2009).
7) J.Katakura et al.: JAERI 1343 (2001).
8) T.R.England et al.: LA-11151-MS (1988).
9) R.Sher, C.Beck: EPRI NP-1771 (1981).
10) H.Derrien et al.: 2006 Vancouver (PHYSOR2006), B071 (2006).
11) M.B.Chadwick et al.: Nucl Data Sheets, 107, 2931 (2006).
12) Y.Kikuchi, et al.: JAERI-Data/Code 99-025 (1999) in Japanese.
13) E.Sh.Soukhovitskii et al.: Phys. Rev. C72, 024604 (2005).
14) D.Karamanis et al.: Nucl. Inst. Meth. A505, 381 (2003).
15) P.Raics et al.: Phys. Rev. C32, 87 (1985).
16) A.A.Filatenkov et al.: Khlopin Radiev. Inst., Leningrad
Reports No.252 (1999).
17) Y.Nakagome, et al.: Pys. Rev., C43, 1824 (1991).
18) W.P.Poenitz: BNL-NCS-51363, Vol.I, p.249 (1981).
S.Chiba, D.L.Smith: ANL/NDM-121 (1991).
19) D.W.Muir, L.R.Veeser: 1971 Knoxville, Vol.1, p.292 (1971).
20) J.Casanova, et al.: Acta Polytech. Sc., 69, 71 (1973).
21) J.Blons, et al.: Phys. Rev. Lett., 35, 1749 (1975).
22) C.Nordborg, et al.: 1978 Harwell, p.910 (1978).
23) P.D'Hondt, et al.: Ann. Nucl. Energy, 7, 367 (1980).
24) J.W.Behrens, et al.: Nucl. Sci. Eng., 81, 512 (1982).
25) J.W.Meadows: ANL/NDM-83 (1983).
26) R.B.Perez, et al.: Phys. Rev. C28, 1635 (1983).
27) J.Blons, et al.: Nucl. Phys., A414, 1 (1984).
28) I.Garlea, et al.: Rev. Roum. Phys., 29, 421 (1984).
29) R.P.Anand, et al.: 1985 Jaipur, Vol. 2, p.350 (1985).
30) K.Kanda, et al.: JAERI-M 85-035, p.220 (1985).
31) A.A.Goverdovskii, et al.: Sov. At. Energy, 60, 416 (1986).
32) A.A.Goverdovskii, et al.: Sov. At. Energy, 61, 958 (1986).
33) K.Kanda, et al.: 1985 Santa Fe, Vol.1, p.569 (1985).
34) J.W.Meadows: J. Ann. Nucl. Energy, 15, 421 (1988).
35) B.I.Fursov, et al.: Sov. At. Energy, 71, 827 (1991).
36) Ch.V.Sastry, et al.: 1992 Bombay, p.288 (1992).
37) I.Garlea, et al.: Rev. Roum. Phys., 37, 19 (1992).
38) O.Shcherbakov, et al.: 2001 Tsukuba, Vol.1, p.230 (2001).
39) G.Aerts et al.: Phys. Rev. C73, 054610 (2006).
40) A.Borella et al.: Nucl. Sci. Eng. 152, 1 (2006).
41) V.V.Verbinski et al.: Phys. Rev., C7, 1173 (1973).
42) T.Kawano, K.Shibata, JAERI-Data/Code 97-037 (1997) in
Japanese.
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44) A.J.Koning, M.C.Duijvestijn: Nucl. Phys. A744, 15 (2004).
45) J.M.Akkermans, H.Gruppelaar: Phys. Lett. 157B, 95 (1985).
46) P.A.Moldauer: Nucl. Phys. A344, 185 (1980).
47) D.L.Hill, J.A.Wheeler: Phys. Rev. 89, 1102 (1953).
48) J.Kopecky, M.Uhl: Phys. Rev. C41, 1941 (1990).
49) J.Kopecky, M.Uhl, R.E.Chrien: Phys. Rev. C47, 312 (1990).
******************************************************************
Appendix A.1 Resolved resonance parameters (from ENDF/B-VII.0)
******************************************************************
EVALUATION OF THE RESONANCE PARAMETERS IN THE ENERGY RANGE 0 to
4 keV - L.C. Leal and H. Derrien, ORNL(2005)
The resonance parameters were obtained from a sequential Bayes
analysis, with the computer code SAMMY, of an experimental data
base including Olsen(1) neutron transmission data(ORELA),
Schillebeeckx(2) capture data(GELINA), and Gunsing(3) capture
data(nTof) in the energy range 1 eV to 4 keV. In the thermal
energy range the capture data of Chrien(4) and of Lundgreen(5)
were normalized to a value of 7.35 b recommended by Trkov(6) and
fitted by SAMMY along with the total cross section of Olsen(1) in
the energy range up to 1 eV.
The contribution of the external resonances(negative energy
resonances and resonances at energies larger than 4 keV) was
obtained from two fictitious resonances, one at -2000 eV and the
other at 6000 eV. The parameters of these resonances allow the
representation of the Olsen thick samples transmission data with
an accuracy of 1% on average, and a constant value of R'=9.686 fm
could be used over the entire energy range analyzed, in agreement
with Olsen(7) evaluated value. A ladder of 7 s-wave negative
energy resonances from -3 eV to -110 eV was used to help the fit
of the thermal energy range. The resonance at -3.52 eV could be
used to adjust the cross sections at 0.0253 eV.
The resonance set contain 244 s-wave resonances and 669 p-wave
resonances. The large s-wave resonances were identified from their
shape; some other resonances were assigned s-wave because leading
to too large reduced neutron width when assigned p. A large
number of resonances assigned p-wave are not seen in the
experimental data; they were used to obtain the agreement with
the Wigner distribution of the spacing and the Porter-Thomas
distribution of the reduced neutron width. It can be shown that
a set of resonances that does not contain p-wave resonances of
reduced neutron width smaller than 1.6 meV calculated average
capture cross section too small by 0.5% in the energy range below
1 keV, and too small by about 3% in the energy range 3 to 4 keV.
The prior values of the resonance parameters in the SAMMY fit
were those from the Olsen(7) evaluation with a constant value of
24.4 meV for the capture width of all the resonances. The value of
24.4 meV was kept for the p-wave resonances. In the SAMMY fit the
capture width was allowed to vary for the large s-wave resonances
since for most of these resonances the capture area is sensitive
to the capture width. However, the average of the varied capture
agrees within 4% with the value of 24.4 meV.
The cross sections calculated at 0.0253 eV with the resonance
parameters are 20.40 b and 7.34 b respectively for the total and
capture cross sections compared to 20.38 b and 7.40 b calculated
from ENDF/B-VI. The capture resonance integral in the energy
range 0.5 eV to 4000 eV is 81.74 b from the present evaluation and
83.62 b from ENDF/B-VI, i.e 2.3% lower than ENDF/B-VI. The total
cross section calculated with the resonance parameters is not
consistent with Olsen experimental data in the energy range near
0.0253 eV due to the Bragg scattering effect in the measured total
cross section.
The average capture cross sections calculated in several energy
ranges are compared to the ENDF/B-VI values in the following
table (SAMMY calculation):
-----------------------------------------------------------------
Energy Range Present Results ENDF/B-VI Difference
eV Barn Barn Barn %
-----------------------------------------------------------------
0.1 -1.0 1.475 1.630 0.155 10.5
1.0 -20. 0.212 0.335 0.123 58.0
20. -100. 25.920 26.000 0.080 0.3
100.-500. 9.049 9.356 0.307 3.4
500.-1000. 3.115 3.284 0.169 5.4
1000.-2000. 2.063 2.177 0.114 5.5
2000.-3000. 1.584 1.650 0.066 4.2
3000.-4000. 1.141 1.267 0.126 11.0
_________________________________________________________________
More details on the evaluation will be described on ORNL report
The covariances of resolved resonance parameters were obtained
automatically from the above-described analysis with the
SAMMY code.
REFERENCES-
1/ D.K. Olsen and R.W. Ingle, ORNL/TM-7661(ENDF-307),1981.
2/ P. Schillebeeckx, Private Communication.
3/ F. Gunsing, Private Communication.
4/ R.E. Chrien et al., NSE,65(2), 347(1978).
5/ G. Lundgreen et al., NUK,11,61(1968).
6/ A. Trkov, Private Communication.
7/ D.K. Olsen, ORNL/TM-8056(ENDF-319),1981.