90-Th-229 JAEA+ EVAL-JAN10 O.Iwamoto, T.Nakagawa, et al.
DIST-DEC21 20100323
----JENDL-5 MATERIAL 9031
-----INCIDENT NEUTRON DATA
------ENDF-6 FORMAT
History
07-06 New theoretical calculation was made with CCONE code.
07-07 Data were compiled as JENDL/AC-2008/1/.
09-08 (MF1,MT458) was evaluated.
10-01 Data of prompt gamma rays due to fission were given.
10-02 Nu-total, nu-d and nu-p were revised.
10-03 Covariance data were given.
21-11 revised by O.Iwamoto
(MF3/MT19-21,38) deleted
(MF8/MT4,16-18,37,102) added
MF=1 General information
MT=452 Number of neutrons per fission
Sum of MT's=455 and 456.
MT=455 Delayed neutrons
Average values of systematics by Tuttle/2/, Benedetti et
al./3/ and Waldo et al./4/ Decay constants were adopted from
the evaluation by Brady and England/5/.
MT=456 Prompt neutrons
Thermal data was based on the experimental data of Kroshin
and Zamjatnin/6/, Jaffy and Lerner/7/ and Lebedev
and Kalashnikova/8/. An energy dependent term was based on
systematics recommended by Ohsawa /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 8 eV)
A set of parameters recommended by Mughabghab/14/ was modified
so as to reproduce the fission cross section measured by
Kobayashi et al./15/, and the total cross section of Cote et
al./16/
Unresolved resonance parameters (8 eV - 20 keV)
Parameters (URP) were determined with ASREP code /17/ so as to
reproduce the cross sections in this energy region. URP are
used only for self-shielding calculations.
Thermal cross sections and resonance integrals (at 300K)
-------------------------------------------------------
0.0253 eV reson. integ.
(barns) (barns)
-------------------------------------------------------
total 111.91
elastic 10.43
fission 30.92 315
capture 70.56 1310
-------------------------------------------------------
MF= 3 Neutron cross sections
Cross sections above the resolved resonance region were
calculated with CCONE code/18/.
MT= 1 Total cross section
The cross section was calculated with CC OMP of Soukhovitskii
et al./19/.
MT=18 Fission cross section
Experimental data of Kobayashi et al./15/ and Gokhberg et al.
/20/ were used to adjust parameters of CCONE code.
MF= 4 Angular distributions of secondary neutrons
MT=2 Elastic scattering
Calculated with CCONE code/18/.
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/18/
MT=455 Delayed neutrons
Results of summation calculation made by Brady and England/5/
were adopted.
MF= 6 Energy-angle distributions
Calculated with CCONE code/18/.
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./21/ 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%.
The uncertainty at 0.0 eV was estimated from the experimental
data/6,7,8/.
MF=32 Covariances of resonance parameters
MT=151 Resolved resonance parameterss
Format of LCOMP=0 was adopted.
Uncertainties of parameters were taken from Mughabghab /14/.
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 cross section at the thermal neutron energy.
MF=33 Covariances of neutron cross sections
Covariances were given to all the cross sections by using
KALMAN code/22/ and the covariances of model parameters
used in the cross-section calculations.
Covariances of the total, elastic-scattering, fission and
capture cross sections were determined by considering the
experimental data (see MF=3).
In the resolved resonance region, the following standard
deviations were added to the contributions from resonance
parameters:
Total 20 %
Elastic scattering 20 %
Capture 20 %
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/18/ 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/23/
* Global parametrization of Koning-Duijvestijn/24/
was used.
* Gamma emission channel/25/ was added to simulate direct
and semi-direct capture reaction.
3) Hauser-Feshbach statistical model
* Moldauer width fluctuation correction/26/ 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/27/. 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/28/,/29/
was used. The prameters are shown in Table 7.
------------------------------------------------------------------
Tables
------------------------------------------------------------------
Table 1. Coupled channel calculation
--------------------------------------------------
* rigid rotor model was applied
* coupled levels = 0,2,8,13,23 (see Table 2)
* optical potential parameters /19/
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= 0.99e-4 S1= 2.84e-4 R'= 9.83 fm (En=1 keV)
--------------------------------------------------
Table 2. Level Scheme of Th-229
-------------------
No. Ex(MeV) J PI
-------------------
0 0.00000 5/2 + *
1 0.00001 3/2 +
2 0.02100 7/2 + *
3 0.02919 5/2 +
4 0.04244 7/2 +
5 0.06800 13/2 -
6 0.07182 7/2 +
7 0.07500 11/2 -
8 0.09713 9/2 + *
9 0.12541 9/2 +
10 0.14000 21/2 +
11 0.14635 5/2 -
12 0.14816 7/2 -
13 0.16326 11/2 + *
14 0.16453 3/2 -
15 0.17360 9/2 -
16 0.18700 17/2 +
17 0.19571 11/2 +
18 0.20200 11/2 +
19 0.21234 5/2 +
20 0.21716 5/2 -
21 0.23480 21/2 -
22 0.23736 7/2 -
23 0.24160 13/2 + *
24 0.25594 23/2 -
25 0.26193 1/2 +
26 0.28792 7/2 +
27 0.28852 3/2 +
28 0.30289 7/2 -
29 0.31717 5/2 +
30 0.32054 5/2 +
-------------------
*) 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-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
Th-227 17.6369 0.7965 3.1200 0.4219 -1.2457 3.5201
Th-226 17.5702 1.5965 2.8637 0.4068 -0.2170 4.0544
--------------------------------------------------------
Table 4. Fission barrier parameters
----------------------------------------
Nuclide V_A hw_A V_B hw_B
MeV MeV MeV MeV
----------------------------------------
Th-230 6.000 1.040 5.900 0.500
Th-229 5.500 0.800 6.000 0.520
Th-228 3.900 1.040 6.400 0.600
Th-227 4.100 0.800 6.400 0.520
Th-226 3.900 1.040 8.200 0.600
----------------------------------------
Table 5. Level density above inner saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Th-230 19.9772 1.8463 2.6000 0.3178 -0.3511 3.6463
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
Th-227 19.7533 0.9292 2.6000 0.3352 -1.4822 2.9292
Th-226 19.6786 1.8625 2.6000 0.3359 -0.5488 3.8625
--------------------------------------------------------
Table 6. Level density above outer saddle
--------------------------------------------------------
Nuclide a* Pair Eshell T E0 Ematch
1/MeV MeV MeV MeV MeV MeV
--------------------------------------------------------
Th-230 20.1556 1.8463 -0.2200 0.3610 0.3158 3.6463
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
Th-227 19.7533 0.9292 -0.3400 0.3826 -0.7655 2.9292
Th-226 19.6786 1.8625 -0.3800 0.3840 0.1685 3.8625
--------------------------------------------------------
Table 7. Gamma-ray strength function for Th-230
--------------------------------------------------------
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 = 6.69 (MeV) EG = 4.00 (MeV) SIG = 2.80 (mb)
* E2: ER = 10.28 (MeV) EG = 3.35 (MeV) SIG = 6.26 (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) M.C.Brady, T.R.England: Nucl. Sci. Eng., 103, 129 (1989).
6) N.I.Kroshkin, JU.S.Zamjatnin: Atomic Energy, 29, 95 (1970)
taken from EXFOR.
7) A.H.Jaffey, J.L.Lerner: ANL-6600, p.124 (1961) taken from
EXFOR.
8) V.I.Lebedev,V.I.Kalashnikova: Zhurnal Eksperimental'noi i
Teoret. Fiziki, 35, 535 (1958) taken from EXFOR.
9) T.Ohsawa: J. Nucl. Radiochem. Sci., 9, 19 (2008).
10) G.Audi: Private communication (April 2009).
11) J.Katakura et al.: JAERI 1343 (2001).
12) T.R.England et al.: LA-11151-MS (1988).
13) R.Sher, C.Beck: EPRI NP-1771 (1981).
14) S.F.Mughabghab: "Atlas of Neutron Resonances," Elsevier
(2006).
15) K.Kobayashi, et al.: Nucl. Sci. Eng., 139, 273 (2001).
16) R.E.Cote et al.: Bulletin American Phys. Soc., 6, 417(C1)
(1961).
17) Y.Kikuchi et al.: JAERI-Data/Code 99-025 (1999) in Japanese.
18) O.Iwamoto: J. Nucl. Sci. Technol., 44, 687 (2007).
19) E.Sh.Soukhovitskii et al.: Phys. Rev. C72, 024604 (2005).
20) B.M.Gokhberg et al.: Doklady Akademii Nauk, 128(5), 911
(1959)
21) V.V.Verbinski et al.: Phys. Rev., C7, 1173 (1973).
22) T.Kawano, K.Shibata, JAERI-Data/Code 97-037 (1997) in
Japanese.
23) C.Kalbach: Phys. Rev. C33, 818 (1986).
24) A.J.Koning, M.C.Duijvestijn: Nucl. Phys. A744, 15 (2004).
25) J.M.Akkermans, H.Gruppelaar: Phys. Lett. 157B, 95 (1985).
26) P.A.Moldauer: Nucl. Phys. A344, 185 (1980).
27) D.L.Hill, J.A.Wheeler: Phys. Rev. 89, 1102 (1953).
28) J.Kopecky, M.Uhl: Phys. Rev. C41, 1941 (1990).
29) J.Kopecky, M.Uhl, R.E.Chrien: Phys. Rev. C47, 312 (1990).