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. 43) C.Kalbach: Phys. Rev. C33, 818 (1986). 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.