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. 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