92-U -237 JAEA+ EVAL-JAN10 O.Iwamoto, T.Nakagawa, et al. DIST-MAY10 20100318 ----JENDL-4.0 MATERIAL 9234 -----INCIDENT NEUTRON DATA ------ENDF-6 FORMAT History 06-08 Fission cross section was modified. 07-05 New calculation was performed with CCONE code. Data were compiled as JENDL/AC-2008/1/. 09-02 (MF1,MT452,MT455,MT456) were revised. 09-08 (MF1,MT458) was evaluated. 09-11 (3,18) was revised. 10-01 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=455 and 456. MT=455 Delayed neutron data Determined from systematics by Tuttle/2/, Benedetti et al./3/ and Waldo et al./4/, and partial fission cross sections calculated with CCONE code /5/. Decay constants were taken from the evaluation of Brady and England/6/. MT=456 Number of prompt neutrons per fission Ohsawa's systematics/7/ 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/8/. 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 2000/9/ does not include average neutron energy values, the average values were calculated using the formula shown in the report by T.R. England/10/. The fractions of prompt energy were calculated using the fractions of Sher's evaluation/11/ 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 (MLBW: 1.0E-5 - 200 eV) (same as JENDL-3.3) Below 45 eV, hypothetical resonances were generated from fission width of 0.004 eV, S0 of 1.0E-4 and level spacing of 3.5 eV, and adjusted to reproduce thermal cross sections. Above 46 eV, parameters were estimated from fission-area data measured by McNally et al./12/ Unresolved resonance parameters (200 eV- 40 keV) Parameters were determined with ASREP code/13/ so as to repruduce the cross sections in this region. The parameters are used only for self-shielding calculations. Thermal cross sections and resonance integrals (at 300K) ------------------------------------------------------- 0.0253 eV reson. integ.(*) (barns) (barns) ------------------------------------------------------- total 478.46 elastic 24.44 fission 1.70 45.1 capture 452.32 1080 ------------------------------------------------------- (*) 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 the elastic scattering (MT=2) and fission cross sections (MT=18, 19, 20, 21, 38) were calculated with CCONE code/5/. MT= 1 Total cross section The cross section was calculated with CC OMP of Soukhovitskii et al./14/. MT=2 Elastic scattering cross section Calculated as total - non-elstic scattering cross sections MT=18 Fission cross section Below about 1 MeV, a smooth curve was determined by eye- guiding. Above 1 MeV, the experimental data of Burke et al./15/ were analyzed with GMA code /16/. They measured the fission cross section with a surrogate ratio method in the energy region from 493 keV to 24.9 MeV. 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). 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 neutron spectra Calculated with CCONE code. MT=455 Delayed neutron spectra (same as JENDL-3.3) The spectra adopted were calculated by Brady and England/6/. 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./17/ 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%. MF=32 Covariances of resonance parameters MT=151 Resolved resonance parameterss Format of LCOMP=0 was adopted. Uncertainties of parameters were taken from Mughabghab /18/. Those of neutron widths were due to the uncertainties of the fission area. For the parameters without any information on uncertainty, the following uncertainties were assumed: Resonance energy 0.1 % Neutron width 20 % Capture width 50 % Fission width 50 % MF=33 Covariances of neutron cross sections Covariances were given to all the cross sections by using KALMAN code/19/ and the covariances of model parameters used in the cross-section calculations. For the fission cross section, covariances obtained with the GMA analysis were adopted. Standard deviations (SD) were multiplied by a factor of 1.5. In the resolved resonance region, the following standard deviations were added to the contributions from resonance parameters: Total 30 % Elastic scattering 20 % Capture 30 % 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/5/ 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/20/ * Global parametrization of Koning-Duijvestijn/21/ was used. * Gamma emission channel/22/ was added to simulate direct and semi-direct capture reaction. 3) Hauser-Feshbach statistical model * Moldauer width fluctuation correction/23/ 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/24/. 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/25/,/26/ was used. The prameters are shown in Table 7. ------------------------------------------------------------------ Tables ------------------------------------------------------------------ Table 1. Coupled channel calculation -------------------------------------------------- * rigid rotor model was applied * coupled levels = 0,1,2,3,5 (see Table 2) * optical potential parameters /14/ 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= 0.76e-4 S1= 1.99e-4 R'= 9.48 fm (En=1 keV) -------------------------------------------------- Table 2. Level Scheme of U-237 ------------------- No. Ex(MeV) J PI ------------------- 0 0.00000 1/2 + * 1 0.01139 3/2 + * 2 0.05630 5/2 + * 3 0.08286 7/2 + * 4 0.15996 5/2 + 5 0.16300 9/2 + * 6 0.20419 7/2 + 7 0.20500 11/2 + 8 0.26095 9/2 + 9 0.27400 7/2 - 10 0.31600 9/2 - 11 0.32700 11/2 + 12 0.36700 11/2 - 13 0.42615 7/2 + 14 0.43200 13/2 - 15 0.43200 13/2 + 16 0.48200 9/2 + 17 0.48400 7/2 + 18 0.50600 15/2 - 19 0.53000 13/2 - 20 0.54062 1/2 - 21 0.54500 11/2 - 22 0.55100 11/2 + 23 0.55498 3/2 - 24 0.57500 21/2 + ------------------- *) Coupled levels in CC calculation Table 3. Level density parameters -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- U-238 18.7359 1.5557 3.0121 0.3767 -0.1089 3.8153 U-237 18.6682 0.7795 2.7455 0.3584 -0.6445 2.7495 U-236 18.6005 1.5623 2.7551 0.3859 -0.1547 3.8920 U-235 18.5328 0.7828 2.6265 0.3874 -0.9246 3.1046 U-234 18.4650 1.5689 2.5578 0.3902 -0.1511 3.9087 -------------------------------------------------------- Table 4. Fission barrier parameters ---------------------------------------- Nuclide V_A hw_A V_B hw_B MeV MeV MeV MeV ---------------------------------------- U-238 6.320 0.800 5.200 0.600 U-237 6.150 0.650 5.750 0.500 U-236 6.400 1.040 5.050 0.550 U-235 5.790 0.400 5.470 0.300 U-234 6.180 1.040 5.080 0.600 ---------------------------------------- Table 5. Level density above inner saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- U-238 20.5728 1.8150 2.6000 0.3280 -0.5964 3.8150 U-237 20.4984 0.9094 2.6000 0.3431 -1.7162 3.1094 U-236 20.0594 1.8226 2.6000 0.3473 -0.8150 4.0226 U-235 20.3497 0.9133 2.6000 0.3299 -1.4981 2.9133 U-234 20.2753 1.8304 2.6000 0.3306 -0.5810 3.8304 -------------------------------------------------------- Table 6. Level density above outer saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- U-238 21.1238 1.8150 0.2200 0.3757 -0.0486 4.0150 U-237 20.4984 0.9094 0.1800 0.3828 -0.9590 3.1094 U-236 20.0594 1.8226 0.1400 0.3882 -0.0489 4.0226 U-235 20.3497 0.9133 0.1000 0.3706 -0.7868 2.9133 U-234 20.2753 1.8304 0.0600 0.3719 0.1310 3.8304 -------------------------------------------------------- Table 7. Gamma-ray strength function for U-238 -------------------------------------------------------- K0 = 1.501 E0 = 4.500 (MeV) * E1: ER = 10.90 (MeV) EG = 2.50 (MeV) SIG = 300.00 (mb) ER = 13.80 (MeV) EG = 4.70 (MeV) SIG = 450.00 (mb) * M1: ER = 6.62 (MeV) EG = 4.00 (MeV) SIG = 2.66 (mb) * E2: ER = 10.17 (MeV) EG = 3.25 (MeV) SIG = 6.51 (mb) -------------------------------------------------------- References 1) O.Iwamoto et al.: J. Nucl. Sci. 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