92-U -236 JAEA+ EVAL-JAN10 O.Iwamoto, T.Nakagawa, et al. DIST-MAY10 20100302 ----JENDL-4.0 MATERIAL 9231 -----INCIDENT NEUTRON DATA ------ENDF-6 FORMAT History 05-10 Fission cross section was evaluated with GMA code. 06-06 Resonance parameters were modified. 07-05 Theoretical calculation was made with CCONE code. 07-12 Resonance parameters were modified. Data were compiled as JENDL/AC-2008/1/. 09-03 (MF1,MT455) was modified. 09-08 (MF1,MT458) was evaluated. 09-11 (MF1,MT455) was modified. New theoretical calculation was made with CCONE code. 10-01 Data of prompt gamma rays due to fission were given. 10-02 Covariance data were given. MF=1 General Information MT=452 Total number of neutrons per fission Sum of MT's 455 and 456. MT=455 Delayed neutrons per fission Determined from nu-d of the following three nuclides and partial fission cross sections calculated with CCONE code/2/. U -237 = 0.02250 U -236 = 0.007 U -235 = 0.004 The data for U-237 is average of experimental data of Roschenko et al./3/ For the other nuclide, estimated so as to reproduce the data of Bobkov et al./4/ at 14.7 MeV. Six group decay constants were adopted from Brady and England /5/. MT=456 Prompt neutrons per fission (same as JENDL-3.3) Taken from Malinovskii's paper/6/. Above 5.9 MeV, their recommendation was extrapolated. 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/7/. 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 2000/8/ does not include average neutron energy values, the average values were calculated using the formula shown in the report by T.R. England/9/. The fractions of prompt energy were calculated using the fractions of Sher's evaluation/10/ 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: 1.0-5 eV - 4.0 keV) Parameters were based on the data of Macklin and Alexander/11/, Parker et al./12/, and recommendation of Mughabghab/13/: Parameters above 20 eV: Macklin and Alexander 5.45-eV resonancd: Mughabghab Fission widths: Parker et al. The parameters of 5.45-eV resonance were adjusted so as to reproduce the fission cross section measured by Wagemans et al./14/ and capture resonance integral of about 350 b/15,16, 17/ P-wave resonances were assigned according to Carraro and Brusegan/18/. Capture widths were adjusted so as to reproduce well the capture cross sections measured by Adamchuk et al./19/ and Muradian et al./20/. A negative resonance was assumed at -9.7eV/13/. Its parameters were adjusted to the thermal cross sections. The thermal cross sections to be reproduced: Fission = 0.00022 +- 0.00002 b Wagemans et al./14/ Capture = 5.12 +- 0.09 b Davletshin et al./21/, Vorona et al./22/, Carlson /23/, Schuman et al./16/ etc. Elastic scattering = 10.6 +- 0.7 b Mc Callum /24/ Total = 16.0 +- 0.1 b Vorona et al./22/ Unresolved resonance parameters (4 keV - 100 keV) Determined to reproduce the total and capture cross sections with ASREP code/25/. 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 15.95 elastic 10.83 fission 0.00026 2.22 capture 5.122 353 ------------------------------------------------------- (*) 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/2/. MT= 1 Total cross section The cross section was calculated with CC OMP of Soukhovitskii et al./26/ MT=2 Elastic scattering cross section Calculated as total - non-elstic scattering cross sections. MT=18 Fission cross section Above 300keV, the following experimental data were analyzed with the GMA code/27/: Authors Energy range Data points Reference Behrens+ 0.172 - 20.0 MeV 129 /28/(*1) Meadows 0.596 - 9.91 MeV 57 /29/(*1) Nordborg+ 3.21 - 8.62 MeV 40 /30/(*1) Goverdovskii+ 4.24 - 10.7 MeV 39 /31/(*1) Fursov+ 1.48 - 7.4 MeV 70 /32/(*1) Goverdovskii+ 15.1 - 16.4 MeV 2 /33/(*1) Terayama+ 0.99 - 6.99 MeV 27 /34/(*1) Meadows 14.7 MeV 1 /35/(*1) Shpak+ 0.5 - 3.72 MeV 77 /36/(*1) (*1) Relative to U-235 fission. Data were converted to cross sections using JENDL-3.3 data. The results of GMA were used to determine the parameters in the CCONE calculation. Between 4 and 300 keV, the data in the resolved resonance region and those above 300 keV were connected by eye-guiding. 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 Calculated with CCONE code. The experimental data of Bergman et al./37/, Adamchuk et al./19/, Kazakov et al./38/, and Buleeva et al./39/ were considered to determine the model parameters for 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 neutron spectra Calculated with CCONE code. MT=455 Delayed neutron spectra (same as JENDL-3.3) Summation calculation made by Brady and England /5/ was adopted. 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./40/ 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 Assumed uncertainties: En < 5 MeV 5% /3/ 5 MeV < En < 7 MeV 15% 7 MeV < En < 20 MeV 20% MT=456 Covariance was obtained by fitting a stlight line to data measured by Malinovskii et al./6/ MF=32 Covariances of resonance parameters Format of LCOMP=0 was adopted. Errors of neutron and capture widths for the levels above 29 eV were based on the data of Macklin and Alexander/11/. Those of fission widths were taken from Ref./12/ Error of the 5.456-eV level capture width was recommendation of Mughabghab/13/. For the neutron and capture widths, error of 5 % was assumed. Error of resonance energies was assumed to be 0.02%/11/. Addtional error of 90 % was given to fission cross section below above 10 eV in MF=33. The parameters of 5.45-eV resonance were determined so that the fission cross section measured by Wagemans et al./14/ were reproduced well. Therefore the cross section around this resonance was well determined. Additional error of 8% was assumed below 1 eV. For the capture cross section, contributions of resonance parameter errors to the cross section are only a few %. Since it seemes to be too small, uncertainties of 5% were added in the energy range from 50 eV to 4 keV. For the total and elastic scttering cross sections, error of 5% was added. MF=33 Covariances of neutron cross sections Covariances were given to all the cross sections by using KALMAN code/41/ and the covariances of model parameters used in the theoretical calculations. For the following cross sections, covariances were determined by different methods. MT=18 Fission cross section Evaluated with GMA code/27/. 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/42/ * Global parametrization of Koning-Duijvestijn/43/ was used. * Gamma emission channel/44/ was added to simulate direct and semi-direct capture reaction. 3) Hauser-Feshbach statistical model * Moldauer width fluctuation correction/45/ 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/46/. 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/47/,/48/ 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 /26/ 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 = 0.213213 beta_4 = 0.066 beta_6 = 0.0015 * Calculated strength function S0= 0.89e-4 S1= 2.40e-4 R'= 9.52 fm (En=1 keV) -------------------------------------------------- Table 2. Level Scheme of U-236 ------------------- No. Ex(MeV) J PI ------------------- 0 0.00000 0 + * 1 0.04524 2 + * 2 0.14948 4 + * 3 0.30978 6 + * 4 0.52224 8 + * 5 0.68760 1 - 6 0.74415 3 - 7 0.78230 10 + 8 0.84830 5 - 9 0.91921 0 + 10 0.95799 2 + 11 0.96030 2 + 12 0.96663 1 - 13 0.98767 2 - 14 0.99980 7 - 15 1.00150 3 + 16 1.03560 3 - 17 1.05085 4 + 18 1.05289 4 - 19 1.05861 4 + 20 1.06610 3 + 21 1.07000 4 - 22 1.08530 12 + 23 1.09380 2 + 24 1.10440 5 - 25 1.11067 2 - 26 1.12690 5 + 27 1.14700 4 + 28 1.14940 3 - 29 1.16400 5 - ------------------- *) 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-237 18.3937 0.7795 2.7455 0.3633 -0.6631 2.7715 U-236 18.6005 1.5623 2.7551 0.3859 -0.1547 3.8920 U-235 18.4419 0.7828 2.6265 0.3721 -0.7434 2.8828 U-234 18.4650 1.5689 2.5578 0.3902 -0.1511 3.9087 U-233 18.3972 0.7861 2.4694 0.3708 -0.6995 2.8410 -------------------------------------------------------- Table 4. Fission barrier parameters ---------------------------------------- Nuclide V_A hw_A V_B hw_B MeV MeV MeV MeV ---------------------------------------- U-237 6.100 0.600 5.900 0.600 U-236 6.500 1.100 5.230 0.600 U-235 5.790 0.400 5.470 0.300 U-234 6.180 1.040 5.080 0.600 U-233 5.970 0.800 5.450 0.520 ---------------------------------------- Table 5. Level density above inner saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- U-237 20.4984 0.9094 2.6000 0.3286 -1.5020 2.9094 U-236 21.8830 1.8226 2.6000 0.3308 -0.7586 4.0226 U-235 18.1694 0.9133 2.6000 0.3671 -1.7919 3.1133 U-234 20.2753 1.8304 2.6000 0.3306 -0.5810 3.8304 U-233 20.2008 0.9172 2.6000 0.3312 -1.4942 2.9172 -------------------------------------------------------- Table 6. Level density above outer saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- U-237 21.9626 0.9094 0.1800 0.3813 -1.1131 3.3094 U-236 20.4241 1.8226 0.1400 0.4250 -0.5513 4.6226 U-235 18.1694 0.9133 0.1000 0.4121 -0.9812 3.1133 U-234 20.2753 1.8304 0.0600 0.3719 0.1310 3.8304 U-233 20.2008 0.9172 0.0200 0.3732 -0.7817 2.9172 -------------------------------------------------------- Table 7. Gamma-ray strength function for U-237 -------------------------------------------------------- K0 = 1.650 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 = 6.63 (MeV) EG = 4.00 (MeV) SIG = 2.86 (mb) * E2: ER = 10.18 (MeV) EG = 3.27 (MeV) SIG = 6.51 (mb) -------------------------------------------------------- References 1) O.Iwamoto et al.: J. Nucl. Sci. 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