94-Pu-236 JAEA+ EVAL-FEB10 O.Iwamoto, T.Nakagawa, et al. DIST-MAY10 20100318 ----JENDL-4.0 MATERIAL 9428 -----INCIDENT NEUTRON DATA ------ENDF-6 FORMAT History 06-04 Resonance parameters and fission cross section were revised. 07-02 Theoretical calculation was made with CCONE code. 07-05 Re-calculation with CCONE code was made. Data were compiled as JENDL/AC-2008/1/. 09-02 (1,452), (1,455) and (1,456) were revised. 10-02 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's = 455 and 456. MT=455 Delayed neutron data Average values of 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 assumed to be the same as those of Pu-238 calculated by Brady and England/6/. MT=456 Number of prompt neutrons per fission Based on systematics by Ohsawa/7/. MF= 2 Resonance parameters MT=151 Resolved resonance parameters (below 10 eV) The resonance parameters of ENDF/B-VI were adopted and those of a negative resonance were modified to reproduce the thermal fission cross section of 141+-15 b which were derived from the experimental data of Gindler et al./8/, Hulet et al./9/, Belyaev et al./10/ Unresolved resonance parameters (10 eV - 40 keV) Parameters were determined with ASREP code/11/ to reproduce the fission cross section determined from the experimental data/12,13/, and total and capture cross sections calculated with CCONE code/5/. 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 176.72 elastic 9.20 fission 139.96 971 capture 27.56 248 ------------------------------------------------------- (*) 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 The following experimental data were analyzed in the energy range from 100 eV to 4 MeV with the GMA code/15/: Authors Energy range Data points Reference Gromova+ 7.14 eV - 5.78 MeV 106 /12/ Gerasimov+ 15.8 eV - 34 keV 9 /13/ Below 80 eV, resonance structure was reproduced by eye- guiding. Avove 5.5 MeV, cross sections calculated with CCONE code were adopted. The simulated (n,f) cross sections of Britt and Wilhelmy/16/, and the experimental data of Gromova et al./12/, Gerasimov et al./13/ and Vorotnikov et al./17/ 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 fission neutrons Calculated with CCONE code. 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 which was estimated from its systematics, 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./18/ for Pu-239 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 assumed as follows: Resonance energy 0.1 % Neutron width 10 % Capture width 50 % 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/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. SD's of 15% were assumed in the energy region below 86 eV and above 4 MeV. In the resolved resonance region, the following standard deviations were added to the contributions from resonance parameters: Total 2 b Elastic scattering 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/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 = 0,1,2,3,4 (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 = 0.21978 beta_4 = 0.07414 beta_6 = -0.00968 * Calculated strength function S0= 1.11e-4 S1= 2.50e-4 R'= 9.45 fm (En=1 keV) -------------------------------------------------- Table 2. Level Scheme of Pu-236 ------------------- No. Ex(MeV) J PI ------------------- 0 0.00000 0 + * 1 0.04463 2 + * 2 0.14745 4 + * 3 0.30580 6 + * 4 0.51570 8 + * 5 0.77350 10 + ------------------- *) Coupled levels in CC calculation Table 3. Level density parameters -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Pu-237 18.3022 0.7795 1.8799 0.3586 -0.5090 2.5865 Pu-236 18.2358 1.5623 1.9752 0.3737 0.1216 3.5619 Pu-235 18.1694 0.7828 1.9791 0.3502 -0.4208 2.4828 Pu-234 18.1029 1.5689 2.1707 0.3732 0.1282 3.5689 -------------------------------------------------------- Table 4. Fission barrier parameters ---------------------------------------- Nuclide V_A hw_A V_B hw_B MeV MeV MeV MeV ---------------------------------------- Pu-237 5.800 0.800 5.800 0.520 Pu-236 6.000 1.040 5.000 0.600 Pu-235 6.000 0.800 5.000 0.520 Pu-234 5.600 1.040 4.600 0.600 ---------------------------------------- Table 5. Level density above inner saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Pu-237 20.1324 0.9094 2.6000 0.3320 -1.5137 2.9094 Pu-236 20.0594 1.8226 2.6000 0.3326 -0.6004 3.8226 Pu-235 19.9863 0.9133 2.6000 0.3333 -1.5098 2.9133 Pu-234 19.9132 1.8304 2.6000 0.3339 -0.5927 3.8304 -------------------------------------------------------- Table 6. Level density above outer saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Pu-237 20.1324 0.9094 0.3000 0.3706 -0.7963 2.9094 Pu-236 20.0594 1.8226 0.2600 0.3719 0.1175 3.8226 Pu-235 19.9863 0.9133 0.2200 0.3732 -0.7913 2.9133 Pu-234 19.9132 1.8304 0.1800 0.3744 0.1264 3.8304 -------------------------------------------------------- Table 7. Gamma-ray strength function for Pu-237 -------------------------------------------------------- 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 = 6.63 (MeV) EG = 4.00 (MeV) SIG = 2.67 (mb) * E2: ER = 10.18 (MeV) EG = 3.27 (MeV) SIG = 6.80 (mb) -------------------------------------------------------- References 1) O.Iwamoto et al.: J. Nucl. Sci. 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