98-Cf-252 JAEA+ EVAL-FEB10 O.Iwamoto,T.Nakagawa,+ DIST-MAY10 20100318 ----JENDL-4.0 MATERIAL 9861 -----INCIDENT NEUTRON DATA ------ENDF-6 FORMAT History 05-12 Fission cross section above 1 keV was revised. 07-09 Theoretical calculation was done with CCONE code. Data were compiled as JENDL/AC-2008/1/. 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 Semi-empirical formula by Tuttle/2/. Decay constants were evaluated by Brady and England/3/. MT=456 Number of prompt neutrons per fission Semi-empirical formula by Howerton/4/. MF= 2 Resonance parameters MT=151 Resolved resonance parameters (MLBW: 1.0e-5 - 1.0 keV) (same as JENDL-3.3) Resonance parameters were taken from Moore et al./5/ by assuming an average radiative capture width of 0.035 eV and fission width of 0.035 eV. Two hypothetical resonances at 1.4 and -3.5 EV were adopted to reproduce the 2200-m/s cross sections and resonance integrals/6,7/. Scattering radius of 9.23 fm was estimated from the shape elastic scattering cross section calculated with CASTHY/8/. Unresolved resonance parameters (1 - 150 keV) Parameters (URP) were determined with ASREP code/9/ 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 64.81 elastic 11.06 fission 33.03 109 capture 20.71 47.3 ------------------------------------------------------- (*) 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 the elastic scattering (MT=2) and fission cross sections (MT=18, 19, 20, 21, 38) were calculated with CCONE code/10/. MT= 1 Total cross section The cross section was calculated with CC OMP of Soukhovitskii et al./11/ MT= 2 Elastic scattering cross section Calculated as total - non-elastic scattering cross sections. MT=18 Fission cross section (Above 1 keV) The experimental data of Moore et al./5/ were analyzed with the GMA code /12/. The results of GMA were used to determine the parameters in the CCONE calculation. In the energy region from 4 to 20 MeV, the data of JENDL-3.3 were adopted. 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 netrons Calculated with CCONE code/10/. MT=455 Delayed neutrons Calculated by Brady and England/3/. 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./13/ 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 10%. 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 and capture cross sections at the thermal neutron energy. MF=33 Covariances of neutron cross sections Covariances were given to all the cross sections by using KALMAN code/15/ 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 above 8 MeV were assumed to be 20%. In the resolved resonance region, the following standard deviations were added to the contributions from resonance parameters: 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/10/ 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/16/ * Global parametrization of Koning-Duijvestijn/17/ was used. * Gamma emission channel/18/ was added to simulate direct and semi-direct capture reaction. 3) Hauser-Feshbach statistical model * Moldauer width fluctuation correction/19/ 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/20/. 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/21/,/22/ 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 /11/ 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= 1.42e-4 S1= 3.00e-4 R'= 9.17 fm (En=1 keV) -------------------------------------------------- Table 2. Level Scheme of Cf-252 ------------------- No. Ex(MeV) J PI ------------------- 0 0.00000 0 + * 1 0.04572 2 + * 2 0.15173 4 + * 3 0.31920 6 + * 4 0.54720 8 + * 5 0.80482 2 + 6 0.83081 2 - 7 0.84572 3 + 8 0.86751 3 - 9 0.90030 4 + 10 0.91703 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 -------------------------------------------------------- Cf-253 19.3604 0.7544 2.0655 0.3368 -0.4669 2.4564 Cf-252 19.2945 1.5119 1.7395 0.3655 0.0444 3.5280 Cf-251 19.2285 0.7574 1.2773 0.3926 -0.9361 3.0632 Cf-250 19.1626 1.5179 1.0208 0.3974 -0.1838 3.8400 Cf-249 19.0966 0.7605 0.7689 0.3773 -0.6847 2.7641 -------------------------------------------------------- Table 4. Fission barrier parameters ---------------------------------------- Nuclide V_A hw_A V_B hw_B MeV MeV MeV MeV ---------------------------------------- Cf-253 5.600 1.000 4.600 0.800 Cf-252 6.000 1.040 5.000 0.800 Cf-251 6.200 0.800 5.000 0.600 Cf-250 6.200 1.040 5.400 0.600 Cf-249 6.700 1.200 5.900 0.800 ---------------------------------------- Table 5. Level density above inner saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Cf-253 21.6837 0.8802 2.5000 0.3407 -1.8541 3.1802 Cf-252 21.6098 1.7638 2.5000 0.3202 -0.6492 3.7638 Cf-251 21.5360 0.8837 2.5000 0.3208 -1.5294 2.8837 Cf-250 21.4621 1.7709 2.5000 0.2827 -0.1068 3.2709 Cf-249 20.0514 0.8872 2.5000 0.3486 -1.7837 3.0872 -------------------------------------------------------- Table 6. Level density above outer saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Cf-253 21.6837 0.8802 1.0800 0.3466 -0.8314 2.8802 Cf-252 21.6098 1.7638 1.0400 0.3477 0.0528 3.7638 Cf-251 21.5360 0.8837 1.0000 0.3488 -0.8268 2.8837 Cf-250 21.4621 1.7709 0.9600 0.3499 0.0610 3.7709 Cf-249 20.0514 0.8872 0.9200 0.3794 -1.0059 3.0872 -------------------------------------------------------- Table 7. Gamma-ray strength function for Cf-253 -------------------------------------------------------- K0 = 1.500 E0 = 4.500 (MeV) * E1: ER = 11.40 (MeV) EG = 2.72 (MeV) SIG = 258.47 (mb) ER = 14.19 (MeV) EG = 4.12 (MeV) SIG = 516.94 (mb) * M1: ER = 6.48 (MeV) EG = 4.00 (MeV) SIG = 1.84 (mb) * E2: ER = 9.96 (MeV) EG = 3.07 (MeV) SIG = 7.35 (mb) -------------------------------------------------------- References 1) O.Iwamoto et al.: J. Nucl. Sci. 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