94-Pu-238 JAEA+ EVAL-JAN10 O.Iwamoto,T.Nakagawa + DIST-MAY10 20100303 ----JENDL-4.0 MATERIAL 9434 -----INCIDENT NEUTRON DATA ------ENDF-6 FORMAT History 06-02 Fission cross section was revised. 06-07 Resolved resonance parameters were revised. 07-05 Theoretical calculation was made with CCONE code. Data were compiled as JENDL/AC-2008/1/. 09-08 (MF1,MT458) was evaluated. 09-12 New theoretical calculation was made with CCONE code. 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's = 455 and 456. MT=455 Delayed neutron data Determined from nu-d of the following three nuclides and partial fission cross sections calculated with CCONE code/2/. Pu-239 = 0.004710 Pu-238 = 0.0026 Pu-237 = 0.0018 The value of Pu-239 are averages of systematics by Tuttle/3/, Benedetti et al./4/ and Waldo et al./5/ Other two are 20% decreased from the systematics. Decay constants calculated by Brady and England./6/ were adopted. MT=456 Number of prompt neutrons per fission Based on the systematics recommended by Ohsawa/7/. The result is in very good agreement with experimental data of Kroshin and Zamjatnin/8/, and Jaffy and Lerner/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 500 eV) Based on the resonance parameters reported by Young et al./14/, Silbert et al. /15/ and Alam et al./16/. These parameters were adjusted to the thermal cross sections: Total = 588 b /14/ Fission = 17.7 b /17,18,19,20/ Capture = 412 b /21/ Unresolved resonance parameters (500 eV - 60 keV) Parameters were determined with ASREP code /22/ to reproduce the total, fission and capture cross sections described below Since the fission cross section in this energy region had resonance structure, average cross sections were used in the fitting. 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 585.18 elastic 154.56 fission 17.77 27.6 capture 412.85 146 ------------------------------------------------------- (*) 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 total (MT=1), 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 Below 10 keV, total cross section was calculated as a sum of elastic scattering and capture cross sections calculated with CCONE code /2/ and fission cross section determined from expeimental data (see MT=18). Above 10 keV, the cross-section data calculated with CCONE code were adopted. The calculation was made with CC OMP of Soukhovitskii et al./23/. MT=2 Elastic scattering cross section Below 10 keV, the elastic scattering cross section was calcu- lated with CCONE code. Above 10 keV, it was obtained as (total cross section) - (partial cross sections). MT=18 Fission cross section The following experimental data were analyzed in the energy range above 450 eV with the GMA code/24/: Authors Energy range Data points Reference Fumushkin+ 0.44 - 3.62 MeV 14 /25/(*1) Drake+ 450 eV - 2.58 MeV 774 /26/ Silbert+ 451 eV - 2.97 MeV 4228 /15/ Knitter+ 0.146 - 9.94 MeV 89 /27/(*1) Budtz-Jorgensen+ 0.45 - 265 keV 602 /28/ Aleksandrov+ 2.9 MeV 1 /29/ Fursov+ 0.149 - 14.7 MeV 71 /30/(*2) (*1) Ratio to U-235 fission, (*2) Ratio to Pu-239 fission. JENDL-3.3 data was used to convert them to cross sections. The results of GMA were used to determine the parameters in the CCONE calculation. Above 10 MeV, the cross section was determined with 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 Silbert et al./15/ were used to determine the model parameters of CCONE code. 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. MT=455 Delayed neutron spectra Summation calculation by Brady and England /6/ 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./31/ for Pu-239 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 Error of 15% was assumed below 5 MeV and above 5 MeV, respectively. MT=456 Covariance was obtained by fitting a linear function to the data at the thermal energy and 5 MeV assuming errors of 3% and 5%, respectively. The error at the thermal energy was estimated from experimental data/8,9/ MF=32 Covariances of resonance parameters Format of LCOMP=0 was adopted. Standard deviations were adopted from the data of Silbert et al./15/ Error of the capture width was assumed to be 18%. Error of 0.1% was given to the resonance energies. MF=33 Covariances of neutron cross sections Covariances were given to all the cross sections by using KALMAN code/32/ and the covariances of model parameters used in the theoretical calculations. For the following cross sections, covariances were determined by different methods. MT=1 Total cross section In the energy region from 1 to 500eV, uncertainty of 10 % was added. MT=2 Elastic scattering cross sections In the resonance region (below 500eV), uncertainty of 10 % was added. MT=18 Fission cross section Above the resonance region, cross section was evaluated with GMA code/24/. Standard deviations obtained were multiplied by a factor of 2.0. Above 12 MeV, they were assumed to be 20%. MT=102 Capture cross section In the resonance region, addtional error of 10 % was given. Above 400 eV, covariance matrix was obtained with CCONE and KALMAN codes/32/. 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/33/ * Global parametrization of Koning-Duijvestijn/34/ was used. * Gamma emission channel/35/ was added to simulate direct and semi-direct capture reaction. 3) Hauser-Feshbach statistical model * Moldauer width fluctuation correction/36/ 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/37/. 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/38/,/39/ 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 /23/ 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 = 0.22495 beta_4 = 0.07282 beta_6 = -0.01518 * Calculated strength function S0= 1.11e-4 S1= 2.54e-4 R'= 9.40 fm (En=1 keV) -------------------------------------------------- Table 2. Level Scheme of Pu-238 ------------------- No. Ex(MeV) J PI ------------------- 0 0.00000 0 + * 1 0.04408 2 + * 2 0.14595 4 + * 3 0.30338 6 + * 4 0.51358 8 + * 5 0.60514 1 - 6 0.66140 3 - 7 0.76324 5 - 8 0.77348 10 + 9 0.94146 0 + 10 0.96278 1 - 11 0.96820 2 - 12 0.98309 2 + 13 0.98545 2 - 14 1.01860 3 + 15 1.02854 2 + 16 1.06994 3 + 17 1.08010 12 + 18 1.08256 4 - 19 1.12576 4 + 20 1.13400 0 + 21 1.17440 2 + 22 1.20246 3 - 23 1.22865 0 + 24 1.25200 7 - ------------------- *) 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-239 18.4349 0.7762 1.8503 0.3560 -0.5001 2.5655 Pu-238 18.3685 1.5557 1.9652 0.3804 0.0287 3.6608 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 -------------------------------------------------------- Table 4. Fission barrier parameters ---------------------------------------- Nuclide V_A hw_A V_B hw_B MeV MeV MeV MeV ---------------------------------------- Pu-239 6.050 0.700 5.700 0.600 Pu-238 5.500 0.600 4.800 0.600 Pu-237 5.800 0.800 5.800 0.520 Pu-236 6.000 1.040 5.000 0.600 ---------------------------------------- Table 5. Level density above inner saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Pu-239 20.2784 0.9056 2.6000 0.3523 -1.8394 3.2056 Pu-238 20.2054 1.8150 2.6000 0.3668 -1.1448 4.3150 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 -------------------------------------------------------- Table 6. Level density above outer saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Pu-239 20.2784 0.9056 0.3800 0.3901 -1.0534 3.2056 Pu-238 20.2054 1.8150 0.3400 0.4053 -0.3124 4.3150 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 -------------------------------------------------------- Table 7. Gamma-ray strength function for Pu-239 -------------------------------------------------------- K0 = 1.800 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 = 6.61 (MeV) EG = 4.00 (MeV) SIG = 3.04 (mb) * E2: ER = 10.15 (MeV) EG = 3.24 (MeV) SIG = 6.79 (mb) -------------------------------------------------------- References 1) O.Iwamoto et al.: J. Nucl. Sci. Technol., 46, 510 (2009). 2) O.Iwamoto: J. Nucl. Sci. 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