91-Pa-231 JAEA+ EVAL-JAN10 O.Iwamoto, T.Nakagawa, et al. DIST-MAY10 20100323 ----JENDL-4.0 MATERIAL 9131 -----INCIDENT NEUTRON DATA ------ENDF-6 FORMAT History 05-11 Fission cross section was evaluated with GMA code. 06-08 Resonance parameters were revised. 07-10 Theoretical calculation was performed with CCONE code. Data were compiled as JENDL/AC-2008/1/. 09-04 MF01 was revised. 09-08 (MF1,MT458) was evaluated. 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 fissioning nuclides and partial fission cross sections calculated with CCONE code/2/. Pa-232 = 0.01083 Pa-231 = 0.007461 Pa-230 = 0.005154 They are averages of systematics by Tuttle/3/, Benedetti et al./4/ and Waldo et al./5/ Decay constants were evaluated by Brady and England/6/. MT=456 Number of prompt neutrons per fission Estimated from 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; below 115 eV) The resonance parameters of JENDL-3.3 were based on the following data: Resonance energies, neutron and gamma widths: Hussein et al./12/ Fission area: Plattard et al./13/ Parameters of resonances below 1.24 eV: Mughabghab/14/ Those data were revised by comparing with the total cross section of Simpson et al./15/ and the fission cross section of Kobayashi et al./16/ The resonance formula was changed to MLBW. Total spin of each level was assumed with JCONV code/17/. Thermal cross section and resonance integral calculated from the present resonance parameters are given in the following table. The thermal cross sections to be reproduced were determined from experimental data: Total = 211.0+-3.1 b Simpson et al./15/ Fission = 0.0239+-0.0007 b Wagemans et al./18,19/, Kobayashi et al./20/ Capture = 202.2+-5.3 b Smith et al./21/, Aleksandrov et al./22/, Gryntakis et al./23/, Kobayashi/24/ The capture resonance integrals reported by Jurova et al./25/ and Aleksandrov et al./22/ were 1044b and 1180b, respectively. Unresolved resonance parameters (115 eV - 10 keV) Cross sections were reproduced with average resonance parameters determined by ASREP code/26/. These parameters are used only for self-shielding effects. Thermal cross sections and resonance integrals (at 300K) ------------------------------------------------------- 0.0253 eV reson. integ.(*) (barns) (barns) ------------------------------------------------------- total 212.32 elastic 10.59 fission 0.0236 3.24 capture 201.71 542 ------------------------------------------------------- (*) 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 elastic scattering and fission cross sections (MT's =2, 18-21, 38) were calculated with CCONE code/2/. MT= 1 Total cross section The cross section was calculated with CC OMP of Soukhovitskii et al./27/ with modification of the quadrupole deformation parameter. MT=2 Elastic scattering cross section Calculated as total - non-elstic scattering cross sections MT=18 Fission cross section (Above 115 eV) The following experimental data were analyzed in the energy ranges from 115 eV to 12 keV, and from 110 keV to 12 MeV with the GMA code/28/: Authors Energy range Data points Reference Plattard+ 0.112 - 16.9 MeV 4120 /29/ Fursov+ 0.135 - 7.4 MeV 69 /30/(*1) Kobayashi+ 0.089 - 12.6 keV 44 /16/ Oberstedt+ 0.76 - 3.46 MeV 15 /31/ (*1) The data were measured relatively to Pu-239 fission. They were converted to Pa-231 fission by using JENDL- 3.3 data. The results of the analysis were adopted in the energy ranges from 115 eV to 10 keV and from 120 keV to 9.5 MeV. CCONE calculation was adopted in the energy ranges from 10 to 120 keV and above 9.5 MeV. The results of GMA below 10 MeV, the preliminary experimental data of IRMM/32/ above 15 MeV, and the experimental data of Birgul and Lyle/33/ at 15 MeV 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/2/. MT=18 Fission Isotropic distributions in the laboratory system were assumed. MF= 5 Energy distributions of secondary neutrons MT=18 Prompt neutrons Calculated with CCONE code/2/. MT=455 Delayed neutrons Calculated by Brady and England/6/. MF= 6 Energy-angle distributions Calculated with CCONE code/2/. 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./34/ 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 /35/. 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/36/ and the covariances of model parameters used in the cross-section calculations. Covariances of the total, elastic-scattering and capture cross sections were determined by considering the experimental data (see MF=3). 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 of 18% was assumed in the energy region above 13 MeV. In the resolved resonance region, the following standard deviations were added to the contributions from resonance parameters: Total 2 b Elastic scattering 10 % 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/37/ * Global parametrization of Koning-Duijvestijn/38/ was used. * Gamma emission channel/39/ was added to simulate direct and semi-direct capture reaction. 3) Hauser-Feshbach statistical model * Moldauer width fluctuation correction/40/ 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/41/. 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/42/,/43/ was used. The prameters are shown in Table 7. ------------------------------------------------------------------ Tables ------------------------------------------------------------------ Table 1. Coupled channel calculation -------------------------------------------------- * rigid rotor model was applied * coupled levels = 0,1,2,3,9,14 (see Table 2) * optical potential parameters /27/ 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 = 0.19 beta_4 = 0.066 beta_6 = 0.0015 * Calculated strength function S0= 0.81e-4 S1= 2.50e-4 R'= 9.64 fm (En=1 keV) -------------------------------------------------- Table 2. Level Scheme of Pa-231 ------------------- No. Ex(MeV) J PI ------------------- 0 0.00000 3/2 - * 1 0.00921 1/2 - * 2 0.05857 7/2 - * 3 0.07769 5/2 - * 4 0.08421 5/2 + 5 0.10141 7/2 + 6 0.10227 3/2 + 7 0.11165 9/2 + 8 0.13400 11/2 + 9 0.16860 11/2 - * 10 0.17150 11/2 + 11 0.17416 5/2 - 12 0.18350 5/2 + 13 0.18890 13/2 + 14 0.19350 9/2 - * 15 0.21824 7/2 - 16 0.24732 7/2 + 17 0.27200 9/2 - 18 0.27380 1/2 + 19 0.29660 17/2 + 20 0.30070 15/2 + 21 0.30400 9/2 + 22 0.31150 5/2 + 23 0.31680 17/2 + 24 0.31795 3/2 + 25 0.32021 3/2 - 26 0.32870 15/2 - 27 0.34000 11/2 - 28 0.35150 13/2 - 29 0.35184 5/2 - 30 0.38500 23/2 + ------------------- *) Coupled levels in CC calculation Table 3. Level density parameters -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Pa-232 17.9699 0.0000 2.9784 0.2779 -0.6740 1.0000 Pa-231 17.9034 0.7895 3.1164 0.4176 -1.2470 3.5007 Pa-230 17.8368 0.0000 2.9470 0.2794 -0.6728 1.0000 Pa-229 17.7702 0.7930 3.0707 0.3881 -0.8689 3.0597 Pa-228 17.7035 0.0000 2.9095 0.2810 -0.6716 1.0000 -------------------------------------------------------- Table 4. Fission barrier parameters ---------------------------------------- Nuclide V_A hw_A V_B hw_B MeV MeV MeV MeV ---------------------------------------- Pa-232 5.800 0.800 6.180 0.400 Pa-231 6.000 0.800 5.750 0.520 Pa-230 5.800 0.800 6.180 0.400 Pa-229 6.000 0.800 5.800 0.520 Pa-228 5.800 0.800 6.180 0.400 ---------------------------------------- Table 5. Level density above inner saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Pa-232 20.6654 0.0000 2.6000 0.3415 -2.6081 2.2000 Pa-231 20.5889 0.9211 2.6000 0.3276 -1.4734 2.9211 Pa-230 20.5123 0.0000 2.6000 0.3428 -2.6080 2.2000 Pa-229 20.4357 0.9251 2.6000 0.3435 -1.6829 3.1251 Pa-228 20.3591 0.0000 2.6000 0.3442 -2.6080 2.2000 -------------------------------------------------------- Table 6. Level density above outer saddle -------------------------------------------------------- Nuclide a* Pair Eshell T E0 Ematch 1/MeV MeV MeV MeV MeV MeV -------------------------------------------------------- Pa-232 20.6654 0.0000 -0.0800 0.4050 -2.1087 2.5000 Pa-231 20.5889 0.9211 -0.1200 0.3706 -0.7702 2.9211 Pa-230 20.5123 0.0000 -0.1600 0.3867 -1.8562 2.2000 Pa-229 20.4357 0.9251 -0.2000 0.3880 -0.9302 3.1251 Pa-228 20.3591 0.0000 -0.2400 0.3894 -1.8544 2.2000 -------------------------------------------------------- Table 7. Gamma-ray strength function for Pa-232 -------------------------------------------------------- K0 = 1.502 E0 = 4.500 (MeV) * E1: ER = 11.03 (MeV) EG = 2.71 (MeV) SIG = 302.00 (mb) ER = 13.87 (MeV) EG = 4.77 (MeV) SIG = 449.00 (mb) * M1: ER = 6.67 (MeV) EG = 4.00 (MeV) SIG = 2.79 (mb) * E2: ER = 10.25 (MeV) EG = 3.33 (MeV) SIG = 6.39 (mb) -------------------------------------------------------- References 1) O.Iwamoto et al.: J. Nucl. Sci. 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