JENDL-5 (Neutron sublibrary (activation cs)) Es-251 0 0 0 0 9.925100+4 2.489230+2 0 0 6 19911 1451 1 0.000000+0 1.000000+0 0 0 0 69911 1451 2 1.000000+0 2.000000+7 0 0 10 59911 1451 3 2.936000+2 0.000000+0 4 0 302 129911 1451 4 99-Es-251 JAEA+ EVAL-FEB10 O.Iwamoto, T.Nakagawa, et al. 9911 1451 5 DIST-DEC21 20100304 9911 1451 6 ----JENDL-5 MATERIAL 9911 9911 1451 7 -----INCIDENT NEUTRON DATA 9911 1451 8 ------ENDF-6 FORMAT 9911 1451 9 9911 1451 10 History 9911 1451 11 07-10 Theoretical calculation was performed with CCONE code. 9911 1451 12 07-11 Data were compiled as JENDL/AC-2008/1/. 9911 1451 13 10-02 Data of prompt gamma rays due to fission were given. 9911 1451 14 10-03 Covariance data were given. 9911 1451 15 21-11 revised by O.Iwamoto 9911 1451 16 (MF3/MT19-21,38) deleted 9911 1451 17 (MF8/MT4,16-18,102) added 9911 1451 18 9911 1451 19 9911 1451 20 MF=1 General information 9911 1451 21 MT=452 Number of Neutrons per fission 9911 1451 22 Sum of MT's=455 and 456. 9911 1451 23 9911 1451 24 MT=455 Delayed neutron data 9911 1451 25 Estimated from systematics by Tuttle/2/, Benedetti et al./3/ 9911 1451 26 and Waldo et al./4/ 9911 1451 27 9911 1451 28 MT=456 Number of prompt neutrons per fission 9911 1451 29 Estimated from Howerton's systematics/5/. 9911 1451 30 9911 1451 31 9911 1451 32 MF= 2 Resonance parameters 9911 1451 33 MT=151 9911 1451 34 No resonance parameters are given. 9911 1451 35 9911 1451 36 9911 1451 37 Thermal cross sections and resonance integrals (at 300K) 9911 1451 38 ------------------------------------------------------- 9911 1451 39 0.0253 eV reson. integ.(*) 9911 1451 40 (barns) (barns) 9911 1451 41 ------------------------------------------------------- 9911 1451 42 total 253.2 9911 1451 43 elastic 9.92 9911 1451 44 fission 43.02 23.5 9911 1451 45 capture 200.1 1300 9911 1451 46 ------------------------------------------------------- 9911 1451 47 (*) In the energy range from 0.5 eV to 10 MeV. 9911 1451 48 9911 1451 49 9911 1451 50 MF= 3 Neutron cross sections 9911 1451 51 Below 0.7 eV: 9911 1451 52 * Elastic scattering cross section is 9.9 b calculated from 9911 1451 53 scattering radius of 8.893 fm/6/. 9911 1451 54 * Fission cross section calculated with CCONE code/6/ at 1 eV 9911 1451 55 was extrapolated assming 1/v form. 9911 1451 56 * Capture cross section at 0.0253 eV was assumed to be 200 b 9911 1451 57 from systematics. 9911 1451 58 9911 1451 59 Above 0.7 eV: 9911 1451 60 Cross sections calculated with CCONE code/6/ were adopted. 9911 1451 61 9911 1451 62 MT= 1 Total cross section 9911 1451 63 The cross section was calculated with CC OMP of Soukhovitskii 9911 1451 64 et al./7/ 9911 1451 65 9911 1451 66 9911 1451 67 MF= 4 Angular distributions of secondary neutrons 9911 1451 68 MT=2 Elastic scattering 9911 1451 69 Calculated with CCONE code/6/. 9911 1451 70 9911 1451 71 MT=18 Fission 9911 1451 72 Isotropic distributions in the laboratory system were assumed.9911 1451 73 9911 1451 74 9911 1451 75 MF= 5 Energy distributions of secondary neutrons 9911 1451 76 MT=18 Prompt netrons 9911 1451 77 Calculated with CCONE code/6/. 9911 1451 78 9911 1451 79 9911 1451 80 MF= 6 Energy-angle distributions 9911 1451 81 Calculated with CCONE code/6/. 9911 1451 82 Distributions from fission (MT=18) are not included. 9911 1451 83 9911 1451 84 9911 1451 85 MF=12 Photon production multiplicities 9911 1451 86 MT=18 Fission 9911 1451 87 Calculated from the total energy released by the prompt 9911 1451 88 gamma-rays due to fission which was estimated from its 9911 1451 89 systematics, and the average energy of gamma-rays. 9911 1451 90 9911 1451 91 9911 1451 92 MF=14 Photon angular distributions 9911 1451 93 MT=18 Fission 9911 1451 94 Isotoropic distributions were assumed. 9911 1451 95 9911 1451 96 9911 1451 97 MF=15 Continuous photon energy spectra 9911 1451 98 MT=18 Fission 9911 1451 99 Experimental data measured by Verbinski et al./8/ for 9911 1451 100 Pu-239 thermal fission were adopted. 9911 1451 101 9911 1451 102 9911 1451 103 MF=31 Covariances of average number of neutrons per fission 9911 1451 104 MT=452 Number of neutrons per fission 9911 1451 105 Sum of covariances for MT=455 and MT=456. 9911 1451 106 9911 1451 107 MT=455 9911 1451 108 Error of 15% was assumed. 9911 1451 109 9911 1451 110 MT=456 9911 1451 111 Covariance was obtained by fitting a linear function to the 9911 1451 112 at 0.0 and 5.0 MeV with an uncertainty of 10%. 9911 1451 113 9911 1451 114 9911 1451 115 MF=33 Covariances of neutron cross sections 9911 1451 116 Covariances were given to all the cross sections by using 9911 1451 117 KALMAN code/9/ and the covariances of model parameters 9911 1451 118 used in the cross-section calculations. 9911 1451 119 9911 1451 120 For the following cross sections, standard deviations in the 9911 1451 121 energy region below 0.7 eV were assumed as follows: 9911 1451 122 9911 1451 123 Total 73 % 9911 1451 124 Elastic scattering 90 % 9911 1451 125 Fission 90 % 9911 1451 126 Capture 90 % 9911 1451 127 9911 1451 128 9911 1451 129 MF=34 Covariances for Angular Distributions 9911 1451 130 MT=2 Elastic scattering 9911 1451 131 Covariances were given only to P1 components. 9911 1451 132 9911 1451 133 9911 1451 134 MF=35 Covariances for Energy Distributions 9911 1451 135 MT=18 Fission spectra 9911 1451 136 Estimated with CCONE and KALMAN codes. 9911 1451 137 9911 1451 138 9911 1451 139 ***************************************************************** 9911 1451 140 Calculation with CCONE code 9911 1451 141 ***************************************************************** 9911 1451 142 9911 1451 143 Models and parameters used in the CCONE/6/ calculation 9911 1451 144 1) Coupled channel optical model 9911 1451 145 Levels in the rotational band were included. Optical model 9911 1451 146 potential and coupled levels are shown in Table 1. 9911 1451 147 9911 1451 148 2) Two-component exciton model/10/ 9911 1451 149 * Global parametrization of Koning-Duijvestijn/11/ 9911 1451 150 was used. 9911 1451 151 * Gamma emission channel/12/ was added to simulate direct 9911 1451 152 and semi-direct capture reaction. 9911 1451 153 9911 1451 154 3) Hauser-Feshbach statistical model 9911 1451 155 * Moldauer width fluctuation correction/13/ was included. 9911 1451 156 * Neutron, gamma and fission decay channel were included. 9911 1451 157 * Transmission coefficients of neutrons were taken from 9911 1451 158 coupled channel calculation in Table 1. 9911 1451 159 * The level scheme of the target is shown in Table 2. 9911 1451 160 * Level density formula of constant temperature and Fermi-gas 9911 1451 161 model were used with shell energy correction and collective 9911 1451 162 enhancement factor. Parameters are shown in Table 3. 9911 1451 163 * Fission channel: 9911 1451 164 Double humped fission barriers were assumed. 9911 1451 165 Fission barrier penetrabilities were calculated with 9911 1451 166 Hill-Wheler formula/14/. Fission barrier parameters were 9911 1451 167 shown in Table 4. Transition state model was used and 9911 1451 168 continuum levels are assumed above the saddles. The level 9911 1451 169 density parameters for inner and outer saddles are shown in 9911 1451 170 Tables 5 and 6, respectively. 9911 1451 171 * Gamma-ray strength function of Kopecky et al/15/,/16/ 9911 1451 172 was used. The prameters are shown in Table 7. 9911 1451 173 9911 1451 174 9911 1451 175 ------------------------------------------------------------------9911 1451 176 Tables 9911 1451 177 ------------------------------------------------------------------9911 1451 178 9911 1451 179 Table 1. Coupled channel calculation 9911 1451 180 -------------------------------------------------- 9911 1451 181 * rigid rotor model was applied 9911 1451 182 * coupled levels = 0,2,4,6,8 (see Table 2) 9911 1451 183 * optical potential parameters /7/ 9911 1451 184 Volume: 9911 1451 185 V_0 = 49.97 MeV 9911 1451 186 lambda_HF = 0.01004 1/MeV 9911 1451 187 C_viso = 15.9 MeV 9911 1451 188 A_v = 12.04 MeV 9911 1451 189 B_v = 81.36 MeV 9911 1451 190 E_a = 385 MeV 9911 1451 191 r_v = 1.2568 fm 9911 1451 192 a_v = 0.633 fm 9911 1451 193 Surface: 9911 1451 194 W_0 = 17.2 MeV 9911 1451 195 B_s = 11.19 MeV 9911 1451 196 C_s = 0.01361 1/MeV 9911 1451 197 C_wiso = 23.5 MeV 9911 1451 198 r_s = 1.1803 fm 9911 1451 199 a_s = 0.601 fm 9911 1451 200 Spin-orbit: 9911 1451 201 V_so = 5.75 MeV 9911 1451 202 lambda_so = 0.005 1/MeV 9911 1451 203 W_so = -3.1 MeV 9911 1451 204 B_so = 160 MeV 9911 1451 205 r_so = 1.1214 fm 9911 1451 206 a_so = 0.59 fm 9911 1451 207 Coulomb: 9911 1451 208 C_coul = 1.3 9911 1451 209 r_c = 1.2452 fm 9911 1451 210 a_c = 0.545 fm 9911 1451 211 Deformation: 9911 1451 212 beta_2 = 0.213 9911 1451 213 beta_4 = 0.066 9911 1451 214 beta_6 = 0.0015 9911 1451 215 9911 1451 216 * Calculated strength function 9911 1451 217 S0= 1.45e-4 S1= 4.05e-4 R'= 8.89 fm (En=1 keV) 9911 1451 218 -------------------------------------------------- 9911 1451 219 9911 1451 220 Table 2. Level Scheme of Es-251 9911 1451 221 ------------------- 9911 1451 222 No. Ex(MeV) J PI 9911 1451 223 ------------------- 9911 1451 224 0 0.00000 3/2 - * 9911 1451 225 1 0.00840 7/2 + 9911 1451 226 2 0.03170 5/2 - * 9911 1451 227 3 0.05580 9/2 + 9911 1451 228 4 0.07620 7/2 - * 9911 1451 229 5 0.11410 11/2 + 9911 1451 230 ------------------- 9911 1451 231 *) Coupled levels in CC calculation 9911 1451 232 9911 1451 233 Table 3. Level density parameters 9911 1451 234 -------------------------------------------------------- 9911 1451 235 Nuclide a* Pair Eshell T E0 Ematch 9911 1451 236 1/MeV MeV MeV MeV MeV MeV 9911 1451 237 -------------------------------------------------------- 9911 1451 238 Es-252 19.2945 0.0000 0.8872 0.2854 -0.6910 1.0000 9911 1451 239 Es-251 19.2285 0.7574 0.6125 0.4218 -1.1719 3.3703 9911 1451 240 Es-250 19.1626 0.0000 0.3240 0.2925 -0.6921 1.0000 9911 1451 241 Es-249 19.0966 0.7605 0.5382 0.3949 -0.8363 2.9605 9911 1451 242 -------------------------------------------------------- 9911 1451 243 9911 1451 244 Table 4. Fission barrier parameters 9911 1451 245 ---------------------------------------- 9911 1451 246 Nuclide V_A hw_A V_B hw_B 9911 1451 247 MeV MeV MeV MeV 9911 1451 248 ---------------------------------------- 9911 1451 249 Es-252 6.200 0.650 5.800 0.450 9911 1451 250 Es-251 6.200 0.800 5.400 0.520 9911 1451 251 Es-250 6.200 0.650 5.800 0.450 9911 1451 252 Es-249 6.200 0.800 5.400 0.520 9911 1451 253 ---------------------------------------- 9911 1451 254 9911 1451 255 Table 5. Level density above inner saddle 9911 1451 256 -------------------------------------------------------- 9911 1451 257 Nuclide a* Pair Eshell T E0 Ematch 9911 1451 258 1/MeV MeV MeV MeV MeV MeV 9911 1451 259 -------------------------------------------------------- 9911 1451 260 Es-252 21.6098 0.0000 2.4000 0.3211 -2.4150 2.0000 9911 1451 261 Es-251 21.5360 0.8837 2.4000 0.3217 -1.5314 2.8837 9911 1451 262 Es-250 21.4621 0.0000 2.4000 0.3223 -2.4151 2.0000 9911 1451 263 Es-249 21.3881 0.8872 2.4000 0.3229 -1.5279 2.8872 9911 1451 264 -------------------------------------------------------- 9911 1451 265 9911 1451 266 Table 6. Level density above outer saddle 9911 1451 267 -------------------------------------------------------- 9911 1451 268 Nuclide a* Pair Eshell T E0 Ematch 9911 1451 269 1/MeV MeV MeV MeV MeV MeV 9911 1451 270 -------------------------------------------------------- 9911 1451 271 Es-252 21.6098 0.0000 1.0000 0.3481 -1.7109 2.0000 9911 1451 272 Es-251 21.5360 0.8837 0.9600 0.3492 -0.8267 2.8837 9911 1451 273 Es-250 21.4621 0.0000 0.9200 0.3503 -1.7097 2.0000 9911 1451 274 Es-249 21.3881 0.8872 0.8800 0.3515 -0.8220 2.8872 9911 1451 275 -------------------------------------------------------- 9911 1451 276 9911 1451 277 Table 7. Gamma-ray strength function for Es-252 9911 1451 278 -------------------------------------------------------- 9911 1451 279 K0 = 1.500 E0 = 4.500 (MeV) 9911 1451 280 * E1: ER = 11.35 (MeV) EG = 2.69 (MeV) SIG = 258.31 (mb) 9911 1451 281 ER = 14.25 (MeV) EG = 4.16 (MeV) SIG = 516.63 (mb) 9911 1451 282 * M1: ER = 6.49 (MeV) EG = 4.00 (MeV) SIG = 1.85 (mb) 9911 1451 283 * E2: ER = 9.97 (MeV) EG = 3.09 (MeV) SIG = 7.50 (mb) 9911 1451 284 -------------------------------------------------------- 9911 1451 285 9911 1451 286 9911 1451 287 References 9911 1451 288 1) O.Iwamoto et al.: J. Nucl. Sci. Technol., 46, 510 (2009). 9911 1451 289 2) R.J.Tuttld: INDC(NDS)-107/G+Special, p.29 (1979). 9911 1451 290 3) G.Benedetti et al.: Nucl. Sci. Eng., 80, 379 (1982). 9911 1451 291 4) R.Waldo et al.: Phys. Rev., C23, 1113 (1981). 9911 1451 292 5) R.J.Howerton: Nucl. Sci. Eng., 62, 438 (1977). 9911 1451 293 6) O.Iwamoto: J. Nucl. Sci. Technol., 44, 687 (2007). 9911 1451 294 7) E.Sh.Soukhovitskii et al.: Phys. Rev. C72, 024604 (2005). 9911 1451 295 8) V.V.Verbinski et al.: Phys. Rev., C7, 1173 (1973). 9911 1451 296 9) T.Kawano, K.Shibata, JAERI-Data/Code 97-037 (1997) in 9911 1451 297 Japanese. 9911 1451 298 10) C.Kalbach: Phys. Rev. C33, 818 (1986). 9911 1451 299 11) A.J.Koning, M.C.Duijvestijn: Nucl. Phys. A744, 15 (2004). 9911 1451 300 12) J.M.Akkermans, H.Gruppelaar: Phys. Lett. 157B, 95 (1985). 9911 1451 301 13) P.A.Moldauer: Nucl. Phys. A344, 185 (1980). 9911 1451 302 14) D.L.Hill, J.A.Wheeler: Phys. Rev. 89, 1102 (1953). 9911 1451 303 15) J.Kopecky, M.Uhl: Phys. Rev. C41, 1941 (1990). 9911 1451 304 16) J.Kopecky, M.Uhl, R.E.Chrien: Phys. Rev. C47, 312 (1990). 9911 1451 305 9911 1451 306 1 451 318 19911 1451 307 2 151 4 19911 1451 308 3 4 28 19911 1451 309 3 16 13 19911 1451 310 3 17 8 19911 1451 311 3 18 126 19911 1451 312 3 102 171 19911 1451 313 8 4 2 19911 1451 314 8 16 2 19911 1451 315 8 17 2 19911 1451 316 8 18 2 19911 1451 317 8 102 2 19911 1451 318 9911 1 099999 9911 0 0 0 9.925100+4 2.489230+2 0 0 1 09911 2151 1 9.925100+4 1.000000+0 0 0 1 09911 2151 2 1.000000-5 7.000000-1 0 0 0 09911 2151 3 1.500000+0 8.893000-1 0 0 0 09911 2151 4 9911 2 099999 9911 0 0 0 9.925100+4 2.489230+2 0 0 0 09911 3 4 1 0.000000+0-8.400000+3 0 0 1 749911 3 4 2 74 2 9911 3 4 3 8.433750+3 0.000000+0 1.000000+4 7.461900-2 2.000000+4 2.188790-19911 3 4 4 3.000000+4 3.036660-1 3.182730+4 3.157830-1 5.000000+4 8.274170-19911 3 4 5 5.602420+4 9.157370-1 7.000000+4 1.084927+0 7.650610+4 1.149815+09911 3 4 6 1.000000+5 1.414418+0 1.081430+5 1.479559+0 1.145580+5 1.530906+09911 3 4 7 1.200000+5 1.570249+0 1.400000+5 1.696917+0 1.700000+5 1.853781+09911 3 4 8 2.000000+5 1.996442+0 2.500000+5 2.340429+0 3.000000+5 2.418062+09911 3 4 9 4.000000+5 2.729728+0 5.000000+5 2.969294+0 6.000000+5 2.969666+09911 3 4 10 7.000000+5 2.911280+0 8.000000+5 2.786779+0 9.000000+5 2.682203+09911 3 4 11 1.000000+6 2.621766+0 1.100000+6 2.584566+0 1.200000+6 2.564689+09911 3 4 12 1.300000+6 2.548410+0 1.400000+6 2.537493+0 1.500000+6 2.515731+09911 3 4 13 1.600000+6 2.493957+0 1.700000+6 2.459263+0 1.800000+6 2.423193+09911 3 4 14 1.900000+6 2.376794+0 2.000000+6 2.328995+0 2.100000+6 2.275173+09911 3 4 15 2.300000+6 2.163409+0 2.500000+6 2.049084+0 2.700000+6 1.938117+09911 3 4 16 3.000000+6 1.792827+0 3.500000+6 1.617636+0 4.000000+6 1.527834+09911 3 4 17 4.500000+6 1.489544+0 5.000000+6 1.478092+0 5.500000+6 1.459700+09911 3 4 18 6.000000+6 1.309710+0 6.500000+6 1.042325+0 7.000000+6 8.232715-19911 3 4 19 7.500000+6 6.736600-1 8.000000+6 5.773334-1 8.500000+6 5.158125-19911 3 4 20 9.000000+6 4.750680-1 9.500000+6 4.461147-1 1.000000+7 4.239326-19911 3 4 21 1.050000+7 4.056570-1 1.100000+7 3.896512-1 1.150000+7 3.750020-19911 3 4 22 1.200000+7 3.612238-1 1.250000+7 3.481131-1 1.300000+7 3.355679-19911 3 4 23 1.350000+7 3.235779-1 1.400000+7 3.121644-1 1.450000+7 3.013727-19911 3 4 24 1.500000+7 2.911629-1 1.550000+7 2.817737-1 1.600000+7 2.725535-19911 3 4 25 1.650000+7 2.642933-1 1.700000+7 2.561963-1 1.750000+7 2.489179-19911 3 4 26 1.800000+7 2.417836-1 1.850000+7 2.353386-1 1.900000+7 2.290249-19911 3 4 27 1.950000+7 2.233037-1 2.000000+7 2.176767-1 9911 3 4 28 9911 3 099999 9.925100+4 2.489230+2 0 0 0 09911 3 16 1 -6.786120+6-6.786120+6 0 0 1 289911 3 16 2 28 2 9911 3 16 3 6.813380+6 0.000000+0 7.000000+6 1.379900-4 7.500000+6 1.278670-29911 3 16 4 8.000000+6 4.915090-2 8.500000+6 9.384870-2 9.000000+6 1.359000-19911 3 16 5 9.500000+6 1.695150-1 1.000000+7 1.943740-1 1.050000+7 2.108160-19911 3 16 6 1.100000+7 2.234330-1 1.150000+7 2.330040-1 1.200000+7 2.408020-19911 3 16 7 1.250000+7 2.461480-1 1.300000+7 2.489830-1 1.350000+7 2.426750-19911 3 16 8 1.400000+7 2.261890-1 1.450000+7 2.025240-1 1.500000+7 1.787030-19911 3 16 9 1.550000+7 1.558970-1 1.600000+7 1.376820-1 1.650000+7 1.225050-19911 3 16 10 1.700000+7 1.106340-1 1.750000+7 1.016210-1 1.800000+7 9.465550-29911 3 16 11 1.850000+7 8.925080-2 1.900000+7 8.494100-2 1.950000+7 8.144830-29911 3 16 12 2.000000+7 7.842820-2 9911 3 16 13 9911 3 099999 9.925100+4 2.489230+2 0 0 0 09911 3 17 1 -1.280640+7-1.280640+7 0 0 1 159911 3 17 2 15 2 9911 3 17 3 1.285790+7 0.000000+0 1.350000+7 5.791190-5 1.400000+7 8.432920-49911 3 17 4 1.450000+7 2.373490-3 1.500000+7 4.631870-3 1.550000+7 6.017180-39911 3 17 5 1.600000+7 8.643950-3 1.650000+7 9.857990-3 1.700000+7 1.206340-29911 3 17 6 1.750000+7 1.298050-2 1.800000+7 1.389200-2 1.850000+7 1.485770-29911 3 17 7 1.900000+7 1.588490-2 1.950000+7 1.632480-2 2.000000+7 1.727030-29911 3 17 8 9911 3 099999 9.925100+4 2.489230+2 0 0 0 09911 3 18 1 2.158000+8 2.158000+8 0 0 1 3689911 3 18 2 368 2 9911 3 18 3 1.000000-5 2.188421+3 1.103037-5 2.083674+3 1.216691-5 1.983938+39911 3 18 4 1.342055-5 1.888974+3 1.480336-5 1.798552+3 1.632865-5 1.712455+39911 3 18 5 1.801111-5 1.630477+3 1.986691-5 1.552420+3 2.191394-5 1.478096+39911 3 18 6 2.417189-5 1.407327+3 2.666248-5 1.339943+3 2.940971-5 1.275782+39911 3 18 7 3.243999-5 1.214689+3 3.578251-5 1.156517+3 3.946943-5 1.101128+39911 3 18 8 4.353624-5 1.048387+3 4.802208-5 9.981678+2 5.297013-5 9.503501+29911 3 18 9 5.842801-5 9.048188+2 6.444825-5 8.614645+2 7.108881-5 8.201832+29911 3 18 10 7.841358-5 7.808758+2 8.649308-5 7.434478+2 9.540506-5 7.078094+29911 3 18 11 1.052353-4 6.738752+2 1.160784-4 6.415637+2 1.280388-4 6.107975+29911 3 18 12 1.412315-4 5.815027+2 1.557836-4 5.536093+2 1.718351-4 5.270503+29911 3 18 13 1.895404-4 5.017621+2 2.090701-4 4.776842+2 2.306120-4 4.547589+29911 3 18 14 2.543736-4 4.329311+2 2.805835-4 4.121488+2 3.094939-4 3.923619+29911 3 18 15 3.413832-4 3.735232+2 3.765583-4 3.555873+2 4.153577-4 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