JENDL-5 (Neutron sublibrary (activation cs)) U -235 0 0 0 0 9.223500+4 2.330250+2 0 0 6 19228 1451 1 0.000000+0 1.000000+0 0 0 0 69228 1451 2 1.000000+0 2.000000+7 0 0 10 59228 1451 3 2.936000+2 0.000000+0 4 0 874 149228 1451 4 92-U -235 JAEA+ EVAL-OCT09 O.Iwamoto,N.Otuka,S.Chiba,+ 9228 1451 5 DIST-DEC21 20111206 9228 1451 6 ----JENDL-5 MATERIAL 9228 9228 1451 7 -----INCIDENT NEUTRON DATA 9228 1451 8 ------ENDF-6 FORMAT 9228 1451 9 9228 1451 10 History 9228 1451 11 07-07 Calculation with CCONE code was performed. 9228 1451 12 07-09 Fission spectra up to 5 MeV were replaced with JENDL-3.3. 9228 1451 13 07-11 Fission cross section was revised with simultaneous 9228 1451 14 evaluation. 9228 1451 15 07-12 Fission cross section was revised with new results of 9228 1451 16 simultaneous evaluation. 9228 1451 17 08-01 Fission cross section was revised. New CCONE calculation 9228 1451 18 was adopted. 9228 1451 19 08-02 Fission and capture cross sections, and nu-p were revised. 9228 1451 20 CCONE calculation was made with revised parameters. 9228 1451 21 Data were compiled as JENDL/AC-2008/1/. 9228 1451 22 09-08 (MF1,MT458) was evaluated. 9228 1451 23 09-10 nu-p and fission cross section were revised. 9228 1451 24 10-03 Covarinace data were given. 9228 1451 25 11-07 Covariance data in RRR were revised. 9228 1451 26 18-09 JENDL-5a 9228 1451 27 (MF2/MT151) RRP from ENDF/B-VIII.0 9228 1451 28 (MF3/MT18) preliminary SOK result 9228 1451 29 (MF3/MT19,20,21,38) renormalized 9228 1451 30 19-12 JENDL-5a2 9228 1451 31 (MF2/MT151) RPs of neg. and second resonances were modified 9228 1451 32 (MF3/MT18) SOK result in 2019 9228 1451 33 (MF3/MT19,20,21,38) renormalized 9228 1451 34 20-03 JENDL-5a3 9228 1451 35 (MF2/MT151) AWR was changed to the same vale as others 9228 1451 36 (MF5/MT18) ENDF/B-VIII.0 was adopted (En < 5 MeV) 9228 1451 37 (MF31/MT452) AWR was changed to the same vale as others 9228 1451 38 20-07 (MT1/MF456) revised 9228 1451 39 (MT3/MF18) IAEA standard was adopted (2.25-10 keV) 9228 1451 40 (MF3/MT19,20,21,38) deleted 9228 1451 41 20-10 JENDL-5a4 9228 1451 42 (MF3/MT18) SOK(20201009) was adopted above 10 keV 9228 1451 43 21-06 JENDL-5b1 9228 1451 44 (MF1/MT456) revised below 700 keV 9228 1451 45 (MF2/MT151) RRP from ENDF/B-VIII.0 9228 1451 46 (MF3/MT18) SOK(20210404) was adopted above 10 keV 9228 1451 47 (MF5/MT18) new evaluation below 5 MeV 9228 1451 48 21-07 JENDL-5b2 9228 1451 49 (MF2/MT151) adjuisted RRP above 100 eV 9228 1451 50 (MF3/MT1) sum of partial 9228 1451 51 (MF3/MT2) adjusted 9228 1451 52 (MF3/MT18) adjusted 9228 1451 53 (MF5/MT102) adjusted 9228 1451 54 21-11 revised by O.Iwamoto 9228 1451 55 (MF8/MT16-18,37,102) JENDL/AD-2017 adopted 9228 1451 56 (MF8/MT4) added 9228 1451 57 21-11 above 20 MeV, JENDL-4.0/HE merged by O.Iwamoto 9228 1451 58 21-11 (MF6/MT5) recoil spectrum added by O.Iwamoto 9228 1451 59 21-12 (MF33/MT1,2,18,102) modified by O.Iwamoto 9228 1451 60 ENDF/B-VIII.0 (En < 2.25 keV) 9228 1451 61 21-12 (MF33/MT18) modified by O.Iwamoto 9228 1451 62 IAEA neutron data standards 2017 (2.25 keV < En < 10 keV) 9228 1451 63 SOK(20210404,rectangle) (En > 10 keV) 9228 1451 64 21-12 (MF3/MT18) above 20 MeV SOK(20210404) adoped by O.Iwamoto 9228 1451 65 21-12 (MF1/MT452,456) by O.Iwamoto 9228 1451 66 revise nu-p (En > 20 MeV) by a systematics 9228 1451 67 (MF6/MT5) by O.Iwamoto 9228 1451 68 modify multiplicity of ZAP=1 to compensate 9228 1451 69 the revision of nu-p 9228 1451 70 9228 1451 71 9228 1451 72 MF= 1 9228 1451 73 MT=452 Total number of neutrons per fission 9228 1451 74 Sum of MT=455 and 456. 9228 1451 75 9228 1451 76 MT=455 Delayed neutron data 9228 1451 77 (same as JENDL-3.3/2/) 9228 1451 78 Evaluated by using the least-squares method on the basis of 9228 1451 79 the following experimental data in each energy region. 9228 1451 80 9228 1451 81 Thermal region: Keepin/3/, Conant/4/, Synetos/5/, 9228 1451 82 Reeder/6/, Borzakov/7/ 9228 1451 83 50 keV - 7 MeV: Keepin/3/, Maksyutenko/8/, Masters/9/, 9228 1451 84 Krick/10/, Evans/11/, Cox/12/, 9228 1451 85 Besant/13/, Gudkov/14/, Loaiza/15/ 9228 1451 86 14 - 15 MeV : Keepin/16/ 9228 1451 87 9228 1451 88 Decay constants at the thermal energy were adopted from 9228 1451 89 Keepin et al./17/ 9228 1451 90 9228 1451 91 MT=456 Number of prompt neutrons per fission 9228 1451 92 Below 500 eV, JENDL-3.3 was adopted, which was evaluated on 9228 1451 93 the basis of experimental data of Gwin et al./18,19/ 9228 1451 94 9228 1451 95 Above 500 eV, experimental data were anlyzed by the GMA code 9228 1451 96 /20/ with Chiba-Smith approach/21/ for PPP minimization. 9228 1451 97 Experimental data are renormalized with nu-p of CF-252 9228 1451 98 spontaneous fission (3.756+/-0.031) reported by Vorobyev et 9228 1451 99 al./22/ if standards to derive original data were known. 9228 1451 100 9228 1451 101 Experimental data sets are summarized below. 9228 1451 102 r: re-normalized by nu-p(252Cf spon) of A.S.Vorobyev et al. 9228 1451 103 --------------------------------------------------------------9228 1451 104 EXFOR Energy range (eV) Authors Reference 9228 1451 105 --------------------------------------------------------------9228 1451 106 r 12326.004 2.80E+5 - 1.45E+7 J.C.Hopkins+ /23/ 9228 1451 107 r 12870.004 1.70E+7 - 1.96E+7 R.E.Howe /24/ 9228 1451 108 r 13101.003 5.00E+2 - 9.00E+6 R.Gwin+ /25/ 9228 1451 109 r 20427.002 2.25E+5 - 1.36E+6 F.Kaeppeler+ /26/ 9228 1451 110 21696.004 2.50E+6 - 1.41E+7 I.Johnstone /27/ 9228 1451 111 r 21785.003 1.14E+6 - 1.47E+7 J.Frehaut+ /28/ 9228 1451 112 r 40262.002 8.60E+5 - 5.35E+6 M.V.Savin+ /29/ 9228 1451 113 r 40493.002 1.98E+5 - 9.85E+5 M.V.Savin+ /30/ 9228 1451 114 40785.002 1.43E+7 Ju.A.Vasilev+ /31/ 9228 1451 115 --------------------------------------------------------------9228 1451 116 9228 1451 117 In the energy region from 1 keV to 1 MeV, GMA results were 9228 1451 118 increased by 0.2%. 9228 1451 119 9228 1451 120 MT=458 Components of energy release due to fission 9228 1451 121 Total energy and prompt energy were calculated from mass 9228 1451 122 balance using JENDL-4 fission yields data and mass excess 9228 1451 123 evaluation. Mass excess values were from Audi's 2009 9228 1451 124 evaluation/32/. Delayed energy values were calculated from 9228 1451 125 the energy release for infinite irradiation using JENDL FP 9228 1451 126 Decay Data File 2000 and JENDL-4 yields data. For delayed 9228 1451 127 neutron energy, as the JENDL FP Decay Data File 2000/33/ does 9228 1451 128 not include average neutron energy values, the average values 9228 1451 129 were calculated using the formula shown in the report by 9228 1451 130 T.R. England/34/. The fractions of prompt energy were 9228 1451 131 calculated using the fractions of Sher's evaluation/35/ when 9228 1451 132 they were provided. When the fractions were not given by Sher,9228 1451 133 averaged fractions were used. 9228 1451 134 9228 1451 135 9228 1451 136 MF= 2 Resonance parameters 9228 1451 137 MT=151 9228 1451 138 Resolved resonance parameters (RM: 1.0E-5 - 500 eV) 9228 1451 139 Adopted are parameters for Reich-Moore formula evaluated by 9228 1451 140 Leal et al./36/ In the present file, the upper boundary of 9228 1451 141 resolved resonance region is set to 500 eV. 9228 1451 142 9228 1451 143 See Appendix A-1 9228 1451 144 9228 1451 145 Unresolved resonance parameters (500 eV - 30 keV) 9228 1451 146 Unresolved resonance parameters were determined with ASREP 9228 1451 147 code/37/ so as to reproduce the cross sections. 9228 1451 148 The parameters are used only for calculation of self-shielding9228 1451 149 factors. 9228 1451 150 9228 1451 151 Thermal cross sections and resonance integrals (at 300K) 9228 1451 152 ------------------------------------------------------- 9228 1451 153 0.0253 eV reson. integ.(*) 9228 1451 154 (barns) (barns) 9228 1451 155 ------------------------------------------------------- 9228 1451 156 total 698.90 9228 1451 157 elastic 15.12 9228 1451 158 fission 585.08 274 9228 1451 159 capture 98.71 139 9228 1451 160 ------------------------------------------------------- 9228 1451 161 (*) In the energy range from 0.5 eV to 10 MeV. 9228 1451 162 9228 1451 163 9228 1451 164 MF= 3 Neutron cross sections 9228 1451 165 Between 500 eV and 2.25 keV: 9228 1451 166 Cross sections were calculated with resonance parameters of 9228 1451 167 JENDL-3.3 which were taken from ENDF/B-VI.5/36/ and 9228 1451 168 broadened with a resolution function of R(E)=0.03*E. 9228 1451 169 The capture cross section was multiplied by ratios of average 9228 1451 170 capture cross sections of JENDL-3.2 and JENDL-3.3 to lower the9228 1451 171 cross sections to those of JENDL-3.2. 9228 1451 172 9228 1451 173 Above 2.25 keV: 9228 1451 174 Cross sections except for the total (M=1), elastic scattering 9228 1451 175 (MT=2), fission (MT=18, 19, 20, 21, 38) and capture cross 9228 1451 176 sections were calculated with CCONE code/38/. 9228 1451 177 The model parameters were determined by considering integral 9228 1451 178 experimental data as well as measured cross-section data. 9228 1451 179 9228 1451 180 MT= 1 Total cross section 9228 1451 181 In the energy range from 2.25 to 500 keV, cross section was 9228 1451 182 calculated with CCONE code/38/. 9228 1451 183 Above 500 keV, the cross section was determined by spline 9228 1451 184 fitting to experimental data of Schwartz et al./39/, Poenitz 9228 1451 185 et al./40,41/, Harvey et al./42/, Cabe and Cance/43/, and 9228 1451 186 Uttley et al./44/ These experimental data were used also 9228 1451 187 for adjustment of the OMP of Soukhovitskii et al./45/ 9228 1451 188 9228 1451 189 MT=2 Elastic scattering cross section 9228 1451 190 Calculated as total - non-elstic scattering cross section 9228 1451 191 9228 1451 192 MT=16 (n,2n) cross section 9228 1451 193 Calculated with CCONE code. The experimental data of Frehaut 9228 1451 194 et al./46/ were considered to determine the model parameters 9228 1451 195 of CCONE calculation. 9228 1451 196 9228 1451 197 MT=18 Fission cross sections 9228 1451 198 From 2.25 keV to 10 keV, JENDL-3.3/2/ was adopted. The data 9228 1451 199 of JENDL-3.3 were based on the experimental data of Weston 9228 1451 200 and Todd/47/. 9228 1451 201 9228 1451 202 Above 10 keV, experimental data measured after 1980 were 9228 1451 203 analyzed by simultaneous fitting of U-233, U-235, U-238, 9228 1451 204 Pu-239, Pu-240 and Pu-241 fission cross section and its ratio 9228 1451 205 by the SOK code /48/. 9228 1451 206 9228 1451 207 --------------------------------------------------------------9228 1451 208 EXFOR Energy range (eV) Authors Reference 9228 1451 209 --------------------------------------------------------------9228 1451 210 41112.002 1.88E+6 - 2.37E+6 V.A.Kalinin+ /49/ 9228 1451 211 22304.006 2.60E+6 - 1.47E+7 K.Merla+ /50/ 9228 1451 212 22304.002 4.45E+6 - 1.88E+7 K.Merla+ /50/ 9228 1451 213 12924.002 1.07E+6 - 5.99E+6 R.G.Johnson+ /51/ 9228 1451 214 40969.011 6.24E+5 - 7.85E+5 N.N.Buleeva+ /52/ 9228 1451 215 22091.002 1.35E+7 - 1.49E+7 T.Iwasaki+ /53/ 9228 1451 216 30721.002 1.42E+7 J.W.Li+ /54/ 9228 1451 217 12877.004 5.05E+3 - 2.05E+5 L.W.Weston+ /47/ 9228 1451 218 10987.002 3.10E+5 - 2.82E+6 A.D.Carlson+ /55/ 9228 1451 219 30634.002 1.47E+7 J.W.Li+ /56/ 9228 1451 220 12826.002 1.46E+7 M.Mahdavi+ /57/ 9228 1451 221 10971.002 1.41E+7 O.A.Wasson+ /58/ 9228 1451 222 21620.002 2.50E+6 - 4.45E+6 M.Cance+ /59/ 9228 1451 223 21777.002 5.40E+3 - 8.25E+4 F.Corvi+ /60/ 9228 1451 224 10950.002 2.45E+5 - 1.20E+6 O.A.Wasson+ /61/ 9228 1451 225 40601.002 6.00E+3 - 4.50E+4 A.A.Bergman+ /62/ 9228 1451 226 -----.--- 3.03E+6 - 2.96E+7 A.D.Carlson+ /63/ 9228 1451 227 --------------------------------------------------------------9228 1451 228 9228 1451 229 The obtained cross section from 1 to 4 MeV and from 7 to 8 9228 1451 230 MeV was slightly modified for JENDL-4. 9228 1451 231 9228 1451 232 The fission cross section of JENDL-3.3 were used to determine 9228 1451 233 the parameters in the CCONE calculation. 9228 1451 234 9228 1451 235 MT=19, 20, 21, 38 Multi-chance fission cross sections 9228 1451 236 Calculated with CCONE code, and renormalized to the total 9228 1451 237 fission cross section (MT=18). 9228 1451 238 9228 1451 239 MT=102 Capture cross section 9228 1451 240 From 2.25 keV to 1 MeV, experimental data measured after 1970 9228 1451 241 were analyzed by the GMA code/20/ with the Chiba and Smith 9228 1451 242 approach/21/ for PPP minimization/64/. All experimental 9228 1451 243 data are given in the form of alpha-value (=ratios to the 9228 1451 244 U-235(n,f) cross section), which were normalized to absolute 9228 1451 245 cross section by the JENDL-3.3 U-235(n,f) cross section. Data 9228 1451 246 points of Kononov et al./65/ below 20 keV were not 9228 1451 247 considered because their systematic error was very large in 9228 1451 248 this energy region. 9228 1451 249 9228 1451 250 Experimental data sets are summarized below. 9228 1451 251 --------------------------------------------------------------9228 1451 252 EXFOR Energy range (eV) Authors Reference 9228 1451 253 --------------------------------------------------------------9228 1451 254 12424.003 3.47E+3 - 2.56E+4 J.B.Czirr+ /66/ 9228 1451 255 20158.002 8.50E+3 - 5.50E+4 R.E.Bandl+ /67/ 9228 1451 256 20880.002 1.06E+4 - 1.96E+5 H.Beer+ /68/ 9228 1451 257 20880.003 1.04E+5 - 3.07E+5 H.Beer+ /68/ 9228 1451 258 20880.004 1.70E+4 - 6.40E+4 H.Beer+ /68/ 9228 1451 259 20880.005 3.79E+5 - 4.81E+5 H.Beer+ /68/ 9228 1451 260 21777.004 2.50E+3 - 8.25E+4 F.Corvi+ /60/ 9228 1451 261 40412.002 2.04E+4 - 1.10E+6 V.N.Kononov+ /65/ 9228 1451 262 40502.002 3.49E+3 - 8.89E+3 Ju.V.Ryabov /69/ 9228 1451 263 40581.002 2.50E+3 - 4.50E+4 G.V.Muradyan+ /70/ 9228 1451 264 40609.004 2.45E+4 V.P.Vertebnyy+ /71/ 9228 1451 265 12409.003 2.00E+5 - 6.00E+5 G.de Saussure+ /72/ 9228 1451 266 12407.002 1.23E+4 - 6.90E+5 L.W.Weston+ /73/ 9228 1451 267 12331.005 3.00E+4 - 1.00E+6 J.C.Hopkins+ /74/ 9228 1451 268 12416.002 1.78E+5 - 1.01E+6 B.C.Diven+ /75/ 9228 1451 269 --------------------------------------------------------------9228 1451 270 9228 1451 271 The results of the GMA were used to determine the parameters 9228 1451 272 in the CCONE calculation. 9228 1451 273 9228 1451 274 Above 1.3 MeV, results of the CCONE calculation were adopted. 9228 1451 275 9228 1451 276 The present results were slightly modified by considering 9228 1451 277 integral data. 9228 1451 278 9228 1451 279 9228 1451 280 MF= 4 Angular distributions of secondary neutrons 9228 1451 281 MT=2 Elastic scattering 9228 1451 282 Calculated with CCONE code. 9228 1451 283 9228 1451 284 MT=18 Fission 9228 1451 285 Isotropic distributions in the laboratory system were assumed.9228 1451 286 9228 1451 287 9228 1451 288 MF=5 Energy Distributions of Secondary Neutrons 9228 1451 289 MT=18 Prompt fission neutron spectra 9228 1451 290 Below 5 MeV, spectra given in JENDL-3.3/2/ were adopted. 9228 1451 291 Relevant part of JENDL-3.3 comments: 9228 1451 292 *DISTRIBUTIONS WERE CALCULATED WITH A MODIFIED MADLAND-NIX 9228 1451 293 MODEL WITH CONSIDERATION FOR MULTIMODAL NATURE OF THE FISSION9228 1451 294 PROCESS/76,77/. THE COMPOUND NUCLEUS FORMATION CROSS SEC- 9228 1451 295 TIONS FOR FISSION FRAGMENTS WERE CALCULATED USING BECCHETTI- 9228 1451 296 GREENLEES POTENTIAL/78/. THE IGNATYUK FORMULA/79/ WERE 9228 1451 297 USED TO GENERATE THE LEVEL DENSITY PARAMETERS. UP TO 9228 1451 298 3rd-CHANCE-FISSION WERE CONSIDERED AT HIGH INCIDENT NEUTRON 9228 1451 299 ENERGIES. 9228 1451 300 9228 1451 301 PARAMETERS ADOPTED FOR THERMAL-NEUTRON FISSION: 9228 1451 302 (S1: STANDARD-1, S2: STANDARD-2, SL: SUPERLONG MODES) 9228 1451 303 TOTAL AVERAGE FRAGMENT KINETIC ENERGY 9228 1451 304 = 187 MEV FOR S1 9228 1451 305 = 167 MEV FOR S2 9228 1451 306 = 157 MEV FOR SL 9228 1451 307 AVERAGE ENERGY RELEASE 9228 1451 308 = 194.49 MEV FOR S1 9228 1451 309 = 184.86 MEV FOR S2 9228 1451 310 = 190.95 MEV FOR SL 9228 1451 311 AVERAGE MASS NUMBER OF LIGHT FF = 96 9228 1451 312 AVERAGE MASS NUMBER OF HEAVY FF = 140 9228 1451 313 LEVEL DENSITY OF THE LIGHT FF = 10.31(S2), 11.43(S1) 9228 1451 314 LEVEL DENSITY OF THE HEAVY FF = 8.89(S1), 13.25(S2) 9228 1451 315 MODE BRANCHING RATIO = 0.18342(S1), 0.81589(S2), 9228 1451 316 0.00069(SL) 9228 1451 317 NOTE THAT THE PARAMETERS VARY WITH THE INCIDENT ENERGY 9228 1451 318 WITHIN THE INDICATED RANGE. 9228 1451 319 9228 1451 320 Above 5.5 MeV, calculated with CCONE code/38/. 9228 1451 321 9228 1451 322 MT=455 Delayed neutron spectra 9228 1451 323 (same as JENDL-3.3) 9228 1451 324 Taken from Brady and England/80/. Group abundace parameters 9228 1451 325 were adjusted so as to reproduce total delayed neutron 9228 1451 326 emission rate measured by Keepin/17/, Piksaikin/81/ and 9228 1451 327 East/82/. 9228 1451 328 9228 1451 329 9228 1451 330 MF= 6 Energy-angle distributions 9228 1451 331 Calculated with CCONE code. 9228 1451 332 Distributions from fission (MT=18) are not included. 9228 1451 333 9228 1451 334 9228 1451 335 MF=12 Photon Production Multiplicities (option 1) 9228 1451 336 MT=18 Fission 9228 1451 337 (same as JENDL-3.3) 9228 1451 338 The thermal neutron-induced fission gamma spectrum measured 9228 1451 339 by Verbinski et al./83/ was adopted. 9228 1451 340 9228 1451 341 9228 1451 342 MF=14 Photon Angular Distributions 9228 1451 343 MT=18 9228 1451 344 (same as JENDL-3.3) 9228 1451 345 Isotropic distributions were assumed. 9228 1451 346 9228 1451 347 9228 1451 348 MF=15 Continuous Photon Energy Spectra 9228 1451 349 MT=18 9228 1451 350 (same as JENDL-3.3) 9228 1451 351 Experimental data by Verbinski et al./83/ were adopted. 9228 1451 352 9228 1451 353 9228 1451 354 MF=31 Covariances of average number of neutrons per fission 9228 1451 355 MT=452 Number of neutrons per fission 9228 1451 356 Combination of covariances for MT=455 and MT=456. 9228 1451 357 9228 1451 358 MT=455 9228 1451 359 (Same as JENDL-3.3/2/) 9228 1451 360 9228 1451 361 MT=456 9228 1451 362 Below 500 eV, the covariance of JENDL-3.3 was adopted. 9228 1451 363 Above 500 eV, it was obtained by fitting to the experimental 9228 1451 364 data described above. The error of nu-p was multiplied by 9228 1451 365 a factor of 2.0. 9228 1451 366 9228 1451 367 9228 1451 368 MF=33 Covariances of neutron cross sections 9228 1451 369 Covariances were given to all the cross sections by using 9228 1451 370 KALMAN code/85/ and the covariances of model parameters 9228 1451 371 used in the theoretical calculations. 9228 1451 372 9228 1451 373 For the following cross sections, covariances were determined 9228 1451 374 by different methods. 9228 1451 375 9228 1451 376 MT= 1, 2 Total and elastic scattering cross sections 9228 1451 377 Below 500 eV, covariance matrices was calculated from those 9228 1451 378 of resonance parameters/84/. 9228 1451 379 In the energy range from 200 to 500 eV, uncertainty of 2% 9228 1451 380 was assumed for the total cross section, and 4% for the 9228 1451 381 elastic scattering. From 0.5 to 2.25 keV, uncertainty of 5% 9228 1451 382 was assumed. Above 2.25 keV, covariance of the CCONE 9228 1451 383 calculation was adopted. 9228 1451 384 9228 1451 385 MT=18 Fission cross section 9228 1451 386 Below 500 eV, covariance matrices was calculated from those 9228 1451 387 of resonance parameters/84/. 9228 1451 388 In the energy range from 200 to 500 eV, uncertainty of 2% 9228 1451 389 was assumed. From 500 eV to 9 keV, uncertainty was assumed 9228 1451 390 to be 5%. 9228 1451 391 Above 9 keV, covariance matrix was obtained by simultaneous 9228 1451 392 evaluation among the fission cross sections of U-233, U-235, 9228 1451 393 U-238, Pu-239, Pu-240 and Pu-241(See MF=3, MT=18, and /1/). 9228 1451 394 Since the variances are very small, they were adopted by 9228 1451 395 multiplying a factor of 2. 9228 1451 396 9228 1451 397 MT=102 Capture cross section 9228 1451 398 Below 500 eV, covariance matrices was calculated from those 9228 1451 399 of resonance parameters/84/. 9228 1451 400 In the energy range from 200 to 500 eV, uncertainty of 3% 9228 1451 401 was assumed. 9228 1451 402 From 500 eV to 2.25 keV, uncertainty was assumed to be 10%. 9228 1451 403 In the energy region from 2.25 keV to 1 MeV, capture cross 9228 1451 404 section was obtained with GMA code/64/. Its covariance matrix 9228 1451 405 was obtained simultaneously. 9228 1451 406 Above 1 MeV, covariance of the CCONE calculation was adopted. 9228 1451 407 9228 1451 408 9228 1451 409 MF=34 Covariances for Angular Distributions 9228 1451 410 MT=2 Elastic scattering 9228 1451 411 Covariances were given only to P1 components. 9228 1451 412 9228 1451 413 9228 1451 414 MF=35 Covariances for Energy Distributions 9228 1451 415 MT=18 Fission spectra 9228 1451 416 Below 5 MeV, based on the covarinaces given in JENDL-3.3. 9228 1451 417 Above 5 MeV, estimated with CCONE and KALMAN codes. 9228 1451 418 9228 1451 419 9228 1451 420 ***************************************************************** 9228 1451 421 Calculation with CCONE code 9228 1451 422 ***************************************************************** 9228 1451 423 9228 1451 424 Models and parameters used in the CCONE/38/ calculation 9228 1451 425 1) Coupled channel optical model 9228 1451 426 Levels in the rotational band were included. Optical model 9228 1451 427 potential and coupled levels are shown in Table 1. 9228 1451 428 9228 1451 429 2) Two-component exciton model/86/ 9228 1451 430 * Global parametrization of Koning-Duijvestijn/87/ 9228 1451 431 was used. 9228 1451 432 * Gamma emission channel/88/ was added to simulate direct 9228 1451 433 and semi-direct capture reaction. 9228 1451 434 9228 1451 435 3) Hauser-Feshbach statistical model 9228 1451 436 * Moldauer width fluctuation correction/89/ was included. 9228 1451 437 * Neutron, gamma and fission decay channel were included. 9228 1451 438 * Transmission coefficients of neutrons were taken from 9228 1451 439 coupled channel calculation in Table 1. 9228 1451 440 * The level scheme of the target is shown in Table 2. 9228 1451 441 * Level density formula of constant temperature and Fermi-gas 9228 1451 442 model were used with shell energy correction and collective 9228 1451 443 enhancement factor. Parameters are shown in Table 3. 9228 1451 444 * Fission channel: 9228 1451 445 Double humped fission barriers were assumed. 9228 1451 446 Fission barrier penetrabilities were calculated with 9228 1451 447 Hill-Wheler formula/90/. Fission barrier parameters were 9228 1451 448 shown in Table 4. Transition state model was used and 9228 1451 449 continuum levels are assumed above the saddles. The level 9228 1451 450 density parameters for inner and outer saddles are shown in 9228 1451 451 Tables 5 and 6, respectively. 9228 1451 452 * Gamma-ray strength function of Kopecky et al/91/,/92/ 9228 1451 453 was used. The prameters are shown in Table 7. 9228 1451 454 9228 1451 455 9228 1451 456 ------------------------------------------------------------------9228 1451 457 Tables 9228 1451 458 ------------------------------------------------------------------9228 1451 459 9228 1451 460 Table 1. Coupled channel calculation 9228 1451 461 -------------------------------------------------- 9228 1451 462 * rigid rotor model was applied 9228 1451 463 * coupled levels = 0,3,6,9 (see Table 2) 9228 1451 464 * optical potential parameters /45/ 9228 1451 465 Volume: 9228 1451 466 V_0 = 49.8613 MeV 9228 1451 467 lambda_HF = 0.01004 1/MeV 9228 1451 468 C_viso = 15.9 MeV 9228 1451 469 A_v = 12.04 MeV 9228 1451 470 B_v = 81.36 MeV 9228 1451 471 E_a = 385 MeV 9228 1451 472 r_v = 1.2568 fm 9228 1451 473 a_v = 0.61 fm 9228 1451 474 Surface: 9228 1451 475 W_0 = 17.1117 MeV 9228 1451 476 B_s = 11.19 MeV 9228 1451 477 C_s = 0.01361 1/MeV 9228 1451 478 C_wiso = 23.5 MeV 9228 1451 479 r_s = 1.1803 fm 9228 1451 480 a_s = 0.61 fm 9228 1451 481 Spin-orbit: 9228 1451 482 V_so = 5.75 MeV 9228 1451 483 lambda_so = 0.005 1/MeV 9228 1451 484 W_so = -3.1 MeV 9228 1451 485 B_so = 160 MeV 9228 1451 486 r_so = 1.1214 fm 9228 1451 487 a_so = 0.59 fm 9228 1451 488 Coulomb: 9228 1451 489 C_coul = 1.3 9228 1451 490 r_c = 1.2452 fm 9228 1451 491 a_c = 0.545 fm 9228 1451 492 Deformation: 9228 1451 493 beta_2 = 0.201044 9228 1451 494 beta_4 = 0.11 9228 1451 495 beta_6 = 0.0015 9228 1451 496 9228 1451 497 * Calculated strength function 9228 1451 498 S0= 0.93e-4 S1= 2.11e-4 R'= 9.50 fm (En=1 keV) 9228 1451 499 -------------------------------------------------- 9228 1451 500 9228 1451 501 Table 2. Level Scheme of U-235 9228 1451 502 ------------------- 9228 1451 503 No. Ex(MeV) J PI 9228 1451 504 ------------------- 9228 1451 505 0 0.00000 7/2 - * 9228 1451 506 1 0.00008 1/2 + 9228 1451 507 2 0.01304 3/2 + 9228 1451 508 3 0.04621 9/2 - * 9228 1451 509 4 0.05171 5/2 + 9228 1451 510 5 0.08174 7/2 + 9228 1451 511 6 0.10304 11/2 - * 9228 1451 512 7 0.12930 5/2 + 9228 1451 513 8 0.15047 9/2 + 9228 1451 514 9 0.17071 13/2 - * 9228 1451 515 10 0.17139 7/2 + 9228 1451 516 11 0.19712 11/2 + 9228 1451 517 12 0.22542 9/2 + 9228 1451 518 13 0.24913 15/2 - 9228 1451 519 14 0.25900 7/2 + 9228 1451 520 15 0.29114 11/2 + 9228 1451 521 16 0.29467 13/2 + 9228 1451 522 17 0.33285 5/2 + 9228 1451 523 18 0.33852 17/2 - 9228 1451 524 19 0.35730 15/2 + 9228 1451 525 20 0.36707 7/2 + 9228 1451 526 21 0.36900 13/2 + 9228 1451 527 22 0.39322 3/2 + 9228 1451 528 23 0.41478 9/2 + 9228 1451 529 24 0.42675 5/2 + 9228 1451 530 25 0.43860 19/2 - 9228 1451 531 26 0.44572 7/2 + 9228 1451 532 27 0.45450 15/2 + 9228 1451 533 28 0.47130 11/2 + 9228 1451 534 29 0.47430 7/2 + 9228 1451 535 30 0.48500 17/2 + 9228 1451 536 31 0.50992 9/2 + 9228 1451 537 32 0.53240 13/2 + 9228 1451 538 33 0.53323 9/2 + 9228 1451 539 34 0.55040 21/2 - 9228 1451 540 35 0.56800 19/2 + 9228 1451 541 36 0.58780 11/2 + 9228 1451 542 37 0.60808 11/2 + 9228 1451 543 38 0.61640 15/2 + 9228 1451 544 39 0.63317 5/2 - 9228 1451 545 40 0.63781 3/2 - 9228 1451 546 ------------------- 9228 1451 547 *) Coupled levels in CC calculation 9228 1451 548 9228 1451 549 Table 3. Level density parameters 9228 1451 550 -------------------------------------------------------- 9228 1451 551 Nuclide a* Pair Eshell T E0 Ematch 9228 1451 552 1/MeV MeV MeV MeV MeV MeV 9228 1451 553 -------------------------------------------------------- 9228 1451 554 U-236 18.6157 1.5623 2.7551 0.3856 -0.1537 3.8909 9228 1451 555 U-235 18.4419 0.7828 2.6265 0.3721 -0.7434 2.8828 9228 1451 556 U-234 18.4800 1.5689 2.5578 0.3899 -0.1502 3.9076 9228 1451 557 U-233 18.4122 0.7861 2.4694 0.3817 -0.8188 2.9881 9228 1451 558 U-232 18.3442 1.5757 2.6095 0.3885 -0.1133 3.8795 9228 1451 559 -------------------------------------------------------- 9228 1451 560 9228 1451 561 Table 4. Fission barrier parameters 9228 1451 562 ---------------------------------------- 9228 1451 563 Nuclide V_A hw_A V_B hw_B 9228 1451 564 MeV MeV MeV MeV 9228 1451 565 ---------------------------------------- 9228 1451 566 U-236 6.201 1.040 5.417 0.550 9228 1451 567 U-235 5.700 0.400 5.600 0.300 9228 1451 568 U-234 6.050 1.040 5.400 0.600 9228 1451 569 U-233 5.970 0.800 5.450 0.520 9228 1451 570 U-232 5.800 1.040 5.100 0.600 9228 1451 571 ---------------------------------------- 9228 1451 572 9228 1451 573 Table 5. Level density above inner saddle 9228 1451 574 -------------------------------------------------------- 9228 1451 575 Nuclide a* Pair Eshell T E0 Ematch 9228 1451 576 1/MeV MeV MeV MeV MeV MeV 9228 1451 577 -------------------------------------------------------- 9228 1451 578 U-236 20.9712 1.8226 2.6000 0.3244 -0.5720 3.8226 9228 1451 579 U-235 20.3497 0.9133 2.6000 0.3515 -1.8195 3.2133 9228 1451 580 U-234 20.2753 1.8304 2.6000 0.3522 -0.9023 4.1304 9228 1451 581 U-233 20.2008 0.9172 2.6000 0.3312 -1.4942 2.9172 9228 1451 582 U-232 20.1263 1.8383 2.6000 0.3319 -0.5731 3.8383 9228 1451 583 -------------------------------------------------------- 9228 1451 584 9228 1451 585 Table 6. Level density above outer saddle 9228 1451 586 -------------------------------------------------------- 9228 1451 587 Nuclide a* Pair Eshell T E0 Ematch 9228 1451 588 1/MeV MeV MeV MeV MeV MeV 9228 1451 589 -------------------------------------------------------- 9228 1451 590 U-236 21.5182 1.8226 0.1400 0.3654 0.0498 3.9226 9228 1451 591 U-235 20.3497 0.9133 0.1000 0.4065 -1.2054 3.4133 9228 1451 592 U-234 20.2753 1.8304 0.0600 0.3939 -0.1191 4.1304 9228 1451 593 U-233 20.2008 0.9172 0.0200 0.3732 -0.7817 2.9172 9228 1451 594 U-232 20.1263 1.8383 -0.0200 0.3745 0.1401 3.8383 9228 1451 595 -------------------------------------------------------- 9228 1451 596 9228 1451 597 Table 7. Gamma-ray strength function for U-236 9228 1451 598 -------------------------------------------------------- 9228 1451 599 K0 = 1.500 E0 = 4.500 (MeV) 9228 1451 600 * E1: ER = 10.90 (MeV) EG = 2.50 (MeV) SIG = 303.18 (mb) 9228 1451 601 ER = 13.80 (MeV) EG = 4.70 (MeV) SIG = 450.00 (mb) 9228 1451 602 * M1: ER = 6.63 (MeV) EG = 4.00 (MeV) SIG = 2.69 (mb) 9228 1451 603 * E2: ER = 10.19 (MeV) EG = 3.28 (MeV) SIG = 6.51 (mb) 9228 1451 604 -------------------------------------------------------- 9228 1451 605 9228 1451 606 9228 1451 607 References 9228 1451 608 1) O.Iwamoto et al.: J. Nucl. Sci. Technol., 46, 510 (2009). 9228 1451 609 2) T.Kawano et al.: JAERI-Research 2003-026 (2003). 9228 1451 610 3) G.R.Keepin et al.: J. Nucl. Ener, 6, 1 (1957). 9228 1451 611 4) J.F.Conant, P.F.Palmedo: Nucl. Sci. Eng., 44, 173 (1971). 9228 1451 612 5) S.Synetos, J.G.Williams: INDC(NDS)-107, 183 (1979). 9228 1451 613 6) P.L.Reeder, J.G.Williams: Phys. 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Lett. 157B, 95 (1985). 9228 1451 700 89) P.A.Moldauer: Nucl. Phys. A344, 185 (1980). 9228 1451 701 90) D.L.Hill, J.A.Wheeler: Phys. Rev. 89, 1102 (1953). 9228 1451 702 91) J.Kopecky, M.Uhl: Phys. Rev. C41, 1941 (1990). 9228 1451 703 92) J.Kopecky, M.Uhl, R.E.Chrien: Phys. Rev. C47, 312 (1990). 9228 1451 704 9228 1451 705 9228 1451 706 ***************************************************************** 9228 1451 707 Appendix A-1 from ENDF/B-VI.8 9228 1451 708 ***************************************************************** 9228 1451 709 File 2 9228 1451 710 MT=151 Resonance parameters, from a new analysis by Leal 9228 1451 711 et al. [LE97], using the multilevel R-matrix analysis code 9228 1451 712 SAMMY [LA96]. Energy range for U235 is 0 to 2.25 keV. 9228 1451 713 For the first time, integral data were fitted during the 9228 1451 714 analysis process: Thermal cross sections (fission, 9228 1451 715 capture, and elastic), Westcott g-factors (fission and 9228 1451 716 absorption) are from the ENDF/B-6 standards [CA93], and 9228 1451 717 the K1 value is from Hardy [HA79]. 9228 1451 718 Thermal parameters obtained in the present evaluation, 9228 1451 719 first using the microscopic experimental data only, and 9228 1451 720 second including the integral data as well, are compared 9228 1451 721 to the SAMMY input in the following Tabld: 9228 1451 722 9228 1451 723 Parameter SAMMY input Fit to Fit to diff. 9228 1451 724 value diff data & integ. 9228 1451 725 alone data 9228 1451 726 ----------- ----------------- -------- ------------ 9228 1451 727 Fission 584.25 +/- 1.11 582.28 584.88 9228 1451 728 Capture 98.96 +/- 0.74 99.18 98.66 9228 1451 729 Scattering 15.46 +/- 1.06 15.44 15.12 9228 1451 730 Westcott gf 0.9771 +/- 0.0008 0.9743 0.9764 9228 1451 731 Westcott ga 0.9790 +/- 0.0008 0.9774 0.9785 9228 1451 732 Westcott gg 0.9956 0.9910 9228 1451 733 K1(barn) 722.70 +/- 3.90 717.48 722.43 9228 1451 734 9228 1451 735 The final adjustment of nu by SAMMY to the recommended K1 9228 1451 736 value of 722.7 gave nu = 2.4367 +/- 0.0005, with fission 9228 1451 737 and absorption cross sections calculated from the final 9228 1451 738 resonance parameters. 9228 1451 739 In the following Tables, the fission and capture cross 9228 1451 740 sections calculated in this evaluation with the code 9228 1451 741 SAMMY are compared with experimental data. 9228 1451 742 9228 1451 743 Experimental and calculated total cross sections. 9228 1451 744 9228 1451 745 Energy Range Calculated Schrack Weston Weston 9228 1451 746 (eV) (b.eV) (b.eV) (b.eV) (b.eV) 9228 1451 747 --------------- ---------- ------- ------ ------ 9228 1451 748 0.5 - 20.0 910.4 929.9 9228 1451 749 20.0 - 60.0 1867.8 1882.8 1869.9 9228 1451 750 60.0 - 100.0 954.0 968.0 954.2 9228 1451 751 100.0 - 200.0 2032.7 2092.7 2089.5 2073.9 9228 1451 752 200.0 - 300.0 2062.2 2007.0 2060.0 2054.6 9228 1451 753 300.0 - 400.0 1280.8 1321.6 1297.1 1292.9 9228 1451 754 400.0 - 500.0 1333.2 1391.5 1351.8 1347.9 9228 1451 755 500.0 - 600.0 1489.2 1467.9 1499.2 1494.3 9228 1451 756 600.0 - 700.0 1126.6 1156.4 1134.1 1132.6 9228 1451 757 700.0 - 800.0 1088.7 1085.8 1093.3 1075.7 9228 1451 758 800.0 - 900.0 797.6 784.0 813.0 804.9 9228 1451 759 900.0 - 1000.0 724.4 723.9 738.2 721.4 9228 1451 760 1000.0 - 2000.0 7036.1 7054.2 9228 1451 761 9228 1451 762 Experimental and calculated capture cross sections. 9228 1451 763 9228 1451 764 Energy Range Calculated De Saussure Perez 9228 1451 765 (eV) (b.eV) (b.eV) (b.eV) 9228 1451 766 --------------- ---------- ----------- ------ 9228 1451 767 0.5 - 20.0 653.5 647 9228 1451 768 20.0 - 60.0 1066.1 1084 1057 9228 1451 769 60.0 - 100.0 490.2 477 504 9228 1451 770 100.0 - 200.0 1158.8 1148 1138 9228 1451 771 200.0 - 300.0 907.8 904 940 9228 1451 772 300.0 - 400.0 660.2 658 642 9228 1451 773 400.0 - 500.0 495.9 506 478 9228 1451 774 500.0 - 600.0 533.3 506 562 9228 1451 775 600.0 - 700.0 494.8 481 449 9228 1451 776 700.0 - 800.0 490.1 513 475 9228 1451 777 800.0 - 900.0 439.8 444 397 9228 1451 778 900.0 - 1000.0 504.2 542 482 9228 1451 779 1000.0 - 1100.0 509.6 522 463 9228 1451 780 1100.0 - 1200.0 413.7 395 332 9228 1451 781 1200.0 - 1300.0 340.4 372 267 9228 1451 782 1300.0 - 1400.0 304.1 304 225 9228 1451 783 1400.0 - 1500.0 355.7 301 254 9228 1451 784 --------------- ---------- ----------- ------ 9228 1451 785 20.0 - 1500.0 9164.7 9046 8665 9228 1451 786 9228 1451 787 The fission and capture resonance integral calculated from 9228 1451 788 the present evaluation are 276.04 b and 140.49 b, respectively, 9228 1451 789 giving a capture-to-fission ratio (alpha value) of 0.509 in 9228 1451 790 excellent agreement with the value obtained from integral 9228 1451 791 measurements. 9228 1451 792 The following energy-differential data were included in the 9228 1451 793 analysis: 9228 1451 794 (1) Transmission data of Harvey et al. [HA86] on the ORELA 9228 1451 795 18-meter flight path, with sample thickness of 0.03269 9228 1451 796 atoms/barn, cooled to 77 K (0.4 to 68 eV). 9228 1451 797 (2) Transmission data of Harvey et al. [HA86] on the ORELA 9228 1451 798 80-meter flight path, with sample thickness of 0.00233 9228 1451 799 atoms/barn, cooled to 77 K (4 to 2250 eV). 9228 1451 800 (3) Transmission data of Harvey et al. [HA86] on the ORELA 9228 1451 801 80-meter flight path, with sample thickness of 0.03269 9228 1451 802 atoms/barn, cooled to 77 K (4 to 2250 eV). 9228 1451 803 (4) Fission data of Schrack [SC88] on the RPI Linac at 8.4 9228 1451 804 meter flight path (0.02 to 20 eV). 9228 1451 805 (5,6) Fission and capture data of de Saussure et al. [DE67] 9228 1451 806 on the ORELA 25.2-meter flight path (0.01 to 2250 eV). 9228 1451 807 (7,8) Fission and capture data of Perez et al. [PE73] on the 9228 1451 808 ORELA 39-meter flight path (0.01 to 100 eV). 9228 1451 809 (9) Fission data of Gwin et al. [GW84] on the ORELA 25.6-meter 9228 1451 810 flight path (0.01 to 20 eV). 9228 1451 811 (10) Transmission data of Spencer et al. [SP84] on the ORELA 9228 1451 812 ORELA 18-meter flight path, sample thickness of 0.001468 9228 1451 813 atom/barn (0.01 to 1.0 eV). 9228 1451 814 (11) Fission data of Wagemans et al. [WA88] on the Geel 18- 9228 1451 815 meter flight path (0.001 to 1.0 eV) 9228 1451 816 (12,13) Absorption and fission data of Gwin [GW96] at ORELA 9228 1451 817 (0.01 to 4.0 eV). 9228 1451 818 (14) Fission data of Weston and Todd [WE84] on the ORELA 9228 1451 819 18.9-meter flight path (14 to 2250 eV). 9228 1451 820 (15) Eta data of Wartena et al. [WA87] at 8 meters (0.0018 to 9228 1451 821 1.0 eV). 9228 1451 822 (16) Eta (chopper) data of Weigmann et al [WE90] (0.0015 to 9228 1451 823 0.15 eV). 9228 1451 824 (17) Fission data of Weston and Todd [WE92] on the ORELA 9228 1451 825 86.5-meter flight path (100 to 2000 eV). 9228 1451 826 (18) Fission yield data of Moxon et al. [MO92] at ORELA 9228 1451 827 (0.01 to 50.0 eV). 9228 1451 828 9228 1451 829 ---------------------------------------------------------------- 9228 1451 830 REFERENCES FOR RESOLVED RESONANCE REGION 9228 1451 831 9228 1451 832 [CA93] A. Carlson, W.P. Poenitz, G.M. Hale et al., "The ENDF/B-6 9228 1451 833 Neutron Cross Section Measurements Standards," National 9228 1451 834 Institute of Standards and Technology report NISTIR-5177 9228 1451 835 (1993) 9228 1451 836 [DE67] G. de Saussure, R. Gwin, L.W. Weston, and R.W. Ingle, 9228 1451 837 "Simultaneous Measurements of the Neutron Fission and Capture 9228 1451 838 Cross Section for 235U for Incident Neutron Energy from 9228 1451 839 0.04 eV to 3 keV," Oak Ridge National Laboratory report 9228 1451 840 ORNL/TM-1804 (1967) 9228 1451 841 [GW84] R. Gwin, R.R. Spencer, R.W. Ingle, J.H. Todd, and S.W. 9228 1451 842 Scoles, Nuc.Sci.Eng. 88, 37 (1984) 9228 1451 843 [GW96] R. Gwin, To be published in Nuclear Science Engineering 9228 1451 844 [HA79] J. Hardy, Brookhaven National Laboratory, report 9228 1451 845 BNL-NCS-51123 [ENDF-300] (1979) Sec. B.1 9228 1451 846 [HA86] J.A. Harvey, N.W. Hill, F.G. Perey et al., Nuclear Data 9228 1451 847 for Science and Technology, Proc. Int. Conf. May 30-June 3, 9228 1451 848 1988, Mito, Japan. (Saikon Publishing, 1988) p. 115 9228 1451 849 [LA96] N.M. Larson, "Updated Users' Guide to SAMMY" report 9228 1451 850 ORNL/TM-9179/R3 (1996) 9228 1451 851 [LE97] L.C. Leal, H. Derrien, N.M. Larson, R.Q. Wright, 9228 1451 852 "R-Matrix Analysis of 235U Neutron Transmission and Cross 9228 1451 853 Sections in the Energy Range 0 eV to 2.25 keV," Oak Ridge 9228 1451 854 National Laboratory report ORNL/TM-13516 (1997). 9228 1451 855 [MO92] M.C. Moxon, J.A. Harvey, and N.W. Hill, private 9228 1451 856 communication, Oak Ridge National Laboratory (1992). 9228 1451 857 [PE73] R.B. Perez, G. de Saussure, and E.G. 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Todd, Nucl.Sci.Eng. 111, 415 (1992) 9228 1451 877 9228 1451 878 1 451 892 19228 1451 879 2 151 4 19228 1451 880 3 4 52 19228 1451 881 3 16 14 19228 1451 882 3 17 9 19228 1451 883 3 18 15130 19228 1451 884 3 37 5 19228 1451 885 3 102 16481 19228 1451 886 8 4 2 19228 1451 887 8 16 2 19228 1451 888 8 17 2 19228 1451 889 8 18 2 19228 1451 890 8 37 2 19228 1451 891 8 102 2 19228 1451 892 9228 1 099999 9228 0 0 0 9.223500+4 2.330250+2 0 0 1 09228 2151 1 9.223500+4 1.000000+0 0 0 1 09228 2151 2 1.000000-5 2.250000+3 0 0 0 09228 2151 3 3.500000+0 9.602000-1 0 0 0 09228 2151 4 9228 2 099999 9228 0 0 0 9.223500+4 2.330250+2 0 0 0 09228 3 4 1 0.000000+0-7.700000+1 0 0 1 1459228 3 4 2 145 2 9228 3 4 3 7.641681+1 0.000000+0 7.733040+1 5.95440-13 7.842139+1 1.25360-119228 3 4 4 9.987661+2 1.059090-8 9.991517+2 1.063770-8 9.993831+2 1.072250-89228 3 4 5 9.996144+2 1.088200-8 9.998458+2 1.112050-8 1.000220+3 1.157240-89228 3 4 6 1.000441+3 1.179070-8 1.000661+3 1.193910-8 1.000882+3 1.202590-89228 3 4 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