JENDL-3.3 Pu239 pointwise at 0K 0 0 9.423900+4 2.369990+2 2 1 0 49437 1451 1 0.000000+0 1.000000+0 0 0 0 69437 1451 2 1.000000+0 2.000000+7 0 0 10 39437 1451 3 0.000000+0 0.000000+0 1 0 857 1499437 1451 4 94-PU-239 NAIG EVAL-MAR87 M.KAWAI, T.YOSHIDA, K.HIDA 9437 1451 5 DIST-MAR02 REV4-MAR00 20020214 9437 1451 6 ----JENDL-3.3 MATERIAL 9437 9437 1451 7 -----INCIDENT NEUTRON DATA 9437 1451 8 ------ENDF-6 FORMAT 9437 1451 9 9437 1451 10 HISTORY 9437 1451 11 87-03 Evaluation was made by 9437 1451 12 M.Kawai and K.Hida(naig) : cross sections above 9437 1451 13 resonance region and other quantities, 9437 1451 14 T.Yoshida(naig) : resonance parameters and background 9437 1451 15 cross sections, 9437 1451 16 Data were compiled by T.Nakagawa (jaeri). 9437 1451 17 88-08 Partly modified. 9437 1451 18 Nu-bar, resolved resons., (n,2n). 9437 1451 19 89-02 FP yields were taken from JNDC FP decay data file version-2.9437 1451 20 89-03 Unresolved resonance parameters were slightly modified. 9437 1451 21 93-02 JENDL-3.2. 9437 1451 22 Resonance parameters evaluated by H.Derrien (jaeri)/1/. 9437 1451 23 Fission spectra calculated by T.Ohsawa (kinki univ.) 9437 1451 24 Compiled by T.Nakagawa (ndc/jaeri) 9437 1451 25 9437 1451 26 ***** modified parts for JENDL-3.2 ******************** 9437 1451 27 (2,151) Resolved resonance parameters up to 2.5 keV 9437 1451 28 (5,18) 9437 1451 29 *********************************************************** 9437 1451 30 9437 1451 31 2000-03 JENDL-3.3 compiled by K.Shibata (jaeri) 9437 1451 32 ***** modified parts for JENDL-3.3 ******************** 9437 1451 33 (1,451), (1,455), (2,151), (3,2), (3,18), (3,102), 9437 1451 34 (5,16), (5,17), (5,91), (5,455) 9437 1451 35 ************************************************************ 9437 1451 36 9437 1451 37 2000-05 Fission spectra were re-evaluated by T.Ohsawa (Kinki U.). 9437 1451 38 JENDL-3.2 was adopted at 14 and 20 MeV. 9437 1451 39 9437 1451 40 2001-06 Fission spectra were replaced with the calculations by 9437 1451 41 Kawano et al./2/ above 10 MeV. 9437 1451 42 9437 1451 43 2002-01 Covariances were taken from JENDL-3.2 covariance file 9437 1451 44 except for mf/mt=3/18. 9437 1451 45 9437 1451 46 mf=1 General information 9437 1451 47 mt=451 Descriptive data and dictionary 9437 1451 48 mt=452 Number of neutrons per fission 9437 1451 49 Sum of nu-p (mt=456) and nu-d (mt=455). 9437 1451 50 mt=455 delayed neutron data 9437 1451 51 Evaluated data by Tuttle /3/ were adopted. 9437 1451 52 Decay constants were adopted from Keepin et al./4/ 9437 1451 53 mt=456 Number of prompt neutrons per fission 9437 1451 54 Standard Cf-252 sf nu-p was taken to be 3.756. Thermal nu-p 9437 1451 55 was 2.8781 that was a mean value of experimental data. The 9437 1451 56 energy dependent nu-p was obtained from 9437 1451 57 below 10 eV : ref./5/ multiplied by 1.001 9437 1451 58 10 eV 8 MeV 9437 1451 104 Ws = 3.6 + 0.4*En (MeV), En < 7 MeV 9437 1451 105 6.4 + 0.1*(En-7) (MeV), En > 7 MeV 9437 1451 106 Vso = 6.2 (mev) 9437 1451 107 r: rv = 1.26 , rs= 1.24 rso= 1.12 (fm) 9437 1451 108 a: av = 0.615, as= 0.50 , aso= 0.47 (fm) 9437 1451 109 beta-2= 0.21, beta-4= 0.065 9437 1451 110 The compound component was calculated with optical and 9437 1451 111 statistical model code casthy /21/, taking into account 9437 1451 112 level fluctuation and interference effects. The fission, 9437 1451 113 (n,2n), (n,3n), and (n,4n) reactions were considered as 9437 1451 114 competing processes. 9437 1451 115 9437 1451 116 The neutron transmission coefficients for the incident 9437 1451 117 channel were generated with ecis, whereas those for the exit 9437 1451 118 channel were calculated with casthy using spherical optical 9437 1451 119 potential parameters adopted for JENDL-2 evaluation: 9437 1451 120 V = 40.72 - 0.05*En (MeV) 9437 1451 121 Ws = 6.78 - 0.29*En (MeV) 9437 1451 122 Vso= 7.0 (MeV) 9437 1451 123 r = rso= 1.32, rs =1.357 (fm) 9437 1451 124 a = aso= b = 0.47 (fm) 9437 1451 125 The surface absorption is of derivative Woods-Saxon type. 9437 1451 126 The level scheme was taken from ref./22/: 9437 1451 127 no. energy(keV) spin-parity coupled level 9437 1451 128 g.s. 0.0 1/2 + * 9437 1451 129 1 7.86 3/2 + * 9437 1451 130 2 57.28 5/2 + * 9437 1451 131 3 75.71 7/2 + * 9437 1451 132 4 163.76 9/2 + * 9437 1451 133 5 194. 11/2 + * 9437 1451 134 6 285.46 5/2 + 9437 1451 135 7 317. 13/2 + * 9437 1451 136 8 330.13 7/2 + 9437 1451 137 9 360. 15/2 + * 9437 1451 138 10 387.41 9/2 + 9437 1451 139 11 391.6 7/2 - 9437 1451 140 12 435. 9/2 - 9437 1451 141 13 462. 11/2 + 9437 1451 142 14 469.8 1/2 - 9437 1451 143 15 488. 11/2 - 9437 1451 144 16 492.1 3/2 - 9437 1451 145 17 505.5 5/2 - 9437 1451 146 18 511.84 7/2 + 9437 1451 147 9437 1451 148 Continuum levels were assumed above 538 keV. 9437 1451 149 9437 1451 150 mt= 16, 17, 37 (n,2n), (n,3n), and (n,4n) 9437 1451 151 Calculated with a modified version of gnash /23/. The 9437 1451 152 neutron transmission coefficients were generated with ecis 9437 1451 153 /19/ and optical model code eliese-3 /24/, respectively, 9437 1451 154 using the above-mentioned deformed and spherical potentials. 9437 1451 155 The level schemes for pu-236, -237, -238, -239 and -240 were 9437 1451 156 taken from refs. /22,25,26,27,28/. The Gilbert-Cameron's 9437 1451 157 composite formula /29/ was used to represent the level 9437 1451 158 density. Level density parameters were determined from the 9437 1451 159 observed s-wave resonance spacing /30/ and the level schemes.9437 1451 160 the spin cut-off factors in the constant temperature model 9437 1451 161 were represented by Gruppelaar's prescription /31/. 9437 1451 162 9437 1451 163 pu-236 pu-237 pu-238 pu-239 pu-240 9437 1451 164 a (1/MeV) 25.50 28.00 26.23 29.44 26.96 9437 1451 165 t (MeV) 0.442 0.416 0.422 0.398 0.412 9437 1451 166 c (1/MeV) 3.06 14.5 2.88 15.0 3.30 9437 1451 167 E-joint(MeV) 4.71 4.09 4.38 3.97 4.26 9437 1451 168 sigma**2 8.63 8.18 6.47 11.6 9.69 9437 1451 169 no. levels 4.0 19.0 22.0 19.0 28.0 9437 1451 170 E-max (MeV) 0.307 0.4735 1.3103 0.5118 1.2621 9437 1451 171 D-obs (eV) 0.395 10.7 0.383 9.0 2.3 9437 1451 172 Gamma-g(eV) 0.043 0.027 0.043 0.034 0.043 9437 1451 173 9437 1451 174 D-obs of pu-236, -237 and -238 were not available from ref. 9437 1451 175 /30/, and hence the parameters "a" for these nuclei were 9437 1451 176 determined assuming its linear dependence on the mass a: 9437 1451 177 a = 0.365*a - 60.64 for even-even pu isotopes 9437 1451 178 a = 0.659*a - 128.18 for odd-mass pu isotopes 9437 1451 179 which were derived by analyzing the data of pu-241, -242, 9437 1451 180 -243, and -244 as well as pu-239 and -240. Low-lying levels 9437 1451 181 were hardly observed for pu-236 and it was assumed to be 9437 1451 182 identical to that of pu-238 to determine the constant 9437 1451 183 temperature parameters. 9437 1451 184 9437 1451 185 Evaluated fission cross section described below was fed to 9437 1451 186 gnash as a competing process/32/. The preequilibrium process9437 1451 187 was taken into account. Though the parameter f2 was 9437 1451 188 adjusted, the calculated (n,2n) cross section failed to well 9437 1451 189 reproduce the measured data. Therefore, the measured (n,2n) 9437 1451 190 cross section of Frehaut et al./33/ was adopted in place of 9437 1451 191 the calculated one. 9437 1451 192 9437 1451 193 mt=18 Fission 9437 1451 194 Below 30 keV 9437 1451 195 Based on measurements of ref./34/ and ref./35/. 9437 1451 196 Above 30 keV 9437 1451 197 New simultaneous evaluation was performed by 9437 1451 198 Kawano et al./36/ 9437 1451 199 9437 1451 200 mt=102 Capture 9437 1451 201 The cross section in the energy range below 1 MeV was derived9437 1451 202 as a product of the evaluated fission cross section and alpha9437 1451 203 value. The alpha values are identical to those of JENDL-2. 9437 1451 204 Above 1 MeV the results of the statistical model calculation 9437 1451 205 with casthy /21/ linked with ecis /19/ were adopted. The 9437 1451 206 photon strength function was normalized in the casthy 9437 1451 207 calculation so as to reproduce the capture cross section of 9437 1451 208 280 mb at 100 keV. 9437 1451 209 Direct and semi-direct calculations were performed by Kawano 9437 1451 210 /37/ above 500 keV. 9437 1451 211 9437 1451 212 mf=4 Angular distributions of secondary neutrons 9437 1451 213 mt=2,51-68,91 Calculated with ecis /19/ and casthy /21/. 9437 1451 214 mt=16,17,18,37 Isotropic in the laboratory system. 9437 1451 215 9437 1451 216 mf=5 Energy distributions secondary neutrons 9437 1451 217 mt=16,17,37,91 9437 1451 218 Calculated with threshold cross section calculation code 9437 1451 219 pegasus /38/ on the basis of preequilibrium and multi-step 9437 1451 220 evaporation model. 9437 1451 221 Data for mt=16,17,91 were replaced with gnash calculations 9437 1451 222 performed by Kawano/37/. 9437 1451 223 mt=18 9437 1451 224 Distributions were calculated with a modified Madland-Nix 9437 1451 225 model with consideration for multimodal nature of the fission9437 1451 226 process/39,40/. The compound nucleus formation cross sec- 9437 1451 227 tions for fission fragments were calculated using Becchetti- 9437 1451 228 Greenlees potential/41/. Up to 3rd-chance-fission were 9437 1451 229 considered at high incident neutron energies. 9437 1451 230 A preequilibrium emission was taken into account above 10 MeV9437 1451 231 as described in Ref./2/. The prefission neutron spectrum 9437 1451 232 was calculated with the Feshbach-Kerman-Koonin theory /42/. 9437 1451 233 The Ignatyuk formula/43/ were used to generate the level 9437 1451 234 density parameters. 9437 1451 235 Parameters adopted for thermal-neutron fission/40/: 9437 1451 236 (S1: standard-1, S2: standard-2, S3: standard-3 modes) 9437 1451 237 total average fragment kinetic energy 9437 1451 238 = 190.4 MeV for S1 9437 1451 239 = 174.2 MeV for S2 9437 1451 240 = 164.2 MeV for S3 9437 1451 241 average energy release = 205.400 MeV for S1 9437 1451 242 = 196.279 MeV for S2 9437 1451 243 = 182.123 MeV for S3 9437 1451 244 average mass number of light ff = 105 for S1 9437 1451 245 = 99 for S2 9437 1451 246 = 83 for s3 9437 1451 247 average mass number of heavy ff = 135 for S1 9437 1451 248 = 141 for S2 9437 1451 249 = 157 for s3 9437 1451 250 level density of the light ff = 11.236(S1), 9437 1451 251 10.764(S2), 6.669(S3) 9437 1451 252 level density of the heavy ff = 9.577(S1), 9437 1451 253 13.104(S1),16.284(S3) 9437 1451 254 mode branching ratio = 0.248(S1), 0.742(S2), 0.01(S3) 9437 1451 255 These data are essentially based on Schillebeeckx et al. 9437 1451 256 /44/. 9437 1451 257 Note that the parameters vary with the incident energy. 9437 1451 258 Energy-dependent mode branching ratio data of Brosa et al.9437 1451 259 /45/ was used. 9437 1451 260 mt=455 9437 1451 261 Taken from Brady and England /46/. Group abundance parameters9437 1451 262 were adjusted so as to reproduce total delayed neutron 9437 1451 263 emission rate measured by Keepin et al./4/, Besant et al. 9437 1451 264 /47/ and Maksyutenko /48/ 9437 1451 265 9437 1451 266 mf=12 Photon production multiplicities and transition 9437 1451 267 probability arrays 9437 1451 268 mt=16,17,37,91,102 (n,2n),(n,3n),(n,4n),inelastic scattering 9437 1451 269 to the continuum, and capture 9437 1451 270 Data calculated with gnash /23/ were stored under option-1 9437 1451 271 (multiplicities). The photon branching data were taken from9437 1451 272 refs. /22/ and /25,26,27,28/. Some assumptions were made 9437 1451 273 for levels of pu-237 and -239 which had no information on 9437 1451 274 branching: if e1 transitions were allowed to lower levels, 9437 1451 275 the transition probabilities were equally shared among them.9437 1451 276 If not, equally shared collective E2 transitions were 9437 1451 277 assumed. The photon strength functions were represented by 9437 1451 278 the Brink-Axel type giant dipole resonance with conventional9437 1451 279 resonance positions and widths. They were normalized to 9437 1451 280 input values at the thermal energy. The pygmy resonance was9437 1451 281 introduced only for pu-240. The parameters were assumed to 9437 1451 282 be the same as those of u-238 /49/. 9437 1451 283 9437 1451 284 mt=18 Fission 9437 1451 285 Stored under option-1 (multiplicities). The thermal neutron9437 1451 286 induced fission gamma spectrum measured by Verbinski /50/ 9437 1451 287 was adopted and used up to 20 MeV neutron. Since no data 9437 1451 288 were given for the photons below 0.14 MeV, it was assumed to9437 1451 289 be the same as that of the photons between 0.14 and 0.3 MeV.9437 1451 290 9437 1451 291 mt=51-68 Inelastic scattering 9437 1451 292 Stored under option-2 (transition probability arrays). Data9437 1451 293 were taken from ref./22/, and the same assumptions as 9437 1451 294 described above were applied to the levels to which no data 9437 1451 295 were given. 9437 1451 296 9437 1451 297 mf=14 Photon angular distributions 9437 1451 298 mt=16,17,18,37,51-68,91,102 Isotropic. 9437 1451 299 9437 1451 300 mf=15 Continuous photon energy spectra 9437 1451 301 mt=16,17,37,91,102 Calculated with gnash /23/ 9437 1451 302 mt=18 Experimental data by Verbinski /50/ 9437 1451 303 were adopted. 9437 1451 304 9437 1451 305 mf=31 Covariances of average number of neutrons per fission 9437 1451 306 mt=452 9437 1451 307 Constructed from mt=455 and 456. 9437 1451 308 mt=455 9437 1451 309 Based on experimental data. A chi-value was 0.46. 9437 1451 310 mt=456 9437 1451 311 Based on experimental data. A chi-value was 1.16. 9437 1451 312 9437 1451 313 mf=32 Covariances of resonance paremeters 9437 1451 314 mt=151 9437 1451 315 Resolved resonance 9437 1451 316 The covariances were obtained by using kalman./51/ 9437 1451 317 Unresolved resonance 9437 1451 318 The covariances were obtained by using kalman./52/ 9437 1451 319 9437 1451 320 mf=33 Covariances of cross sections (ref.43) 9437 1451 321 mt=1 9437 1451 322 Based on experimental data. A chi-value was 1.29. 9437 1451 323 mt=2 9437 1451 324 Constructed from mt=1, 4, 16, 17, 18, 37, and 102. 9437 1451 325 mt=4, 51-68, 91 9437 1451 326 The covariances were obtained by using kalman /52/. 9437 1451 327 A chi-value was 1.66. 9437 1451 328 mt=16 9437 1451 329 Based on experimental data. A chi-value was 1.0. 9437 1451 330 mt=17 9437 1451 331 Systematics. 9437 1451 332 mt=18 9437 1451 333 Based on simultaneous evaluation /36/. 9437 1451 334 mt=37 9437 1451 335 Systematics. 9437 1451 336 mt=102 9437 1451 337 Based on experimental data. A chi-value was 0.47. 9437 1451 338 9437 1451 339 mf=34 Covariances of angular distributions (ref.52) 9437 1451 340 mt=2 9437 1451 341 The covariances of p1 coefficients were obtained by using 9437 1451 342 kalman. A chi-value was 0.41. 9437 1451 343 9437 1451 344 mf=35 Covariances of energy distributions 9437 1451 345 mt=18 9437 1451 346 The covariances were obtained by using kalman./53/ 9437 1451 347 9437 1451 348 9437 1451 349 References 9437 1451 350 1) Derrien H.: J. Nucl. Sci. Technol., 30, 845 (1993). 9437 1451 351 2) Kawano T. et al.: Phys. Rev., C63, 034601 (2001). 9437 1451 352 3) Tuttle R.J.: INDC(NDS)-107/G + special, 29 (1980). 9437 1451 353 4) Keepin G.R. et al.: Phy. Rev., 107, 1044 (1957). 9437 1451 354 5) Gwin R. et al.: Nucl. Sci. Eng., 94, 365 (1986). 9437 1451 355 6) Frehaut J.: NEANDC(E)-238/L (1986). 9437 1451 356 7) Gwin R. et al.: Nucl. Sci. 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Nucl. energy, 7, 495 (1980). 9437 1451 385 36) Kawano T. et al.: JAERI-Research 2000-004 (2000). 9437 1451 386 37) Kawano T.: Private communication (1999). 9437 1451 387 38) Iijima S. et al.: JAERI-M 87-025, p.337 (1987). 9437 1451 388 39) Madland D.G. and Nix J.R.: Nucl. Sci. Eng., 81, 213 (1982). 9437 1451 389 40) Ohsawa, T. et al.: Nucl. Phys. A665, 3 (2000). 9437 1451 390 41) Becchetti Jr.F.D. and Greenlees G.W.: Phys. Rev., 182, 1190 9437 1451 391 (1969). 9437 1451 392 42) Feshbach H., et al.: Ann. Phys. (N.Y.) 125, 429 (1980). 9437 1451 393 43) Ignatyuk A.V.: Sov. J. Nucl. Phys., 29, 450 (1979). 9437 1451 394 44) Schillebeeckx P. et al.: Nucl. Phys. A545, 623 (1992). 9437 1451 395 45) Brosa U. et al.: Phys. Rev. C59, 767 (1999). 9437 1451 396 46) Brady M.C. and England T.R.: Nucl. Sci. Eng., 103, 129 (1989).9437 1451 397 47) Besant C.B. et al.: J. Br. Nucl. Energy Soc., 16, 161 9437 1451 398 (1977) 9437 1451 399 48) Maksyutenko B.P.: Yad. Fiz. (English Translation) 15, 9437 1451 400 848 (1963) 9437 1451 401 49) Hida K.: JAERI-M 85-035, 166 (1985). 9437 1451 402 50) Verbinski V.V. et al.: Phys. Rev., C7, 1173 (1973). 9437 1451 403 51) Kawano T.: Private communication (2000). 9437 1451 404 52) Shibata K. et al.: JAERI-Research 97-074 (1997). 9437 1451 405 53) Kawano T. et al.: JAERI-Research 99-009 (1999). 9437 1451 406 9437 1451 407 ================================================================= 9437 1451 408 APPENDIX RESONANCE DATA 9437 1451 409 ================================================================= 9437 1451 410 9437 1451 411 THE PRESENT FILE CONTAINS THE RESONANCE PARAMETERS OBTAINED 9437 1451 412 FROM A SAMMY FIT ANALYSIS OF HIGH RESOLUTION EXPERIMENTAL DATA, 9437 1451 413 PERFORMED AT ORNL(OAK RIDGE NATIONNAL LABORATORY,USA) BY H.DERRIEN9437 1451 414 AND G.DE SAUSSURE AND AT JAERI(TOKAI-MURA RESEARCH ESTABLISHMENT, 9437 1451 415 JAPAN) BY H.DERRIEN. 9437 1451 416 THE FILE CONTAINS THREE INDEPENDANT SECTIONS: 9437 1451 417 1/ THE FIRST CORRESPONDS TO THE ENERGY RANGE 0 KEV TO 1 KEV. 9437 1451 418 THE CORRESPONDING SET OF RESONANCE PARAMETRES CONTAINS 398 RESO- 9437 1451 419 NANCES IN THE ENERGY RANGE 0 KEV TO 1 KEV, 4 FICTICIOUS NEGATIVE 9437 1451 420 ENERGY RESONANCES AND 3 FICTICIOUS RESONANCES ABOVE 1 KEV; 9437 1451 421 2/ THE SECOND CORRESPONDS TO THE ENERGY RANGE 1 KEV TO 2 KEV. 9437 1451 422 THE CORRESPONDING SET OF RESONANCE PARAMETERS CONTAINS 435 RESON- 9437 1451 423 ANCES IN THE ENERGY RANGE 0.980 KEV TO 2.02 KEV, 3 FICTICIOUS 9437 1451 424 RESONANCES BELOW 0.9 KEV AND 3 FICTICIOUS RESONANCES ABOVE 2.02 9437 1451 425 KEV; 9437 1451 426 3/ THE THIRD CORRESPONDS TO THE ENERGY RANGE 2 KEV TO 2.5 KEV. 9437 1451 427 THE CORRESPONDING SET OF RESONANCE PARAMETERS CONTAINS 218 RESO- 9437 1451 428 NANCES IN THE ENERGY RANGE 1.98 KEV TO 2.53 KEV, 3 FICTICIOUS 9437 1451 429 RESONANCES BELOW 1.98 KEV AND 3 FICTICIOUS RESONANCES ABOVE 2.53 9437 1451 430 KEV. 9437 1451 431 IN ALL SECTIONS THE FICTICIOUS RESONANCE PARAMETERS TAKE INTO 9437 1451 432 ACCOUNT THE CONTRIBUTION OF ALL THE EXTERNAL TRUNCATED RESONANCES 9437 1451 433 IN SUCH A WAY THAT NO TOTAL, SCATTERING, FISSION AND CAPTURE 9437 1451 434 SMOOTH FILES ARE NEEDED IN THE CORRESPONDING ENERGY RANGES FOR THE9437 1451 435 REPRODUCTION OF THE CROSS SECTIONS WITHIN THE EXPERIMENTAL ERRORS.9437 1451 436 THE FOLLOWING EXPERIMENTAL DATA BASE HAS BEEN USED IN THE SAMMY9437 1451 437 FITS: 9437 1451 438 -ABSORPTION AND FISSION FROM R.GWIN ET AL./1,2/; 9437 1451 439 -FISSION FROM R.GWIN ET AL./3,4/, J.BLONS/5/, L.W.WESTON ET 9437 1451 440 AL./6,7/; 9437 1451 441 -TRANSMISSION FROM R.R.SPENCER ET AL./8/, J.A.HARVEY ET AL./9/ 9437 1451 442 PRIOR TO THE FITS THE EXPERIMENTAL FISSION AND ABSORPTION CROSS 9437 1451 443 SECTIONS WERE NORMALISED, DIRECTLY OR INDIRECTLY TO THE 0.0253 EV 9437 1451 444 VALUES OBTAINED BY THE ENDF/B-VI STANDARD EVALUATION GROUP/10/. 9437 1451 445 THE TRANSMISSION DATA WERE CONSIDERED AS ACCURATE ABSOLUTE MEASU- 9437 1451 446 REMENTS(R.R.SPENCER TOTAL CROSS SECTION AT 0.0253 EV IS 1025.0 B 9437 1451 447 IN EXCELLENT AGREEMENT WITH THE 1027.3 B STANDARD VALUE). 9437 1451 448 DETAILS ON THE ANALYSIS ARE FOUND IN REFERENCES/11,12,13/ 9437 1451 449 9437 1451 450 ***************************************************************** 9437 1451 451 COMMENTS ON THE THERMAL AND LOW ENERGY RANGES 9437 1451 452 ***************************************************************** 9437 1451 453 9437 1451 454 THE THERMAL CROSS SECTION VALUES CALCULATED AT 293 K BY THE 9437 1451 455 RESONANCE PARAMETERS OF THE FIRST SECTION ARE GIVEN IN THE FOLLO- 9437 1451 456 WING TABLE: 9437 1451 457 9437 1451 458 9437 1451 459 SAMMY RESENDD PROPOSED 9437 1451 460 293 K (BARN) STANDARD VALUES(BARN)/10/ 9437 1451 461 **************************************************************** 9437 1451 462 FISSION 747.64 747.90 747.99+-1.87 9437 1451 463 CAPTURE 271.10 270.73 271.43+-2.14 9437 1451 464 SCATTERING 7.97 7.99 7.88+-0.97 9437 1451 465 TOTAL 1026.71 1026.62 1027.30+-5.00 9437 1451 466 **************************************************************** 9437 1451 467 9437 1451 468 ONE SHOULD NOTE THAT THE 293 K CROSS SECTIONS CALCULATED AT 9437 1451 469 0.0253 EV DEPEND ON THE WAY THE DOPPLER BROADENING CALCULATION IS 9437 1451 470 PERFORMED. FOR INSTANCE USING A GAUSSIAN BROADENING FUNCTION WILL 9437 1451 471 GIVE A FISSION CROSS SECTION ABOUT 2.5 BARNS LARGER THAN THE ONE 9437 1451 472 OBTAINED FROM THE ACCURATE CALCULATION WHICH CONSERVES THE 1/V 9437 1451 473 SHAPE OF THE THERMAL CROSS SECTION. THE VALUES GIVEN IN THE TABLE 9437 1451 474 ABOVE WERE OBTAINED FROM SAMMY (LEAL-HWANG METHOD)/14,15/ AND FROM9437 1451 475 RESENDD WITH 0.1% FOR THE INTERPOLATION ACCURACY/16/. 9437 1451 476 THE FOLLOWING TABLE SHOWS EXPERIMENTAL CROSS SECTIONS AVE- 9437 1451 477 RAGED OVER THE ENERGY RANGES 0.02 EV TO 0.06 EV AND 0.02 EV TO 9437 1451 478 0.65 EV, COMPARED TO THE CALCULATED VALUES: 9437 1451 479 9437 1451 480 9437 1451 481 AVERAGE CROSS-SECTIONS(BARN) 9437 1451 482 **************************************************************** 9437 1451 483 REFERENCES(1-10) 0.02 TO 0.06 EV 0.02 TO 0.65 EV 9437 1451 484 **************************************************************** 9437 1451 485 EXP CALC (293K) EXP CALC (293K) 9437 1451 486 GWIN71 FISS 631.41 843.71 9437 1451 487 GWIN76 FISS 631.41 838.39 9437 1451 488 GWIN84 FISS(*) 631.41 631.75(+0.05%) 837.18 838.69(+0.18%) 9437 1451 489 DERUYTER70 FISS 631.41 859.43 9437 1451 490 WAGEMANS80 FISS 631.41 862.56 9437 1451 491 WAGEMANS88 FISS 631.41 841.80 9437 1451 492 GWIN71 CAPTURE 243.84 243.22(-0.25%) 524.75 518.13(-1.26%) 9437 1451 493 GWIN76 ABSORPT(*) 875.90 874.29(-0.18%) 1359.96 1357.14(-0.21%) 9437 1451 494 SPENCER84 TOT(*) 883.20 882.86(-0.04%) 1361.69 1367.6 (+0.43%) 9437 1451 495 **************************************************************** 9437 1451 496 (*)THESE DATA HAD THE LARGIEST WEIGHT IN THE THERMAL FIT. THE VA- 9437 1451 497 LUES BETWEEN THE PARENTHESES GIVE THE PERCENTAGE DEVIATION BETWEEN9437 1451 498 THE CALCULATED DATA AND THE EXPERIMENTAL DATA. 9437 1451 499 ***************************************************************** 9437 1451 500 9437 1451 501 THE VALUE OF 631.4 BARNS FOR ALL THE AVERAGED EXPERIMENTAL 9437 1451 502 FISSION CROSS SECTIONS IN THE ENERGY RANGE 0.02 EV TO 0.06 EV 9437 1451 503 CORRESPONDS TO THE RENORMALISATION OF THE FISSION EXPERIMENTS TO 9437 1451 504 748.0+-1. BARNS AT 0.0253 EV. ORNL DATA ARE CONSISTENT WITHIN 0.8%9437 1451 505 OVER THE ENERGY RANGE 0.02 EV TO 0.65 EV (I.E. OVER THE 0.3 EV 9437 1451 506 RESONANCE). DERUYTER 1970 AND WAGEMANS 1980 DATA ARE ABOUT 2.5% 9437 1451 507 LARGER AND WERE NOT INCLUDED IN THE SAMMY FIT. WHEN NORMALIZED ON 9437 1451 508 THE STANDARD VALUE AT 0.0253 EV, GWIN 76 ABSORPTION AGREES WITH 9437 1451 509 THE ABSORPTION OBTAINED FROM SPENCER TOTAL CROSS SECTION WITHIN 9437 1451 510 0.7% OVER THE 0.3 EV RESONANCE. THE PRESENT EVALUATION IS 9437 1451 511 ESSENTIALLY THE RESULT OF A CONSISTENT SAMMY ANALYSIS OF ALL THE 9437 1451 512 AVAILABLE ORNL DATA WITH A LARGER WEIGHT ON GWIN 1984 FISSION, 9437 1451 513 GWIN 1976 ABSORPTION AND SPENCER TRANSMISSION DATA. 9437 1451 514 AFTER RENORMALIZATION OF THE CALCULATED FISSION CROSS SECTION9437 1451 515 ON THE PRELIMINARY 1991 WESTON AND TODD FISSION DATA(SEE NEXT 9437 1451 516 SECTION) A SLIGHT ADJUSTMENT OF THE NEGATIVE RESONANCE PARAMETERS 9437 1451 517 WAS PERFORMED TO KEEP THE VALUES CALCULATED AT 0.0253 EV IN CLOSE 9437 1451 518 AGREEMENT WITH THE STANDARD VALUES. THE 1988 DATA OF WAGEMANS ET 9437 1451 519 AL./17/ AGREE WITHIN 0.4% WITH THE CALCULATED VALUES OVER THE 9437 1451 520 ENERGY RANGE FROM 0.02 EV TO 0.65 EV AFTER ADJUSTMENT OF THE 9437 1451 521 ENERGY SCALE TO THE ORNL SCALE (THE DIFFERENCE WAS 0.27 EV AT 20 9437 1451 522 EV BETWEEN 1988 WAGEMANS AND ORNL SAMMY FIT ENERGY SCALES). 9437 1451 523 9437 1451 524 ***************************************************************** 9437 1451 525 COMMENTS ON THE 0 KEV TO 1 KEV ENERGY RANGE. 9437 1451 526 ***************************************************************** 9437 1451 527 9437 1451 528 AT THE END OF 1987, AN ANALYSIS WAS COMPLETED UP TO 1 KEV. IN A9437 1451 529 PRELIMINARY STEP, A CORRELATED FIT OF HARVEY TRANSMISSION DATA, 9437 1451 530 WESTON 84 FISSION DATA AND BLONS FISSION DATA WAS PERFORMED, WITH 9437 1451 531 POSSIBLE ADJUSTMENT OF THE NORMALIZATION COEFFICIENTS AND OF THE 9437 1451 532 BACKGROUND CORRECTIONS. THIS PRELIMINARY STEP HAS SHOWN THAT THIS 9437 1451 533 ADJUSTMENT WAS NOT NECESSARY TO HAVE CONSISTENCY BETWEEN HARVEY 9437 1451 534 DATA AND WESTON DATA. BLONS DATA NEEDED A LARGE READJUSTMENT OF 9437 1451 535 THE BACKGROUND AND OF THE NORMALIZATION. THEREFORE, THE FINAL FIT 9437 1451 536 WAS PERFORMED ONLY ON HARVEY TRANSMISSION DATA, GWIN 84 FISSION 9437 1451 537 DATA (BELOW 30 EV) AND WESTON 84 FISSION DATA, WITH NO BACKGROUND 9437 1451 538 AND NORMALISATION ADJUSTMENT. BLONS DATA, WHICH HAVE BETTER 9437 1451 539 RESOLUTION THAN WESTON 84 DATA, WERE USED ONLY TO OBTAIN MORE 9437 1451 540 ACCURATE FISSION WIDTHS OF SOME NARROW RESONANCES IN THE HIGH 9437 1451 541 ENERGY RANGE. 9437 1451 542 IN 1989, PRELIMINARY RESULTS OF THE 1988 WESTON FISSION 9437 1451 543 MEASUREMENT/7/ WERE INCLUDED IN THE SAMMY EXPERIMENTAL DATA 9437 1451 544 BASE. ONE EXPECTED FROM THIS MEASUREMENT, WHICH WAS PERFORMED BY 9437 1451 545 USING A 86 M FLIGHT PATH WITH A RESOLUTION COMPARABLE TO THE 9437 1451 546 RESOLUTION OF HARVEY TRANSMISSION, A CONFIRMATION OF THE EXCELLENT9437 1451 547 QUALITY OF THE 1984 MEASUREMENT. A CONSISTENT SAMMY FIT OF HARVEY 9437 1451 548 TRANSMISSION, WESTON 84 FISSION AND PRELIMINARY WESTON 88 FISSION 9437 1451 549 WAS RESTARTED FROM THE PARAMETER AND COVARIANCE FILES OBTAINED IN 9437 1451 550 1987. IT APPEARED THAT LARGE BACKGROUND AND NORMALISATION 9437 1451 551 CORRECTIONS WERE NEEDED ON THE NEW WESTON FISSION TO OBTAIN 9437 1451 552 CONSISTENCY WITH HARVEY TRANSMISSION DATA. THESE CORRECTIONS WERE 9437 1451 553 COMPARABLE TO THOSE FOUND ON BLONS DATA AND WERE NOT UNDERSTOOD BY9437 1451 554 THE AUTHORS OF THE EXPERIMENT. THE LAST SAMMY RUNS WERE PERFORMED 9437 1451 555 BY NOT ALLOWING BACKGROUND AND NORMALIZATION VARIATIONS ON HARVEY 9437 1451 556 TRANSMISSION AND WESTON 84 FISSION(VERY SMALL ERROR BARS WERE 9437 1451 557 ASSIGNED TO THE CORRESPONDING PARAMETERS IN THE COVARIANCE MATRIX)9437 1451 558 AND BY ALLOWING THESE VARIATIONS ON WESTON 88 DATA. A NEW SET OF 9437 1451 559 RESONANCE PARAMETERS WAS OBTAINED,WHICH WAS IMPROVED COMPARED TO 9437 1451 560 THE PREVIOUS SET DUE TO THE VERY HIGH RESOLUTION OF THE NEW WESTON9437 1451 561 FISSION MEASUREMENT. 9437 1451 562 THE CALCULATED AVERAGE FISSION CROSS SECTION IN THE ENERGY 9437 1451 563 RANGE FROM 0.1 KEV TO 1.0 KEV WAS 3.7% SMALLER THAN THE VALUES 9437 1451 564 OBTAINED BY THE ENDF/B-VI STANDARD EVALUATION GROUP, DUE TO THE 9437 1451 565 FACT THAT WESTON 84 DATA WERE 3.1% LOWER THAN THE AVERAGE STANDARD9437 1451 566 VALUE. A NEW MEASUREMENT WAS PERFORMED BY WESTON AND TODD IN 1991 9437 1451 567 /18/ IN ORDER TO CHECK THEIR 1984 DATA. A CAREFUL NORMALIZATION 9437 1451 568 OF THE DATA IN THE THERMAL ENERGY RANGE SHOWED THAT THE 1984 DATA 9437 1451 569 SHOULD BE RENORMALIZED BY ABOUT +3%. TO TAKE INTO ACCOUNT THIS 9437 1451 570 RENORMALIZATION, THE 1989 RESONANCE PARAMETERS WERE MODIFIED AT 9437 1451 571 JAERI/13/ IN THE FOLLOWING WAY: 9437 1451 572 1/ INCREASE OF THE FISSION WIDTH BY 3% AND DECREASE OF THE 9437 1451 573 CAPTURE WIDTH BY A QUANTITY EQUAL TO THE VARIATION OF THE FISSION 9437 1451 574 WIDTH, IN THE NARROW RESONANCES(MAINLY 1+ RESONANCES); THAT DOES 9437 1451 575 NOT MODIFY THE TOTAL CROSS SECTION IN THE CORRESPONDING 9437 1451 576 RESONANCES; 9437 1451 577 2/ ADJUSTMENT OF THE NEUTRON WIDTH OF THE 0+ RESONANCES BY A 9437 1451 578 REFIT OF THE TRANSMISSION DATA AND OF THE RENORMALIZED WESTON AND 9437 1451 579 TODD 1984 DATA IN ENERGY RANGES WHERE THE CONTRIBUTION OF THE 0+ 9437 1451 580 RESONANCES IS DOMINANT, AND INCREASE OF THE OTHER(SMALL) 0+ 9437 1451 581 NEUTRON WIDTHS BY 3%. NO SEVERE INCONSISTENCY WAS OBSERVED BETWEEN9437 1451 582 THE TRANSMISSION DATA AND THE NEW FISSION DATA OVER THE DOMINANT 9437 1451 583 0+ RESONANCES;THE DIFFERENCES BETWEEN THE 1989 FITS OF THE TRANS- 9437 1451 584 MISSION AND THE NEW FITS WERE CONSISTENT WITHIN THE EXPERIMENTAL 9437 1451 585 ERROR BARS. 9437 1451 586 THE FOLLOWING TABLE SHOWS THE FISSION CROSS SECTIONS CALCULA- 9437 1451 587 TED FROM THE RESONANCE PARAMETERS, THE EXPERIMENTAL VALUES AND THE9437 1451 588 RESULTS OF THE ENDF/B-VI STANDARD EVALUATION GROUP AVERAGED IN THE9437 1451 589 SAME ENERGY INTERVALS. WESTON 1991 DATA ARE PRELIMINARY. WESTON 9437 1451 590 1984 DATA ARE NORMALIZED ON PRELIMINARY WESTON 1991: 9437 1451 591 9437 1451 592 CROSS-SECTIONS(BARN) 9437 1451 593 ************************************************* 9437 1451 594 ENERGY CALCUL WESTON WESTON STANDARD 9437 1451 595 (EV) 1991 1984 9437 1451 596 ************************************************* 9437 1451 597 0.010-10. 80.12 79.98 9437 1451 598 9-20 94.74 94.91 9437 1451 599 20-40 17.52 17.76 17.97 9437 1451 600 40-60 50.64 50.90 50.87 9437 1451 601 60-100 54.42 54.38 54.33 9437 1451 602 100-200 18.63 18.59 18.56 18.66 9437 1451 603 200-300 17.85 17.89 17.88 9437 1451 604 300-400 8.31 8.34 8.43 9437 1451 605 400-500 9.59 9.58 9.57 9437 1451 606 ------------------------------------------------- 9437 1451 607 200-500 11.92 11.93 11.93 11.96 9437 1451 608 ------------------------------------------------- 9437 1451 609 500-600 15.39 15.57 15.86 9437 1451 610 600-700 4.37 4.30 4.46 9437 1451 611 700-800 5.51 5.53 5.63 9437 1451 612 800-900 4.84 4.89 4.98 9437 1451 613 900-1000 8.33 8.38 8.30 9437 1451 614 ------------------------------------------------- 9437 1451 615 500-1000 7.69 7.73 7.73 7.79 9437 1451 616 ------------------------------------------------- 9437 1451 617 20-1000 13.09 13.11 13.11 9437 1451 618 ************************************************** 9437 1451 619 9437 1451 620 9437 1451 621 GWIN 1971 AND 1976 ABSORPTION DATA WERE NOT INCLUDED IN THE 9437 1451 622 SAMMY FIT IN THE ENERGY RANGE ABOVE 1 EV. ACCURATE ABSORPTION 9437 1451 623 CROSS SECTIONS SHOULD BE CALCULATED FROM THE PARAMETERS OBTAINED 9437 1451 624 FROM THE ANALYSIS OF THE TRANSMISSION AND FISSION DATA. THE FOLLO-9437 1451 625 WING TABLE SHOWS THE CALCULATED AVERAGE VALUES OF THE CAPTURE, AB-9437 1451 626 SORPTION AND ALPHA COMPARED TO GWIN 1971 AND GWIN 1976 DATA. THE 9437 1451 627 CALCULATIONS WERE PERFORMED WITH RESENDD, 1.0 % ACCURACY: 9437 1451 628 9437 1451 629 CROSS-SECTIONS(BARN) 9437 1451 630 ******************************************************* 9437 1451 631 ENERGY(EV) CALC. VALUES (293K) GWIN DATA 9437 1451 632 ******************************************************* 9437 1451 633 CAPT ABSORP ALPHA ABSORP ALPHA 9437 1451 634 7.3- 16.0 76.61 196.04 0.64 208.00 0.74(*) 9437 1451 635 16.0- 37.5 20.51 44.55 0.85 46.50 0.89(*) 9437 1451 636 37.5- 50.0 48.72 70.00 2.29 83.15 2.96(*) 9437 1451 637 50.0-100.0 33.60 92.13 0.57 92.84 0.63 9437 1451 638 100.0-200.0 15.58 34.29 0.83 33.66 0.87 9437 1451 639 200.0-300.0 15.85 33.68 0.89 34.69 0.94 9437 1451 640 300.0-400.0 9.69 18.01 1.16 18.31 1.16 9437 1451 641 400.0-500.0 3.96 13.56 0.41 13.56 0.44 9437 1451 642 500.0-600.0 10.87 26.30 0.70 26.54 0.72 9437 1451 643 600.0-700.0 6.53 10.90 1.49 11.57 1.54 9437 1451 644 700.0-800.0 4.95 10.47 0.90 10.52 0.97 9437 1451 645 800.0-900.0 3.65 8.50 0.75 9.30 0.82 9437 1451 646 900.0-999.9 5.06 13.51 0.60 13.23 0.70 9437 1451 647 ****************************************************** 9437 1451 648 (*) GWIN 1971 DATA 9437 1451 649 9437 1451 650 IF ONE EXCEPTS THE ENERGY RANGE 37.5-50 EV, THE CALCULATED AB- 9437 1451 651 SORPTION VALUES AGREE WELL WITH GWIN EXPERIMENTAL DATA; THEY ARE 9437 1451 652 ON AVERAGE 1.2% LOWER IN THE ENERGY RANGE FROM 50 EV TO 1000 EV. 9437 1451 653 9437 1451 654 ***************************************************************** 9437 1451 655 COMMENTS ON THE 1 KEV TO 2 KEV ENERGY RANGE 9437 1451 656 ***************************************************************** 9437 1451 657 9437 1451 658 PRELIMINARY RESONANCE PARAMETERS WERE OBTAINED IN 1989 FROM THE9437 1451 659 ANALYSIS OF THE HARVEY THICK SAMPLE TRANSMISSION DATA AND OF THE 9437 1451 660 PRELIMINARY RESULTS OF WESTON 88 FISSION MEASUREMENT. DUE TO LACK9437 1451 661 OF TIME, THE MEDIUM AND THIN SAMPLE TRANSMISSION DATA WERE NOT 9437 1451 662 INCLUDED IN THE SAMMY DATA BASE, AND THE CONTRIBUTION OF THE 9437 1451 663 TRUNCATED EXTERNAL RESONANCES WAS NOT CAREFULLY INVESTIGATED. 9437 1451 664 NEVERTHELESS, THE RESULTS WERE USED IN THE ENDF/B-VI FILE, ALONG 9437 1451 665 WITH A SMOOTH FILE IN ORDER TO AGREE WITH THE AVERAGE VALUES OF A 9437 1451 666 PREVIOUS ENDF/B-VI EVALUATION (THIS PRELIMINARY SET OF PARAMETERS 9437 1451 667 WAS CONSIDERED AS MORE USEFUL THAN THE STATISTICAL PARAMETERS IN 9437 1451 668 THE ENERGY RANGE 1 KEV TO 2 KEV FOR THE CALCULATION OF THE SELF- 9437 1451 669 SHIELDING FACTORS). 9437 1451 670 THE ANALYSIS WAS RESTARTED IN APRIL 1991 AT JAERI(TOKAI 9437 1451 671 RESEARCH ESTABLISHMENT) WITH AN UPDATED VERSION OF SAMMY ADAPTED 9437 1451 672 BY T.NAKAGAWA TO THE FACOM 780. THE PRELIMINARY SET OF PARAMETERS 9437 1451 673 OBTAINED AT OAK RIDGE IN 1989 WAS USED AS PRIOR INFORMATIONS TO 9437 1451 674 START THE SAMMY CALCULATIONS. ALSO PRIOR TO THE ANALYSIS, THE CON-9437 1451 675 TRIBUTION OF THE EXTERNAL RESONANCES WAS CALCULATED BY USING THE 9437 1451 676 SET OF THE 0 KEV TO 1 KEV KNOWN RESONANCES, SHIFTED IN THE ENERGY 9437 1451 677 RANGES -1 KEV TO 0 KEV, 2 KEV TO 3KEV AND 3 KEV TO 4 KEV; EQUIVA- 9437 1451 678 LENT CONTRIBUTION WAS OBTAINED BY USING 3 FICTICIOUS RESONANCES 9437 1451 679 BELOW 1 KEV AND 3 FICTICIOUS RESONANCES ABOVE 2 KEV(SEE DETAILS IN9437 1451 680 REF./13/). THE ANALYSIS WAS PERFORMED ON THE THICK AND MEDIUM 9437 1451 681 SAMPLE TRANSMISSIONS OF HARVEY DATA (THE THIN SAMPLE DATA WAS NOT 9437 1451 682 USEFUL IN THE HIGH ENERGY RANGE) AND ON THE 1988 FISSION DATA RE- 9437 1451 683 LEASED BY WESTON AT THE BEGINNING OF 1991/7/. THE DEFINITIVE 9437 1451 684 SAMMY FITS WERE PERFORMED IN APRIL 1992 AFTER RENORMALIZATION OF 9437 1451 685 THE 1988 DATA OF WESTON ON THE ENDF/B-VI STANDARD VALUES BETWEEN 19437 1451 686 KEV AND 2 KEV, IN AGREEMENT WITH THE 1991 NEW MEASUREMENTS OF 9437 1451 687 WESTON AND TODD. 9437 1451 688 THE AVERAGE CROSS SECTIONS CALCULATED FROM THE RESONANCE 9437 1451 689 PARAMETERS ARE COMPARED TO THE EXPERIMENTAL VALUES IN THE FOLLO- 9437 1451 690 WING TABLE: 9437 1451 691 9437 1451 692 9437 1451 693 ************************************************************** 9437 1451 694 CROSS-SECTIONS(BARN) 9437 1451 695 --------------------------------------------------- 9437 1451 696 TOTAL FISSION CAPTURE 9437 1451 697 ENERGY -------------- ------------- ------------- 9437 1451 698 KEV CALC(A) EXP(B) CALC(A) EXP(C) CALC(A) EXP(D) 9437 1451 699 ************************************************************** 9437 1451 700 1.0-1.1 24.47 24.95 5.549 5.581 4.728 5.04 9437 1451 701 1.1-1.2 22.82 23.10 5.985 6.017 3.757 2.95 9437 1451 702 1.2-1.3 22.29 22.90 4.601 4.501 4.287 4.00 9437 1451 703 1.3-1.4 22.63 22.85 6.997 6.997 3.012 2.52 9437 1451 704 1.4-1.5 20.42 20.95 4.041 4.059 3.450 3.57 9437 1451 705 1.5-1.6 18.30 18.95 2.564 2.613 3.521 3.89 9437 1451 706 1.6-1.7 21.82 21.90 3.952 3.955 3.833 4.36 9437 1451 707 1.7-1.8 21.26 21.35 3.400 3.425 4.091 4.37 9437 1451 708 1.8-1.9 23.76 23.30 5.178 5.187 3.639 3.14 9437 1451 709 1.9-2.0 18.48 18.90 2.152 2.180 3.205 4.06 9437 1451 710 ************************************************************** 9437 1451 711 1.0-2.0 21.63 21.92 4.442 4.446 3.752 3.79 9437 1451 712 ************************************************************** 9437 1451 713 (A) TOTAL, FISSION AND CAPTURE CROSS SECTIONS CALCULATED BY 9437 1451 714 RESENDD FROM THE RESONANCE PARAMETERS. 9437 1451 715 (B) EXPERIMENTAL TOTAL CROSS SECTIONS FROM REFERENCE/19/. 9437 1451 716 (C) WESTON AND TODD 1988 HIGH RESOLUTION FISSION CROSS SECTIONS 9437 1451 717 FROM REFERENCE/7/ NORMALIZED TO ENDF/B-VI STANDARD IN THE 9437 1451 718 ENERGY RANGE FROM 1.0 KEV TO 2.0 KEV. 9437 1451 719 (D) GWIN 1971 EXPERIMENTAL DATA NORMALIZED TO GWIN 1976 DATA. 9437 1451 720 ************************************************************** 9437 1451 721 9437 1451 722 THE DIFFERENCE OF 1.3% BETWEEN THE AVERAGE CALCULATED TOTAL 9437 1451 723 CROSS SECTION AND THE AVERAGE EXPERIMENTAL CROSS SECTION IN THE 9437 1451 724 ENERGY RANGE FROM 1.0 KEV AND 2.0 KEV IS MAINLY DUE TO THE METHOD 9437 1451 725 OF EVALUATING THE TOTAL CROSS SECTION FROM THE EFFECTIVE CROSS 9437 1451 726 SECTION IN REFERENCE/19/. THE ACCURACY OF THE SAMMY FIT OF THE 9437 1451 727 EXPERIMENTAL TRANSMISSION DATA IS BETTER THAN 0.5% ON THE CROSS 9437 1451 728 SECTION. THE CALCULATED FISSION CROSS SECTIONS ARE IN VERY GOOD 9437 1451 729 AGREEMENT WITH THE EXPERIMENTAL DATA. THE CAPTURE DATA /1/ ARE 9437 1451 730 AVERAGE VALUES OBTAINED FROM THE DATA AVAILABLE IN THE EXFOR FILE 9437 1451 731 AND NORMALIZED TO GWIN 1976 AVERAGE VALUES; THERE ARE LARGE 9437 1451 732 DIFFERENCES BETWEEN THE CALCULATED DATA AND THE EXPERIMENTAL DATA 9437 1451 733 AVERAGED OVER 0.1 KEV INTERVALS; BUT ON THE INTERVAL FROM 1.0 KEV 9437 1451 734 TO 2.0 KEV THE AVERAGE VALUES ARE CONSISTENT WITHIN 1.0%. 9437 1451 735 9437 1451 736 ***************************************************************** 9437 1451 737 COMMENTS ON THE 2.0 KEV TO 2.5 KEV REGION 9437 1451 738 ***************************************************************** 9437 1451 739 9437 1451 740 THIS ENERGY RANGE WAS ALSO ANALYSED AT JAERI /13/. NO 9437 1451 741 PRELIMINARY SET OF RESONANCE PARAMETERS WAS AVAILABLE PRIOR TO THE9437 1451 742 ANALYSIS. MORE THAN 90% OF THE RESONANCES, COMPARED TO THE LOW 9437 1451 743 ENERGY RANGE, COULD STILL BE IDENTIFIED IN THE TRANSMISSION DATA 9437 1451 744 BETWEEN 2 KEV AND 2.5 KEV. THEREFORE THE CORRELATED SAMMY ANALYSIS9437 1451 745 OF HARVEY TRANSMISSIONS AND WESTON FISSION WAS STILL FEASIBLE IN 9437 1451 746 THIS ENERGY RANGE. THE RESONANCE PARAMETERS OBTAINED ARE 9437 1451 747 CONSISTENT AND HAS NEARLY THE SAME STATISTICAL PROPERTIES AS THOSE9437 1451 748 OF THE RESONANCES IN THE 0 TO 2 KEV ENERGY RANGE. A QUITE GOOD FIT9437 1451 749 OF THE TRANSMISSION AND FISSION DATA WAS OBTAINED WITHOUT 9437 1451 750 BACKGROUND AND NORMALISATION ADJUSTMENT. HOWEVER, THE CALCULATED 9437 1451 751 FISSION CROSS SECTIONS ARE, ON AVERAGE, 1.4% LOWER THAN THE 9437 1451 752 EXPERIMENTAL VALUES. THIS DIFFERENCE,WHICH HOWEVER IS NOT LARGER 9437 1451 753 THAN THE SYSTEMATIC ERRORS ON THE EXPERIMENTAL DATA, COULD BE DUE 9437 1451 754 TO THE DIFFICULTIES OF IDENTIFYING THE WIDE J=0+ RESONANCES IN THE9437 1451 755 EXPERIMENTAL DATA, BECAUSE THE EFFECTS OF THE INCREASING 9437 1451 756 RESOLUTION AND DOPPLER WIDTHS. PRIOR TO THE SAMMY FITS, THE 9437 1451 757 FISSION DATA OF WESTON AND TODD (1988 HIGH RESOLUTION DATA) WERE 9437 1451 758 NORMALIZED TO THE ENDF/B-VI STANDARD IN THE ENERGY RANGE FROM 1 9437 1451 759 KEV TO 2 KEV. 9437 1451 760 THE CROSS SECTIONS,CALCULATED FROM THE RESONANCE PARAMETERS 9437 1451 761 AND AVERAGED OVER 0.1 KEV INTERVALS,ARE GIVEN IN THE FOLLOWING 9437 1451 762 TABLE: 9437 1451 763 9437 1451 764 ************************************************************** 9437 1451 765 CR0SS-SECTIONS(BARN) 9437 1451 766 ------------------------------------------ 9437 1451 767 TOTAL FISSION CAPTURE 9437 1451 768 ENERGY -------------- -------------- ------- 9437 1451 769 (KEV) CALC(A) EXP(B) CALC(A) EXP(C) CALC(A) 9437 1451 770 ************************************************************** 9437 1451 771 2.0-2.1 17.34 17.30 2.034 2.062 3.223 9437 1451 772 2.1-2.2 20.27 19.80 2.949 2.999 4.051 9437 1451 773 2.2-2.3 19.34 19.10 2.357 2.393 3.324 9437 1451 774 2.3-2.4 21.28 21.20 3.646 3.679 3.640 9437 1451 775 2.4-2.5 20.03 20.60 3.956 4.024 3.128 9437 1451 776 ************************************************************** 9437 1451 777 2.0-2.5 19.65 19.60 2.989 3.031 3.473 9437 1451 778 ************************************************************** 9437 1451 779 (A) TOTAL, FISSION AND CAPTURE CROSS SECTIONS CALCULATED BY 9437 1451 780 RESENDD, 1% ACCURACY, AT 300 K,FROM THE RESONANCE PARAME- 9437 1451 781 TERS. 9437 1451 782 (B) AVERAGE TOTAL CROSS SECTIONS OBTAINED FROM THE AVERAGE 9437 1451 783 EXPERIMENTAL EFFECTIVE CROSS SECTIONS IN REFERENCE/19/. 9437 1451 784 (C) 1988 HIGH RESOLUTION DATA OF WESTON AND TODD NORMALIZED 9437 1451 785 TO ENDF/B-VI STANDARD IN THE ENERGY RANGE FROM 1 KEV TO 9437 1451 786 2 KEV. 9437 1451 787 ***************************************************************** 9437 1451 788 9437 1451 789 9437 1451 790 ***************************************************************** 9437 1451 791 FISSION AND CAPTURE RESONANCE INTEGRALS 9437 1451 792 ***************************************************************** 9437 1451 793 9437 1451 794 THE FISSION AND CAPTURE RESONANCE INTEGRALS ARE COMPARED TO 9437 1451 795 JENDL-3 DATA IN THE FOLLOWING TABLE: 9437 1451 796 9437 1451 797 ********************************************************** 9437 1451 798 ENERGY RANGE(EV) FISSION(BARN) CAPTURE(BARN) 9437 1451 799 ********************************************************** 9437 1451 800 JENDL-3 PRESENT JENDL-3 PRESENT 9437 1451 801 0.5 - 5.0 85.725 84.879 28.651 28.723 9437 1451 802 5.0 - 10.0 25.081 25.147 19.059 18.950 9437 1451 803 10.0 - 50.0 96.856 99.715 77.181 74.686 9437 1451 804 50.0 - 100.0 40.479 41.552 25.930 25.376 9437 1451 805 100.0 - 301.0 19.677 20.252 17.952 17.729 9437 1451 806 301.0 -1000.0 10.047 10.317 8.348 8.418 9437 1451 807 1000.0 -2000.0 3.484 3.206 2.840 2.634 9437 1451 808 2000.0 -2.E+07 17.783 (17.783) 5.224 (5.224) 9437 1451 809 ********************************************************** 9437 1451 810 TOTAL 299.132 302.851 185.185 181.739 9437 1451 811 ********************************************************** 9437 1451 812 9437 1451 813 THE JENDL-3 RESONANCE PARAMETERS ARE THOSE OBTAINED IN 1987 IN 9437 1451 814 THE ENERGY RANGE 0 KEV TO 1 KEV. THEY ARE SLIGTHLY DIFFERENT FROM 9437 1451 815 THOSE PUBLISHED IN 1989. THAT EXPLAINS THE SMALL DIFFERENCES OB- 9437 1451 816 SERVED BETWEEN JENDL-3 AND THE PRESENT RESULTS IN THIS ENERGY RAN-9437 1451 817 GE. IN THE ENERGY RANGE 1 KEV TO 2 KEV JENDL-3 IS UNRESOLVED 9437 1451 818 RANGE. THE FISSION AND CAPTURE RESONANCE INTEGRALS CALCULATED 9437 1451 819 FROM ENDF/B-V AND THOSE FOUND IN BNL-325 ARE THE FOLLOWING: 9437 1451 820 9437 1451 821 ENDF/B-V FISSION: 302.13 B CAPTURE: 194.10 B 9437 1451 822 BNL-325 FISSION: 310+-10 B CAPTURE: 200+-20 B 9437 1451 823 9437 1451 824 THE CONSEQUENCE OF CHANGING FROM THE OLD SETS OF RESONANCE 9437 1451 825 PARAMETERS(ENDF/B-V AND PREVIOUS SETS) TO THE NEW SET IS THAT 9437 1451 826 THE CAPTURE RESONANCE INTEGRAL WILL DECREASE BY 6.7% COMPARED 9437 1451 827 WITH ENDF/B-V VALUE. 9437 1451 828 9437 1451 829 REFERENCES OF APPENDIX 9437 1451 830 1) R.GWIN ET AL.,NUCL.SCI.ENG.,45,25(1971) 9437 1451 831 2) R.GWIN ET AL.,NUCL.SCI.ENG.,59,79(1976) 9437 1451 832 3) R.GWIN ET AL.,NUCL.SCI.ENG.,61,116(1976) 9437 1451 833 4) R.GWIN ET AL.,NUCL.SCI.ENG.,88,37(1984) 9437 1451 834 5) J.BLONS, NUCL.SCI.ENG.,51,130(1973) 9437 1451 835 6) L.W.WESTON ET AL.,NUCL.SCI.ENG.88,567(1984) 9437 1451 836 7) L.W.WESTON ET AL.,TO BE PUBLISHED(HIGH RESOLUTION 1988 DATA) 9437 1451 837 8) R.R.SPENCER ET AL.,NUCL.SCI.ENG.,96,318(1987) 9437 1451 838 9) J.A.HARVEY ,MITO 1988,PAGE 115 9437 1451 839 10) A.CARLSON ET AL.,PRELIMINARY RESULTS OF THE ENDF/B-6 STANDARD 9437 1451 840 EVALUATION(SEPT 8 1987) 9437 1451 841 11) H.DERRIEN AND G. DE SAUSSURE,ORNL-TM-10986(1988) 9437 1451 842 12) H.DERRIEN ET AL.,NUCL.SCI.ENG.,106,434(1990) 9437 1451 843 13) H.DERRIEN, J.NUCL>SCI.TECHNOL.,30,845(1993). 9437 1451 844 14) N.M.LARSON ET AL.,ORNL/TM-7485,ORNL/TM-9179,ORNL/TM-9719/R1 9437 1451 845 15) L.LEAL AND R.N.HWANG,TRANS.AM.NUC.SOC.,55,340(1987) 9437 1451 846 16) T.NAKAGAWA,RESENDD A JAERI VERSION OF RESEND,JAER=-M 84-192 9437 1451 847 (1984). 9437 1451 848 17) C.WAGEMANS ET AL.,MITO 1988,PAGE 91 9437 1451 849 18) L.W.WESTON,PRIVATE COMMUNICATION(1992) 9437 1451 850 19) H.DERRIEN,J.NUCL.SCI.TECHNOL.,29,794(1992). 9437 1451 851 9437 1451 852 ***************** Program LINEAR (VERSION 2000-1) ***************9437 1451 853 For All Data Greater than 1.00000-10 barns in Absolute Value 9437 1451 854 Data Linearized to Within an Accuracy of 0.10000000 per-cent 9437 1451 855 ***************** Program RECENT (VERSION 2000-1) ***************9437 1451 856 for All Data Greater than 1.00000-10 barns in Absolute Value 9437 1451 857 Data Linearized to within an Accuracy of 0.10000000 per-cent 9437 1451 858 ***************** Program LINEAR (VERSION 2000-1) ***************9437 1451 859 For All Data Greater than 1.00000-10 barns in Absolute Value 9437 1451 860 Data Linearized to Within an Accuracy of 0.10000000 per-cent 9437 1451 861 1 451 1010 49437 1451 862 1 452 11 19437 1451 863 1 455 8 49437 1451 864 1 456 11 19437 1451 865 2 151 1220 49437 1451 866 3 1 34314 49437 1451 867 3 2 25256 49437 1451 868 3 4 34 19437 1451 869 3 16 9 19437 1451 870 3 17 6 19437 1451 871 3 18 47116 49437 1451 872 3 37 4 19437 1451 873 3 51 29 19437 1451 874 3 52 29 19437 1451 875 3 53 28 19437 1451 876 3 54 30 19437 1451 877 3 55 32 19437 1451 878 3 56 50 19437 1451 879 3 57 36 19437 1451 880 3 58 47 19437 1451 881 3 59 34 19437 1451 882 3 60 47 19437 1451 883 3 61 47 19437 1451 884 3 62 44 19437 1451 885 3 63 45 19437 1451 886 3 64 46 19437 1451 887 3 65 47 19437 1451 888 3 66 47 19437 1451 889 3 67 45 19437 1451 890 3 68 43 19437 1451 891 3 91 32 19437 1451 892 3 102 65252 49437 1451 893 4 2 199 19437 1451 894 4 16 10 19437 1451 895 4 17 10 19437 1451 896 4 18 10 19437 1451 897 4 37 10 19437 1451 898 4 51 57 19437 1451 899 4 52 57 19437 1451 900 4 53 57 19437 1451 901 4 54 57 19437 1451 902 4 55 57 19437 1451 903 4 56 30 19437 1451 904 4 57 57 19437 1451 905 4 58 30 19437 1451 906 4 59 57 19437 1451 907 4 60 30 19437 1451 908 4 61 30 19437 1451 909 4 62 30 19437 1451 910 4 63 30 19437 1451 911 4 64 30 19437 1451 912 4 65 30 19437 1451 913 4 66 30 19437 1451 914 4 67 28 19437 1451 915 4 68 28 19437 1451 916 4 91 28 19437 1451 917 5 16 174 49437 1451 918 5 17 60 49437 1451 919 5 18 551 49437 1451 920 5 37 16 49437 1451 921 5 91 312 49437 1451 922 5 455 585 49437 1451 923 12 16 9 19437 1451 924 12 17 7 19437 1451 925 12 18 11 19437 1451 926 12 37 5 19437 1451 927 12 51 3 19437 1451 928 12 52 3 19437 1451 929 12 53 3 19437 1451 930 12 54 3 19437 1451 931 12 55 3 19437 1451 932 12 56 4 19437 1451 933 12 57 3 19437 1451 934 12 58 5 19437 1451 935 12 59 3 19437 1451 936 12 60 4 19437 1451 937 12 61 4 19437 1451 938 12 62 3 19437 1451 939 12 63 3 19437 1451 940 12 64 3 19437 1451 941 12 65 3 19437 1451 942 12 66 4 19437 1451 943 12 67 4 19437 1451 944 12 68 5 19437 1451 945 12 91 10 19437 1451 946 12 102 11 19437 1451 947 14 16 1 19437 1451 948 14 17 1 19437 1451 949 14 18 1 19437 1451 950 14 37 1 19437 1451 951 14 51 1 19437 1451 952 14 52 1 19437 1451 953 14 53 1 19437 1451 954 14 54 1 19437 1451 955 14 55 1 19437 1451 956 14 56 1 19437 1451 957 14 57 1 19437 1451 958 14 58 1 19437 1451 959 14 59 1 19437 1451 960 14 60 1 19437 1451 961 14 61 1 19437 1451 962 14 62 1 19437 1451 963 14 63 1 19437 1451 964 14 64 1 19437 1451 965 14 65 1 19437 1451 966 14 66 1 19437 1451 967 14 67 1 19437 1451 968 14 68 1 19437 1451 969 14 91 1 19437 1451 970 14 102 1 19437 1451 971 15 16 124 19437 1451 972 15 17 52 19437 1451 973 15 18 213 19437 1451 974 15 37 16 19437 1451 975 15 91 202 19437 1451 976 15 102 307 19437 1451 977 31 452 5 49437 1451 978 31 455 13 49437 1451 979 31 456 91 49437 1451 980 32 151 53594 49437 1451 981 33 1 66 49437 1451 982 33 2 15 49437 1451 983 33 4 13 49437 1451 984 33 16 16 49437 1451 985 33 17 8 49437 1451 986 33 18 1006 49437 1451 987 33 37 6 49437 1451 988 33 51 53 49437 1451 989 33 52 42 49437 1451 990 33 53 38 49437 1451 991 33 54 32 49437 1451 992 33 55 32 49437 1451 993 33 56 29 49437 1451 994 33 57 29 49437 1451 995 33 58 29 49437 1451 996 33 59 29 49437 1451 997 33 60 29 49437 1451 998 33 61 29 49437 1451 999 33 62 26 49437 1451 1000 33 63 26 49437 1451 1001 33 64 26 49437 1451 1002 33 65 26 49437 1451 1003 33 66 26 49437 1451 1004 33 67 26 49437 1451 1005 33 68 26 49437 1451 1006 33 91 26 49437 1451 1007 33 102 58 49437 1451 1008 34 2 77 49437 1451 1009 35 18 13537 49437 1451 1010 9437 1 099999 9.423900+4 2.369990+2 0 2 0 09437 1452 1 0.000000+0 0.000000+0 0 0 1 249437 1452 2 24 2 0 0 0 09437 1452 3 1.000000-5 2.884320+0 2.530000-2 2.884320+0 5.000000-2 2.884320+09437 1452 4 1.500000-1 2.868120+0 2.500000-1 2.863720+0 7.000000-1 2.872120+09437 1452 5 2.000000+1 2.872120+0 4.000000+1 2.835520+0 4.800000+1 2.838020+09437 1452 6 5.800000+1 2.890220+0 9.600000+1 2.872120+0 1.050000+2 2.826320+09437 1452 7 1.250000+2 2.887220+0 2.000000+2 2.887220+0 3.200000+2 2.858120+09437 1452 8 4.500000+2 2.888220+0 5.000000+2 2.888220+0 5.000000+2 2.915220+09437 1452 9 1.000000+5 2.915230+0 1.000000+5 2.887230+0 1.500000+6 3.076400+09437 1452 10 1.150000+7 4.600710+0 1.960000+7 5.657170+0 2.000000+7 5.693170+09437 1452 11 9437 1 099999 9.423900+4 2.369990+2 0 2 0 09437 1455 1 0.000000+0 0.000000+0 0 0 6 09437 1455 2 1.277000-2 3.014000-2 1.238000-1 3.254000-1 1.122000+0 2.697000+09437 1455 3 0.000000+0 0.000000+0 0 0 1 79437 1455 4 7 2 0 0 0 09437 1455 5 1.000000-5 6.220000-3 2.530000-2 6.220000-3 3.000000+6 6.590000-39437 1455 6 7.000000+6 4.800000-3 1.100000+7 4.800000-3 1.450000+7 4.170000-39437 1455 7 2.000000+7 4.170000-3 9437 1455 8 9437 1 099999 9.423900+4 2.369990+2 0 2 0 09437 1456 1 0.000000+0 0.000000+0 0 0 1 249437 1456 2 24 2 0 0 0 09437 1456 3 1.000000-5 2.878100+0 2.530000-2 2.878100+0 5.000000-2 2.878100+09437 1456 4 1.500000-1 2.861900+0 2.500000-1 2.857500+0 7.000000-1 2.865900+09437 1456 5 2.000000+1 2.865900+0 4.000000+1 2.829300+0 4.800000+1 2.831800+09437 1456 6 5.800000+1 2.884000+0 9.600000+1 2.865900+0 1.050000+2 2.820100+09437 1456 7 1.250000+2 2.881000+0 2.000000+2 2.881000+0 3.200000+2 2.851900+09437 1456 8 4.500000+2 2.882000+0 5.000000+2 2.882000+0 5.000000+2 2.909000+09437 1456 9 1.000000+5 2.909000+0 1.000000+5 2.881000+0 1.500000+6 3.070000+09437 1456 10 1.150000+7 4.596000+0 1.960000+7 5.653000+0 2.000000+7 5.689000+09437 1456 11 9437 1 099999 9437 0 0 0 9.423900+4 2.369990+2 0 0 1 09437 2151 1 9.423900+4 1.000000+0 0 1 4 09437 2151 2 1.000000-5 1.000000+3 1 3 0 09437 2151 3 5.000000-1 9.410000-1 0 0 1 19437 2151 4 2.369990+2 0.000000+0 0 0 2430 4059437 2151 5 -1.500200+2 1.000000+0 4.289000-1 4.572000-2 1.905000-1 0.000000+09437 2151 6 -1.546700+1 1.000000+0 1.355000-4 2.685000-2-2.553000-6 0.000000+09437 2151 7 -6.908700+0 0.000000+0 1.236000-2 2.600000-1-9.417000-1 2.962000-19437 2151 8 -2.194400-1 0.000000+0 3.047000-5 2.591000-3-1.614000-3-5.825000-19437 2151 9 2.956240-1 1.000000+0 7.993000-5 3.930000-2 5.738000-2 0.000000+09437 2151 10 7.815800+0 1.000000+0 7.920000-4 3.775000-2-4.475000-2 0.000000+09437 2151 11 1.092800+1 1.000000+0 1.795000-3 3.612000-2-1.540000-1 0.000000+09437 2151 12 1.189800+1 1.000000+0 9.751000-4 3.796000-2 2.071000-2 0.000000+09437 2151 13 1.432900+1 1.000000+0 6.047000-4 2.921000-2 5.904000-2 0.000000+09437 2151 14 1.467800+1 1.000000+0 1.910000-3 3.916000-2 3.045000-2 0.000000+09437 2151 15 1.541700+1 0.000000+0 2.064000-3 4.200000-2-7.548000-6 7.550000-19437 2151 16 1.765700+1 1.000000+0 1.803000-3 3.824000-2-3.640000-2 0.000000+09437 2151 17 2.226600+1 1.000000+0 2.588000-3 4.158000-2-6.299000-2 0.000000+09437 2151 18 2.393300+1 1.000000+0 8.572000-5 3.534000-2 2.588000-2 0.000000+09437 2151 19 2.626900+1 1.000000+0 1.543000-3 3.904000-2 4.112000-2 0.000000+09437 2151 20 2.728800+1 1.000000+0 1.493000-4 3.871000-2 2.788000-3 0.000000+09437 2151 21 3.232700+1 0.000000+0 8.705000-4 4.252000-2 8.171000-3-1.279000-19437 2151 22 3.548600+1 1.000000+0 2.698000-4 4.092000-2 3.547000-3 0.000000+09437 2151 23 4.145700+1 1.000000+0 3.304000-3 4.893000-2-6.409000-3 0.000000+09437 2151 24 4.173600+1 1.000000+0 9.350000-4 3.770000-2 6.103000-2 0.000000+09437 2151 25 4.453100+1 1.000000+0 6.132000-3 4.003000-2-4.373000-3 0.000000+09437 2151 26 4.753400+1 0.000000+0 4.839000-3 3.146000-2 4.815000-1-1.274000-79437 2151 27 4.957600+1 0.000000+0 4.276000-3 4.200000-2-1.049000+0 4.983000-39437 2151 28 5.014400+1 1.000000+0 3.254000-3 2.250000-2-4.996000-3 0.000000+09437 2151 29 5.264800+1 1.000000+0 9.460000-3 4.394000-2-9.045000-3 0.000000+09437 2151 30 5.570400+1 1.000000+0 1.508000-3 3.756000-2 2.427000-2 0.000000+09437 2151 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2178.60962 1.426854+1 2178.61329 1.473096+19437 3 129989 2178.61696 1.523590+1 2178.62062 1.578792+1 2178.62429 1.639217+19437 3 129990 2178.62796 1.705446+1 2178.63163 1.778137+1 2178.63529 1.858037+19437 3 129991 2178.63896 1.945999+1 2178.64263 2.042992+1 2178.64630 2.150127+19437 3 129992 2178.64997 2.268676+1 2178.65363 2.400103+1 2178.65730 2.546092+19437 3 129993 2178.66097 2.708590+1 2178.66464 2.889847+1 2178.66831 3.092478+19437 3 129994 2178.67014 3.202738+1 2178.67381 3.443276+1 2178.67564 3.574506+19437 3 129995 2178.67747 3.713743+1 2178.67931 3.861566+1 2178.68114 4.018599+19437 3 129996 2178.68298 4.185517+1 2178.68481 4.363050+1 2178.68664 4.551986+19437 3 129997 2178.68848 4.753179+1 2178.69031 4.967547+1 2178.69215 5.196084+19437 3 129998 2178.69398 5.439861+1 2178.69581 5.700031+1 2178.69765 5.977836+19437 3 129999 2178.69948 6.274605+1 2178.70132 6.591767+1 2178.70315 6.930843+19437 3 130000 2178.70498 7.293454+1 2178.70682 7.681317+1 2178.70865 8.096242+19437 3 130001 2178.71048 8.540120+1 2178.71232 9.014917+1 2178.71415 9.522649+19437 3 130002 2178.71599 1.006536+2 2178.71782 1.064507+2 2178.71965 1.126375+29437 3 130003 2178.72149 1.192324+2 2178.72332 1.262518+2 2178.72516 1.337089+29437 3 130004 2178.72699 1.416125+2 2178.72882 1.499660+2 2178.73066 1.587647+29437 3 130005 2178.73249 1.679947+2 2178.73433 1.776304+2 2178.73799 1.979443+29437 3 130006 2178.74716 2.508578+2 2178.74900 2.607741+2 2178.75083 2.700792+29437 3 130007 2178.75266 2.785905+2 2178.75450 2.861308+2 2178.75633 2.925375+29437 3 130008 2178.75817 2.976724+2 2178.76000 3.014298+2 2178.76183 3.037434+29437 3 130009 2178.76367 3.045893+2 2178.76550 3.039877+2 2178.76734 3.019993+29437 3 130010 2178.76917 2.987208+2 2178.77100 2.942772+2 2178.77284 2.888136+29437 3 130011 2178.77467 2.824863+2 2178.77651 2.754552+2 2178.78017 2.598969+29437 3 130012 2178.78934 2.181492+2 2178.79301 2.021450+2 2178.79668 1.871195+29437 3 130013 2178.80035 1.732282+2 2178.80401 1.605196+2 2178.80768 1.489738+29437 3 130014 2178.81135 1.385302+2 2178.81318 1.336965+2 2178.81685 1.247494+29437 3 130015 2178.82052 1.166861+2 2178.82419 1.094168+2 2178.82785 1.028569+29437 3 130016 2178.83152 9.692886+1 2178.83519 9.156253+1 2178.83886 8.669529+19437 3 130017 2178.84069 8.443119+1 2178.84436 8.021042+1 2178.84803 7.636176+19437 3 130018 2178.85170 7.284469+1 2178.85536 6.962357+1 2178.85903 6.666708+19437 3 130019 2178.86270 6.394767+1 2178.86637 6.144110+1 2178.87003 5.912601+19437 3 130020 2178.87370 5.698352+1 2178.87737 5.499697+1 2178.88104 5.315158+19437 3 130021 2178.88471 5.143425+1 2178.88837 4.983330+1 2178.89204 4.833837+19437 3 130022 2178.89938 4.563042+1 2178.90671 4.324725+1 2178.91405 4.113795+19437 3 130023 2178.92138 3.926116+1 2178.92872 3.758302+1 2178.93605 3.607563+19437 3 130024 2178.94706 3.408511+1 2178.95806 3.236471+1 2178.96540 3.134340+19437 3 130025 2178.97273 3.040867+1 2178.98007 2.955056+1 2178.98740 2.876051+19437 3 130026 2179.00207 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1927 164.621181 1.784544+2 164.623199 1.868007+2 164.625218 1.956469+29437 3 2 1928 164.627236 2.050289+2 164.629255 2.149852+2 164.631274 2.255574+29437 3 2 1929 164.633292 2.367901+2 164.635311 2.487317+2 164.637330 2.614337+29437 3 2 1930 164.639348 2.749520+2 164.641367 2.893460+2 164.643385 3.046795+29437 3 2 1931 164.645404 3.210205+2 164.647423 3.384415+2 164.649441 3.570189+29437 3 2 1932 164.651460 3.768336+2 164.653479 3.979702+2 164.655497 4.205166+29437 3 2 1933 164.657516 4.445633+2 164.659534 4.702023+2 164.661553 4.975259+29437 3 2 1934 164.663572 5.266242+2 164.665590 5.575829+2 164.667609 5.904800+29437 3 2 1935 164.669628 6.253816+2 164.671646 6.623367+2 164.673665 7.013713+29437 3 2 1936 164.675683 7.424809+2 164.677702 7.856220+2 164.679721 8.307027+29437 3 2 1937 164.681739 8.775724+2 164.685777 9.757186+2 164.693851 1.178006+39437 3 2 1938 164.697888 1.272119+3 164.699907 1.314601+3 164.701926 1.352864+39437 3 2 1939 164.703944 1.386066+3 164.705963 1.413449+3 164.707981 1.434386+39437 3 2 1940 164.710000 1.448414+3 164.712019 1.455270+3 164.714037 1.454903+39437 3 2 1941 164.716056 1.447475+3 164.718075 1.433345+3 164.720093 1.413043+39437 3 2 1942 164.722112 1.387229+3 164.724130 1.356652+3 164.726149 1.322106+39437 3 2 1943 164.730186 1.244291+3 164.742298 9.887078+2 164.746335 9.082064+29437 3 2 1944 164.750373 8.332011+2 164.754410 7.643129+2 164.756428 7.322132+29437 3 2 1945 164.758447 7.016581+2 164.760466 6.726139+2 164.762484 6.450364+29437 3 2 1946 164.764503 6.188735+2 164.766522 5.940679+2 164.768540 5.705591+29437 3 2 1947 164.770559 5.482851+2 164.772577 5.271835+2 164.774596 5.071927+29437 3 2 1948 164.776615 4.882523+2 164.778633 4.703036+2 164.782671 4.371585+29437 3 2 1949 164.786708 4.073361+2 164.790745 3.804568+2 164.794782 3.561821+29437 3 2 1950 164.798820 3.342130+2 164.802857 3.142861+2 164.806894 2.961706+29437 3 2 1951 164.810931 2.796639+2 164.814969 2.645891+2 164.819006 2.507908+29437 3 2 1952 164.823043 2.381331+2 164.827080 2.264968+2 164.831118 2.157770+29437 3 2 1953 164.835155 2.058813+2 164.839192 1.967285+2 164.843229 1.882465+29437 3 2 1954 164.847267 1.803718+2 164.851304 1.730479+2 164.855341 1.662246+29437 3 2 1955 164.859378 1.598571+2 164.863416 1.539056+2 164.867453 1.483343+29437 3 2 1956 164.871490 1.431111+2 164.875527 1.382074+2 164.879565 1.335973+29437 3 2 1957 164.887639 1.251668+2 164.895714 1.176586+2 164.903788 1.109404+29437 3 2 1958 164.911863 1.049029+2 164.919937 9.945478+1 164.928012 9.451991+19437 3 2 1959 164.936086 9.003393+1 164.944161 8.594236+1 164.952235 8.219879+19437 3 2 1960 164.960310 7.876349+1 164.968384 7.560231+1 164.976459 7.268573+19437 3 2 1961 164.984533 6.998816+1 164.992608 6.748729+1 165.000682 6.516365+19437 3 2 1962 165.008757 6.300012+1 165.016831 6.098165+1 165.024906 5.909494+19437 3 2 1963 165.041055 5.567096+1 165.057204 5.264864+1 165.073353 4.996445+19437 3 2 1964 165.089502 4.756720+1 165.105651 4.541518+1 165.121800 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