20-Ca- 48 ENDF/B-VII.0 Processed by Red Cullen using PREPRO2007. 1 0 0 0 20048.0000 47.5406000 2 0 0 12049 1451 1 0.0 0.0 0 0 0 62049 1451 2 1.00000000 200000000. 1 0 10 72049 1451 3 1200000.00 0.0 1 0 610 1142049 1451 4 20-Ca- 48 NRG EVAL-OCT04 A.J. Koning 2049 1451 5 DIST-DEC06 REV1-MAY05 20050504 2049 1451 6 ----ENDF/B-VII MATERIAL 2049 REVISION 1 2049 1451 7 -----INCIDENT NEUTRON DATA 2049 1451 8 ------ENDF-6 FORMAT 2049 1451 9 ***************************** ENDF/B-VII *************************2049 1451 10 ** **2049 1451 11 ** Original data taken from: JEFF-3.1 **2049 1451 12 ** **2049 1451 13 ******************************************************************2049 1451 14 ***************************** JEFF-3.1 *************************2049 1451 15 ** **2049 1451 16 ** Original data taken from: New evaluation **2049 1451 17 ** **2049 1451 18 ******************************************************************2049 1451 19 2049 1451 20 NRG-2004: n + Ca-48 2049 1451 21 2049 1451 22 Author: A.J. Koning, NRG Petten 2049 1451 23 2049 1451 24 ************** G E N E R A L I N F O R M A T I O N *************2049 1451 25 2049 1451 26 This evaluated data file is based primarily on a theoretical 2049 1451 27 analysis with the nuclear model code TALYS [kon04], version 0.56. 2049 1451 28 The nuclear model parameters of TALYS have been adjusted to 2049 1451 29 reproduce the existing experimental data. The resulting data file 2049 1451 30 provides a complete representation of nuclear data needed for 2049 1451 31 transport, damage, heating, radioactivity, and shielding 2049 1451 32 applications over the incident neutron energy range from 2049 1451 33 1.0E-11 to 200 MeV. 2049 1451 34 2049 1451 35 This file is part of a larger collection of isotopic evaluations, 2049 1451 36 all created by running TALYS with input parameters that do not or 2049 1451 37 slightly deviate from the default values. The mutual quality of 2049 1451 38 these isotopic evaluations is thus relatively consistent. 2049 1451 39 The same set of nuclear models is used and, equally important, 2049 1451 40 the same ENDF-6 formatting procedures for each isotope. We have 2049 1451 41 intended to make this evaluation complete in its description of 2049 1451 42 reaction channels, and use a compact method to store the data. 2049 1451 43 2049 1451 44 For certain reactions and energy ranges TALYS may not be used. 2049 1451 45 This is the case when TALYS is not appropriate, such as for the 2049 1451 46 description of resonances, or when the directly available 2049 1451 47 experimental data is of better quality, as for e.g. low-energy 2049 1451 48 total cross sections. In these cases, we have adopted the best 2049 1451 49 possible data from an existing library, or directly from unfiled 2049 1451 50 experimental data. All transport data for particles, photons and 2049 1451 51 residual nuclides are filed using a combination of MF1,2,3,4 and 2049 1451 52 MF6. This includes cross sections, angular distributions, 2049 1451 53 double-differential spectra, discrete and continuum photon 2049 1451 54 production cross sections, and residual production (activation) 2049 1451 55 cross sections. Moreover, isomeric production data are stored in 2049 1451 56 MF8 and MF10. This evaluation can thus be used as both transport 2049 1451 57 and activation library. The data file has been created 2049 1451 58 automatically using the ENDF-6 format generator TEFAL. 2049 1451 59 2049 1451 60 ##### ORIGIN 2049 1451 61 2049 1451 62 Data < 200 MeV : New evaluation NRG Petten 2049 1451 63 2049 1451 64 Resonance parameters (MF2/MT151): JENDL-3.3 for E < 500 keV 2049 1451 65 All other data : Produced with TALYS code 2049 1451 66 2049 1451 67 *************************** T H E O R Y **************************2049 1451 68 2049 1451 69 TALYS is a computer code system for the prediction and analysis 2049 1451 70 of nuclear reactions. TALYS simulates reactions that involve 2049 1451 71 neutrons, gamma-rays, protons, deuterons, tritons, helions and 2049 1451 72 alpha-particles, in the 1 keV - 200 MeV energy range and for 2049 1451 73 target nuclides of mass 12 and heavier. This is achieved by 2049 1451 74 implementing a suite of nuclear reaction models into a single 2049 1451 75 code system. It enables to evaluate nuclear reactions from 2049 1451 76 the unresolved resonance region up to intermediate energies. This 2049 1451 77 evaluation is based on a theoretical analysis that utilizes the 2049 1451 78 optical model, compound nucleus statistical theory, direct 2049 1451 79 reactions and pre-equilibrium processes, in combination with 2049 1451 80 databases and models for nuclear structure. For Ca-48, the 2049 1451 81 following output of TALYS is stored in this data file: 2049 1451 82 2049 1451 83 - Total, elastic and non-elastic cross sections 2049 1451 84 - Elastic scattering angular distributions 2049 1451 85 - Inelastic cross sections to discrete states 2049 1451 86 - Inelastic scattering angular distributions to discrete states 2049 1451 87 - Exclusive channel cross sections, e.g. (n,g), (n,2n), (n,np),.. 2049 1451 88 - Exclusive channel energy spectra 2049 1451 89 - Exclusive channel double-differential spectra 2049 1451 90 - Exclusive gamma production for discrete states and continuum 2049 1451 91 - Isomeric and ground state cross sections 2049 1451 92 - Residual production cross sections 2049 1451 93 - Total particle cross sections, e.g. (n,xn), (n,xp),.. 2049 1451 94 - Total particle energy spectra 2049 1451 95 - Total particle double-differential spectra 2049 1451 96 2049 1451 97 Here follows a short description of the used nuclear models: 2049 1451 98 2049 1451 99 ##### OPTICAL MODEL 2049 1451 100 2049 1451 101 All optical model calculations are performed by ECIS-97 [ray94], 2049 1451 102 in TALYS used as a subroutine. The default optical model 2049 1451 103 potentials (OMP) used are the local and global parameterizations 2049 1451 104 of Koning and Delaroche [kon03]. These are phenomenological OMPs 2049 1451 105 for neutrons and protons which in principle are valid over the 2049 1451 106 1 keV - 200 MeV energy range, though the low energy boundary of 2049 1451 107 validity may differ from nucleus to nucleus (e.g. for the total 2049 1451 108 cross sections, experimental data are included directly in the 2049 1451 109 file for energies below that boundary). Solving the Schroedinger 2049 1451 110 equation with this OMP yields the total cross section, the 2049 1451 111 shape-elastic cross section, the shape-elastic angular 2049 1451 112 distribution, the wave functions for the direct reaction cross 2049 1451 113 sections (see below), the transmission coefficients for the 2049 1451 114 compound nucleus model (see below) and the reaction cross 2049 1451 115 sections for the pre-equilibrium model (see below). 2049 1451 116 For neutrons and protons, the used parameterization is given in 2049 1451 117 Eq. (7) of [kon03]. 2049 1451 118 To calculate the transmission coefficients and reaction cross 2049 1451 119 sections for deuterons, tritons, helions and alpha particles, we 2049 1451 120 use OMPs that are directly derived from our nucleon potentials 2049 1451 121 using Watanabe's folding approach [mad88]. 2049 1451 122 2049 1451 123 ##### DIRECT REACTIONS 2049 1451 124 2049 1451 125 The built-in ECIS-97 is used for coupled-channels or DWBA 2049 1451 126 calculations for rotational or vibrational (or a combination of 2049 1451 127 these) nuclides. For Ca-48, DWBA was used to compute the direct 2049 1451 128 cross sections to several low-lying discrete levels: 2049 1451 129 2049 1451 130 Level Energy Spin/Parity Deformation parameter delta_L 2049 1451 131 2049 1451 132 1 3.831720 2.0+ 0.106 2049 1451 133 4 4.506960 3.0- 0.230 2049 1451 134 + a few additional states with small deformation parameters. 2049 1451 135 2049 1451 136 In addition, a macroscopic, phenomenological model to describe 2049 1451 137 giant resonances in the inelastic channel is used. For each 2049 1451 138 multipolarity an energy weighted sum rule applies and a DWBA 2049 1451 139 calculation with ECIS-97 is performed for each giant resonance 2049 1451 140 state. The cross section is then spread over the continuum with a 2049 1451 141 Gaussian distribution. 2049 1451 142 2049 1451 143 ##### COMPOUND NUCLEUS 2049 1451 144 2049 1451 145 For binary compound nucleus reactions we use the model of 2049 1451 146 Moldauer [mol80], i.e. the Hauser-Feshbach model [hau52] 2049 1451 147 corrected for width fluctuations. The transmission coefficients 2049 1451 148 have been generated with the aforementioned OMPs and the full 2049 1451 149 j,l-dependence of the transmission coefficients in the 2049 1451 150 Hauser-Feshbach model is used. For each nucleus that can be 2049 1451 151 reached through a binary reaction, several discrete levels and a 2049 1451 152 continuum described by level densities are included 2049 1451 153 simultaneously as competing channels. 2049 1451 154 2049 1451 155 The compound nucleus angular distributions are calculated with 2049 1451 156 the Blatt-Biedenharn formalism [bla52], leading to compound 2049 1451 157 nucleus Legendre coefficients that are added to their direct 2049 1451 158 counterparts. For multiple compound emission, i.e. emitted 2049 1451 159 particles after the binary emission, we use the Hauser-Feshbach 2049 1451 160 model. Again, for each residual nucleus several discrete states 2049 1451 161 are included as well as a continuum described by level densities. 2049 1451 162 Multiple compound emission is continued until all reaction 2049 1451 163 channels are closed and the population distribution of all 2049 1451 164 residual nuclides is depleted, through gamma decay, until they 2049 1451 165 end up in the ground state or in an isomer. 2049 1451 166 2049 1451 167 For the level density, we take the composite formula proposed by 2049 1451 168 Gilbert and Cameron [gil65], consisting of a constant temperature 2049 1451 169 law at low energies and a Fermi gas expression at high energies. 2049 1451 170 For the level density parameter a we use the energy dependent 2049 1451 171 expression proposed by Ignatyuk [ign75] to take into account the 2049 1451 172 damping of shell effects at high excitation energy. We have 2049 1451 173 obtained the parameters for the Ignatyuk formula from a 2049 1451 174 simultaneous fit to all experimental D_0 values as present in the 2049 1451 175 RIPL library. If necessary, we adjust individual parameters to 2049 1451 176 obtain a better fit to experiment. 2049 1451 177 2049 1451 178 Gamma-ray transmission coefficients are generated with the 2049 1451 179 Kopecky-Uhl generalized Lorentzian for strength 2049 1451 180 functions [kop90], with giant dipole resonance parameters taken 2049 1451 181 from the RIPL library [rip98], and normalized with experimental 2049 1451 182 radiative widths [gar84]. 2049 1451 183 2049 1451 184 ##### PRE-EQUILIBRIUM REACTIONS 2049 1451 185 2049 1451 186 For pre-equilibrium reactions, which become important for 2049 1451 187 incident energies above about 10 MeV, we use the two-component 2049 1451 188 exciton model [kon04b], in which the neutron or proton types of 2049 1451 189 particles and holes are followed throughout the reaction. For 2049 1451 190 energies above 20 MeV, multiple pre-equilibrium emission up to 2049 1451 191 any order of particle emission was included in the calculations. 2049 1451 192 A parameterization for the squared matrix element is used that is 2049 1451 193 valid for the whole energy range of this evaluation. 2049 1451 194 2049 1451 195 For deuterons, tritons, helions and alpha-particles, an extra 2049 1451 196 contribution was added from the pick/up and knock-out reaction 2049 1451 197 model by Kalbach [kal01]. 2049 1451 198 2049 1451 199 For photons, the model of Akkermans and Gruppelaar [akk85] was 2049 1451 200 applied, to simulate the direct and semi-direct capture 2049 1451 201 processes. 2049 1451 202 2049 1451 203 The angular distribution systematics by Kalbach [kal88] were used 2049 1451 204 to describe the angular distributions for all continuum 2049 1451 205 particles. An isotopic distribution for photons was adopted. 2049 1451 206 2049 1451 207 ****** C O M P A R I S O N W I T H E X P E R I M E N T *****2049 1451 208 2049 1451 209 This evaluation was performed simultaneously with other adjacent 2049 1451 210 isotopes, both for incident neutrons and protons. This enables, 2049 1451 211 when compared with a single-isotope effort, to put stronger 2049 1451 212 constraints on the produced calculated data, i.e. a globally 2049 1451 213 good comparison between TALYS and experimental data is requested 2049 1451 214 for all isotopes at the same time, while nucleus-specific input 2049 1451 215 (default or adjusted) parameters are consistently used for all 2049 1451 216 isotopes. Also, experimental data that is not available for the 2049 1451 217 isotope under study may be present, and tested, for adjacent 2049 1451 218 nuclides or for other projectiles. If these can be successfully 2049 1451 219 described by the models, a similar performance can be expected 2049 1451 220 for the present data file. 2049 1451 221 A few level density parameters for residual nuclides have been 2049 1451 222 adjusted to enforce agreement with the experimental data. The 2049 1451 223 changes in the level density parameters, a, were all kept within 2049 1451 224 10% of their default values. 2049 1451 225 2049 1451 226 ##### TOTAL AND REACTION CROSS SECTIONS AND ELASTIC SCATTERING 2049 1451 227 2049 1451 228 The spherical OMP was tested against experimental data for total 2049 1451 229 cross sections and elastic scattering angular distributions. 2049 1451 230 Consult [kon03] for the complete experimental database and for a 2049 1451 231 comparison of calculations and measurements over the whole energy 2049 1451 232 range for natural Ca. 2049 1451 233 2049 1451 234 ##### INELASTIC CROSS SECTIONS 2049 1451 235 2049 1451 236 For inelastic scattering to the levels 1-4, the calculations have 2049 1451 237 been tested against the available measurements [van92]. 2049 1451 238 Level 1 and 2 are very well described, whereas for levels 3 and 2049 1451 239 4 the peaks are underestimated by 35% and and 20% respectively. 2049 1451 240 Still, the total inelastic cross section is larger than the 2049 1451 241 other evaluable evaluation from JENDL-3.3. No further 2049 1451 242 renormalization was applied to describe the experiments. 2049 1451 243 2049 1451 244 ##### OTHER PARTIAL CROSS SECTIONS 2049 1451 245 2049 1451 246 - (n,gamma): 2049 1451 247 2049 1451 248 The calculated capture cross section is renormalized, by 2049 1451 249 overruling the default renormalization to the s-wave strength 2049 1451 250 function, to the available experimental data, all taken from the 2049 1451 251 EXFOR database. A normalization factor of 2.0 was used. The 2049 1451 252 pre-equilibrium gamma cross section was adjusted to the data by 2049 1451 253 multiplying the calculated result by a factor of 3.0. 2049 1451 254 2049 1451 255 - (n,2n): 2049 1451 256 2049 1451 257 Many experimental (n,2n) cross sections are available from EXFOR. 2049 1451 258 The present evaluation follows some of the higher single-energy 2049 1451 259 values of this collection. 2049 1451 260 2049 1451 261 - (n,a): 2049 1451 262 2049 1451 263 The two available experimental near-threshold (n,a) cross 2049 1451 264 sections [tir74,maj97] are underestimated. However, no further 2049 1451 265 action was taken since the values are around 1 mb. 2049 1451 266 2049 1451 267 2049 1451 268 ##### PARTICLE SPECTRA 2049 1451 269 2049 1451 270 For Ca-48, an adjustment of the default matrix element 2049 1451 271 parameterization of [kon04b] for pre-equilibrium reactions of a 2049 1451 272 factor of 0.7 was needed, to describe the aforementioned cross 2049 1451 273 sections and emission spectra for nuclides in this mass range. 2049 1451 274 For high-energy neutron and charged particle spectra, the average 2049 1451 275 quality is also determined by the pre-equilibrium model and its 2049 1451 276 global parameterization. No high-energy experiments are 2049 1451 277 available, though neutron induced reaction spectra between 28 and 2049 1451 278 63 MeV on Al [ben02], Si [ben02b] and Fe [sly03] have enabled us 2049 1451 279 to better constrain the results, through the aforementioned 2049 1451 280 matrix element, for particle yields and double-differential 2049 1451 281 spectra for all ejectiles up to alpha particles. 2049 1451 282 2049 1451 283 ***************** F I L E I N F O R M A T I O N ****************2049 1451 284 2049 1451 285 ##### MF1: GENERAL INFORMATION 2049 1451 286 2049 1451 287 - MT451 : Descriptive data and directory 2049 1451 288 2049 1451 289 This text and the full directory of used MF/MT sections. 2049 1451 290 2049 1451 291 ##### MF2: RESONANCE PARAMETERS 2049 1451 292 2049 1451 293 - MT151 : Resonance parameters 2049 1451 294 2049 1451 295 Resolved parameters for MLBW formula were adopted from JENDL-3.3. 2049 1451 296 They are given in the energy region from 1.0e-5 eV to 500 keV. 2049 1451 297 Parameters were taken from the recommended data of BNL [mug81] 2049 1451 298 and the data for a negative resonance were added so as to 2049 1451 299 reproduce the recommended thermal cross sections for capture and 2049 1451 300 scattering [mug81]. The scattering radius was assumed to be 2049 1451 301 3.6 fermi. Calculated 2200 m/sec cross sections and resonance 2049 1451 302 integrals are as follows: 2049 1451 303 2049 1451 304 2200 m/s cross section(b) res. integral(b) 2049 1451 305 elastic 3.717 2049 1451 306 capture 1.092 0.4859 2049 1451 307 total 4.809 2049 1451 308 2049 1451 309 ##### MF3: REACTION CROSS SECTIONS 2049 1451 310 2049 1451 311 Unless stated otherwise, all the data present in the following 2049 1451 312 MT-sections have been calculated with TALYS. If the maximal cross 2049 1451 313 section in an excitation function over the whole energy range 2049 1451 314 does not exceed 1.e-9 b, the MT-number is not included at all. 2049 1451 315 Cross sections lower than 1.e-20 b are assumed to have no 2049 1451 316 physical meaning and are set to zero. 2049 1451 317 2049 1451 318 - MT1 : Total cross section 2049 1451 319 2049 1451 320 Above 500 keV, calculations from the spherical OMP [kon03] were 2049 1451 321 used. 2049 1451 322 2049 1451 323 - MT2 : Elastic scattering cross section 2049 1451 324 2049 1451 325 Obtained by subtracting the non-elastic cross section from the 2049 1451 326 total cross section. Below 500 keV, resonance parameters are 2049 1451 327 used. 2049 1451 328 2049 1451 329 - MT3 : Non-elastic cross section 2049 1451 330 2049 1451 331 Calculated with the optical model over the whole energy range. 2049 1451 332 Below 500 keV, resonance parameters are used. 2049 1451 333 2049 1451 334 - MT4 : Total inelastic cross section 2049 1451 335 2049 1451 336 Sum of MT=51-91. 2049 1451 337 2049 1451 338 - MT5 : (n,anything) cross section 2049 1451 339 2049 1451 340 For energies below 20 MeV, MT5 contains the lumped (n,gamma x) 2049 1451 341 cross section, where x may represent neutron, proton, deuteron, 2049 1451 342 triton, Helium-3 or alpha. Using the relative yields of MF6/MT5, 2049 1451 343 the (n,gamma n), (n,gamma p), ..., (n,gamma alpha) can be 2049 1451 344 recovered. These cross sections are relatively small. However, 2049 1451 345 addition of these cross sections, which can not be stored in any 2049 1451 346 other MT-number, ensures that the partial cross sections add up 2049 1451 347 to the non-elastic cross section. Above 20 MeV, MT5 contains the 2049 1451 348 total non-elastic cross section, with which the information of 2049 1451 349 MF6/MT5 can be combined to obtain particle production cross 2049 1451 350 sections and (double-)differential cross sections. 2049 1451 351 2049 1451 352 - MT16 : (n,2n) cross section 2049 1451 353 - MT17 : (n,3n) cross section 2049 1451 354 - MT22 : (n,na) cross section 2049 1451 355 - MT28 : (n,np) cross section 2049 1451 356 - MT51-70 : (n,n') cross section for 1st-20th excited state 2049 1451 357 - MT91 : (n,n') continuum cross section 2049 1451 358 - MT102 : (n,gamma) cross section 2049 1451 359 2049 1451 360 Below 500 keV, resonance parameters are used. 2049 1451 361 2049 1451 362 - MT103 : (n,p) cross section 2049 1451 363 - MT104 : (n,d) cross section 2049 1451 364 - MT105 : (n,t) cross section 2049 1451 365 - MT106 : (n,h) cross section 2049 1451 366 - MT107 : (n,a) cross section 2049 1451 367 - MT600-604: (n,p) cross section for 0th-4th excited state 2049 1451 368 2049 1451 369 Obtained by mapping continuum (n,p) cross section from 2049 1451 370 pre-equilibrium and compound model on discrete states. 2049 1451 371 2049 1451 372 - MT649 : (n,p) continuum cross section 2049 1451 373 - MT650-655: (n,d) cross section for 0th-5th excited state 2049 1451 374 2049 1451 375 Obtained by mapping continuum (n,d) cross section from 2049 1451 376 pre-equilibrium and compound model on discrete states. 2049 1451 377 2049 1451 378 - MT699 : (n,d) continuum cross section 2049 1451 379 - MT700-705: (n,t) cross section for 0th-5th excited state 2049 1451 380 2049 1451 381 Obtained by mapping continuum (n,t) cross section from 2049 1451 382 pre-equilibrium and compound model on discrete states. 2049 1451 383 2049 1451 384 - MT749 : (n,t) continuum cross section 2049 1451 385 - MT800-803: (n,a) cross section for 0th-3rd excited state 2049 1451 386 2049 1451 387 Obtained by mapping continuum (n,a) cross section from 2049 1451 388 pre-equilibrium and compound model on discrete states. 2049 1451 389 2049 1451 390 - MT849 : (n,a) continuum cross section 2049 1451 391 2049 1451 392 ##### MF4: ANGULAR DISTRIBUTIONS OF SECONDARY PARTICLES 2049 1451 393 2049 1451 394 The versatility of MF6 for the storage of almost any secondary 2049 1451 395 distribution entails that we only use MF4 for the neutron elastic 2049 1451 396 scattering distribution. All data are generated with TALYS. 2049 1451 397 2049 1451 398 - MT2 : Elastic angular distribution 2049 1451 399 2049 1451 400 The flag LTT=3 is used to indicate a switch at 20 MeV from a 2049 1451 401 Legendre representation to a tabulated representation. For 2049 1451 402 incident energies below 20 MeV, the Legendre coefficients are 2049 1451 403 given on a sufficiently precise energy grid. They are a sum of 2049 1451 404 calculated Legendre coefficients for compound nucleus and 2049 1451 405 shape-elastic scattering. For incident energies above 20 MeV, 2049 1451 406 relative angular distributions are tabulated on an angular grid. 2049 1451 407 2049 1451 408 ##### MF6: PRODUCT ENERGY-ANGLE DISTRIBUTIONS 2049 1451 409 2049 1451 410 In MF6 we store all secondary energy, angle, and energy-angle 2049 1451 411 distributions, as well as all residual and discrete + continuum 2049 1451 412 photon production cross sections. We thus do not use MF12-15 for 2049 1451 413 the photon production that accompanies each reaction. All data 2049 1451 414 are generated with TALYS. 2049 1451 415 2049 1451 416 - MT5 : (n,anything) yields and energy-angle distributions 2049 1451 417 2049 1451 418 For energies below 20 MeV, MT5 contains the relative yields of 2049 1451 419 the (n,gamma x) reaction, where x may represent neutron, proton, 2049 1451 420 deuteron, triton, Helium-3 or alpha. Using the (n,gamma x) cross 2049 1451 421 section of MF3/MT3, the (n,gamma p), ..., (n,gamma alpha) cross 2049 1451 422 section can be recovered. For energies above 20 MeV, MT5 contains 2049 1451 423 the production yields of particles and residual products. It also 2049 1451 424 contains the secondary energy-angle distributions for all 2049 1451 425 particles and photons. First, the yields for neutrons are given 2049 1451 426 for the whole energy range. Next, on a secondary energy grid the 2049 1451 427 relative emission spectra are given together with the parameters 2049 1451 428 for the Kalbach systematics for angular distributions. Inelastic 2049 1451 429 scattering cross sections for discrete states have been broadened 2049 1451 430 and added to the continuum spectra. This procedure is repeated 2049 1451 431 for protons, deuterons, tritons, Helium-3, alpha particles and 2049 1451 432 photons. Finally, the residual production yields are given per 2049 1451 433 final product. All these yields and relative distributions can 2049 1451 434 be multiplied with the cross sections given in MF3/MT5 to get 2049 1451 435 the production cross sections and (double-)differential cross 2049 1451 436 sections. 2049 1451 437 2049 1451 438 - MT16 : (n,2n) energy-angle distr. and photon production 2049 1451 439 2049 1451 440 First, for each type of outgoing particle, the (trivial) integer 2049 1451 441 particle yields are given. Next, on a sufficiently dense incident 2049 1451 442 energy grid the secondary energy-angle distributions are 2049 1451 443 specified by means of the relative emission spectra and the 2049 1451 444 parameters for the Kalbach systematics for angular distributions. 2049 1451 445 Next, the photon yield is tabulated as a function of incident 2049 1451 446 energy. For each incident energy, the photon production is given 2049 1451 447 for all discrete gamma lines present in the final nucleus. A 2049 1451 448 continuum photon distribution is added to this. We assume 2049 1451 449 isotropy for all produced gamma rays. 2049 1451 450 2049 1451 451 For the following MT-numbers, the same procedure as for MT16 is 2049 1451 452 followed: 2049 1451 453 ----- 2049 1451 454 - MT17 : (n,3n) energy-angle distr. and photon production 2049 1451 455 - MT22 : (n,na) energy-angle distr. and photon production 2049 1451 456 - MT28 : (n,np) energy-angle distr. and photon production 2049 1451 457 - MT91 : (n,n') continuum energy-angle distr. and phot. prod. 2049 1451 458 - MT102 : (n,gamma) photon production 2049 1451 459 - MT649 : (n,p) continuum energy-angle distr. and photon prod. 2049 1451 460 - MT699 : (n,d) continuum energy-angle distr. and photon prod. 2049 1451 461 - MT749 : (n,t) continuum energy-angle distr. and photon prod. 2049 1451 462 - MT849 : (n,a) continuum energy-angle distr. and photon prod. 2049 1451 463 ----- 2049 1451 464 2049 1451 465 - MT51 : (n,n') angular distribution and photon production 2049 1451 466 for first excited state 2049 1451 467 2049 1451 468 The angular distribution for inelastic scattering to the first 2049 1451 469 inelastic state is given with Legendre coefficients up to 20 MeV. 2049 1451 470 Next, the exclusive yields for all the discrete gamma rays that 2049 1451 471 originate from this particular level are given. 2049 1451 472 2049 1451 473 For the following MT-numbers, the same procedure as for MT51 is 2049 1451 474 followed: 2049 1451 475 ----- 2049 1451 476 - MT52-70 : (n,n') angular distribution and photon production 2049 1451 477 for 2nd-20th excited state 2049 1451 478 - MT600-604: (n,p) angular distribution and photon production 2049 1451 479 for 0th-4th excited state 2049 1451 480 - MT650-655: (n,d) angular distribution and photon production 2049 1451 481 for 0th-5th excited state 2049 1451 482 - MT700-705: (n,t) angular distribution and photon production 2049 1451 483 for 0th-5th excited state 2049 1451 484 - MT800-803: (n,a) angular distribution and photon production 2049 1451 485 for 0th-3rd excited state 2049 1451 486 ----- 2049 1451 487 2049 1451 488 ***** F I L E C H E C K I N G A N D P R O C E S S I N G ****2049 1451 489 2049 1451 490 This file has been checked successfully by the BNL checking 2049 1451 491 codes CHECKR-6.12, FIZCON-6.12 and PSYCHE-6.12 [dun01] and has 2049 1451 492 been processed successfully into an MCNP library by the 2049 1451 493 processing code NJOY99.81 [mac00]. 2049 1451 494 2049 1451 495 *********************** R E F E R E N C E S **********************2049 1451 496 2049 1451 497 [akk85] J.M. Akkermans and H. Gruppelaar, Phys. Lett. 157B, 95 2049 1451 498 (1985). 2049 1451 499 [ben02] S. Benck, I. Slypen, J.-P. Meulders, V. Corcalciuc, and 2049 1451 500 M.B. Chadwick, Nucl. Sci. Eng. 140, 86 (2002). 2049 1451 501 [ben02b] S. Benck, I. Slypen, J.-P. Meulders, and V. Corcalciuc, 2049 1451 502 Nucl. Sci. Eng. 141, 1 (2002). 2049 1451 503 [ber03] O. Bersillon, Bruyeres-le-Chatel, private communication. 2049 1451 504 [bla52] J.M. Blatt and L.C. Biedenharn, Rev. Mod. Phys. 52, 725 2049 1451 505 (1952). 2049 1451 506 [dun01] C. Dunford, ENDF Utility Codes Release 6.12, (2001). 2049 1451 507 [gar84] D.G. Gardner, in Neutron Radiative Capture, OECD/NEA 2049 1451 508 Series on Neutron Physics and Nuclear Data in Science and 2049 1451 509 Technology, eds. A. Michaudon et al., p. 62 (1984). 2049 1451 510 [gil65] A. Gilbert and A.G.W. Cameron, Can. J. Phys. 43, 1446 2049 1451 511 (1965). 2049 1451 512 [hau52] W. Hauser and H. Feshbach, Phys. Rev. 87, 366 (1952). 2049 1451 513 [ign75] A.V. Ignatyuk, G.N. Smirenkin, and A.S. Tishin, Sov. J. 2049 1451 514 Nucl. Phys. 21, no. 3, 255 (1975). 2049 1451 515 [kal88] C. Kalbach, Phys. Rev. C37, 2350 (1988). 2049 1451 516 [kal01] C. Kalbach, PRECO-2000: Exciton model pre-equilibrium 2049 1451 517 code with direct reactions, Duke University 2001, 2049 1451 518 www.nndc.bnl.gov/nndcscr/model-codes/preco-2000/. 2049 1451 519 [kon03] A.J. Koning and J.P. Delaroche, Nucl. Phys. A713, 231 2049 1451 520 (2003). 2049 1451 521 [kon04] A.J. Koning, S. Hilaire and M.C. Duijvestijn, unpublished 2049 1451 522 (2004). 2049 1451 523 [kon04b] A.J. Koning and M.C. Duijvestijn, to be published 2049 1451 524 (2004). 2049 1451 525 [kop90] J. Kopecky and M. Uhl, Phys. Rev. C42, 1941 (1990). 2049 1451 526 [mac00] R.E. Macfarlane, NJOY99 - Code system for producing 2049 1451 527 pointwise and multigroup neutron and photon cross 2049 1451 528 sections from ENDF/B Data, RSIC PSR-480 (2000). 2049 1451 529 [mad88] D.G. Madland, in Proceedings of a Specialists' Meeting on 2049 1451 530 Preequilibrium Reactions, Semmering, Austria, 2049 1451 531 February 10-12 1988, (OECD, Paris 1988), p. 103. 2049 1451 532 [maj97] A.D. Majeddin, V. Semkova, R. Doczi, M. Buczko, J. Csikai 2049 1451 533 J. Csikai, priv. comm. to EXFOR (1997). 2049 1451 534 [mol80] P.A. Moldauer, Nucl. Phys. A344, 185 (1980). 2049 1451 535 [mug81] S.F. Mughabghab, M. Divadeenam, and. N.E. Holden, 2049 1451 536 Neutron Cross Sections, Vol. I, Neutron Resonance 2049 1451 537 Parameters and Thermal Cross Sections (Academic Press, 2049 1451 538 1981). 2049 1451 539 [ray94] J. Raynal, Notes on ECIS94, CEA Saclay Report 2049 1451 540 No. CEA-N-2772, 1994. 2049 1451 541 [rip98] Handbook for calculations of nuclear reaction data: 2049 1451 542 Reference Input Parameter Library, IAEA-TECDOC-1034 2049 1451 543 (1998). 2049 1451 544 [sly03] I. Slypen, N. Nica, A.J. Koning, E. Raeymackers, 2049 1451 545 S. Benck, J.P. Meulders, and V. Corcalciuc, 2049 1451 546 Journ. Phys. G, November 2003 (2003). 2049 1451 547 [tir74] K.G. Tirsell, L.G. Multhauf, S. Raman, Int. Conf. on 2049 1451 548 Nuclear Structure and Spectroscopy, Amsterdam, 2049 1451 549 9-13 Sep 1974, p. 83 (1974). 2049 1451 550 [van92] J.R. Vanhoy, M.T. McEllistrem, S.F. Hicks, R.A. Gatenby, 2049 1451 551 E.M. Baum, E.L. Johnson, G. Molnar, S.W. Yates, Phys. 2049 1451 552 Rev. C45, 1628 (1992). 2049 1451 553 2049 1451 554 ************************* C O N T E N T S ************************2049 1451 555 2049 1451 556 ***************** Program LINEAR (VERSION 2007-1) ***************2049 1451 557 For All Data Greater than 1.0000E-10 barns in Absolute Value 2049 1451 558 Data Linearized Using Energy Dependent Uncertainty 2049 1451 559 Energy Accuracy 2049 1451 560 (eV) (per-cent) 2049 1451 561 ----------- ----------- 2049 1451 562 0.0 .010000000 2049 1451 563 1.00000000 .010000000 2049 1451 564 10.0000000 .100000000 2049 1451 565 2.00000E+9 .100000000 2049 1451 566 ***************** Program RECENT (VERSION 2007-1) ***************2049 1451 567 for All Data Greater than 1.0000E-10 barns in Absolute Value 2049 1451 568 Data Linearized Using Energy Dependent Uncertainty 2049 1451 569 Energy Accuracy 2049 1451 570 (eV) (per-cent) 2049 1451 571 ----------- ----------- 2049 1451 572 0.0 .010000000 2049 1451 573 1.00000000 .010000000 2049 1451 574 10.0000000 .100000000 2049 1451 575 2.00000E+9 .100000000 2049 1451 576 ***************** Program SIGMA1 (VERSION 2007-1) ***************2049 1451 577 Data Doppler Broadened to 1200.00000 Kelvin 2049 1451 578 for All Data Greater than 1.0000E-10 barns in Absolute Value 2049 1451 579 Data Linearized Using Energy Dependent Uncertainty 2049 1451 580 Energy Accuracy 2049 1451 581 (eV) (per-cent) 2049 1451 582 ----------- ----------- 2049 1451 583 0.0 .010000000 2049 1451 584 1.00000000 .010000000 2049 1451 585 10.0000000 .100000000 2049 1451 586 2.00000E+9 .100000000 2049 1451 587 ***************** Program SIGMA1 (VERSION 2007-1) ***************2049 1451 588 Data Doppler Broadened to 1200000.00 Kelvin 2049 1451 589 for All Data Greater than 1.0000E-10 barns in Absolute Value 2049 1451 590 Data Linearized Using Energy Dependent Uncertainty 2049 1451 591 Energy Accuracy 2049 1451 592 (eV) (per-cent) 2049 1451 593 ----------- ----------- 2049 1451 594 0.0 .010000000 2049 1451 595 1.00000000 .010000000 2049 1451 596 10.0000000 .100000000 2049 1451 597 2.00000E+9 .100000000 2049 1451 598 ***************** Program FIXUP (Version 2007-1) ****************2049 1451 599 Corrected ZA/AWR in All Sections-----------------------------Yes 2049 1451 600 Corrected Thresholds-----------------------------------------No 2049 1451 601 Extended Cross Sections to 20 MeV----------------------------No 2049 1451 602 Allow Cross Section Deletion---------------------------------Yes 2049 1451 603 Allow Cross Section Reconstruction---------------------------Yes 2049 1451 604 Make All Cross Sections Non-Negative-------------------------Yes 2049 1451 605 Delete Energies Not in Ascending Order-----------------------Yes 2049 1451 606 Deleted Duplicate Points-------------------------------------Yes 2049 1451 607 Check for Ascending MAT/MF/MT Order--------------------------Yes 2049 1451 608 Check for Legal MF/MT Numbers--------------------------------Yes 2049 1451 609 Allow Creation of Missing Sections---------------------------No 2049 1451 610 Allow Insertion of Energy Points-----------------------------No 2049 1451 611 Create Uniform Energy Grid-----------------------------------No 2049 1451 612 Delete Section if Cross Section =0 at All Energies-----------Yes 2049 1451 613 **************** Program DICTIN (VERSION 2007-1) ****************2049 1451 614 1 451 728 12049 1451 615 2 151 12 12049 1451 616 3 1 670 12049 1451 617 3 2 273 12049 1451 618 3 4 24 12049 1451 619 3 5 75 12049 1451 620 3 16 9 12049 1451 621 3 17 5 12049 1451 622 3 22 6 12049 1451 623 3 28 6 12049 1451 624 3 51 16 12049 1451 625 3 52 16 12049 1451 626 3 53 15 12049 1451 627 3 54 14 12049 1451 628 3 55 16 12049 1451 629 3 56 14 12049 1451 630 3 57 15 12049 1451 631 3 58 14 12049 1451 632 3 59 14 12049 1451 633 3 60 15 12049 1451 634 3 61 14 12049 1451 635 3 62 14 12049 1451 636 3 63 13 12049 1451 637 3 64 13 12049 1451 638 3 65 13 12049 1451 639 3 66 13 12049 1451 640 3 67 13 12049 1451 641 3 68 13 12049 1451 642 3 69 13 12049 1451 643 3 70 13 12049 1451 644 3 91 12 12049 1451 645 3 102 466 12049 1451 646 3 103 9 12049 1451 647 3 104 8 12049 1451 648 3 105 6 12049 1451 649 3 107 10 12049 1451 650 3 600 8 12049 1451 651 3 601 8 12049 1451 652 3 602 8 12049 1451 653 3 603 8 12049 1451 654 3 604 7 12049 1451 655 3 649 7 12049 1451 656 3 650 7 12049 1451 657 3 651 7 12049 1451 658 3 652 6 12049 1451 659 3 653 5 12049 1451 660 3 654 5 12049 1451 661 3 655 5 12049 1451 662 3 699 5 12049 1451 663 3 700 6 12049 1451 664 3 701 6 12049 1451 665 3 702 5 12049 1451 666 3 703 5 12049 1451 667 3 704 5 12049 1451 668 3 705 5 12049 1451 669 3 749 5 12049 1451 670 3 800 10 12049 1451 671 3 801 9 12049 1451 672 3 802 8 12049 1451 673 3 803 8 12049 1451 674 3 849 7 12049 1451 675 4 2 1240 12049 1451 676 6 5 7052 12049 1451 677 6 16 446 12049 1451 678 6 17 98 12049 1451 679 6 22 192 12049 1451 680 6 28 175 12049 1451 681 6 51 108 12049 1451 682 6 52 100 12049 1451 683 6 53 102 12049 1451 684 6 54 99 12049 1451 685 6 55 89 12049 1451 686 6 56 86 12049 1451 687 6 57 90 12049 1451 688 6 58 91 12049 1451 689 6 59 90 12049 1451 690 6 60 90 12049 1451 691 6 61 86 12049 1451 692 6 62 86 12049 1451 693 6 63 85 12049 1451 694 6 64 80 12049 1451 695 6 65 83 12049 1451 696 6 66 78 12049 1451 697 6 67 77 12049 1451 698 6 68 80 12049 1451 699 6 69 78 12049 1451 700 6 70 76 12049 1451 701 6 91 780 12049 1451 702 6 102 974 12049 1451 703 6 600 29 12049 1451 704 6 601 39 12049 1451 705 6 602 39 12049 1451 706 6 603 39 12049 1451 707 6 604 35 12049 1451 708 6 649 188 12049 1451 709 6 650 26 12049 1451 710 6 651 35 12049 1451 711 6 652 35 12049 1451 712 6 653 30 12049 1451 713 6 654 30 12049 1451 714 6 655 32 12049 1451 715 6 699 87 12049 1451 716 6 700 21 12049 1451 717 6 701 30 12049 1451 718 6 702 30 12049 1451 719 6 703 32 12049 1451 720 6 704 32 12049 1451 721 6 705 30 12049 1451 722 6 749 81 12049 1451 723 6 800 34 12049 1451 724 6 801 43 12049 1451 725 6 802 38 12049 1451 726 6 803 39 12049 1451 727 6 849 183 12049 1451 728 2049 1 0 729 2049 0 0 730 20048.0000 47.5406000 0 0 1 02049 2151 731 20048.0000 1.00000000 0 0 1 02049 2151 732 1.00000E-5 500000.000 1 2 0 02049 2151 733 0.0 .360000000 0 0 2 02049 2151 734 47.1322000 0.0 0 0 12 22049 2151 735 -10000.0000 .500000000 803.200000 800.000000 3.20000000 0.0 2049 2151 736 161400.000 .500000000 590.150000 590.000000 .150000000 0.0 2049 2151 737 47.1322000 0.0 1 0 24 42049 2151 738 303600.000 .500000000 2500.30000 2500.00000 .300000000 0.0 2049 2151 739 401200.000 1.50000000 3330.80000 3330.00000 .800000000 0.0 2049 2151 740 415000.000 1.50000000 380.500000 380.000000 .500000000 0.0 2049 2151 741 450000.000 .500000000 4302.50000 4300.00000 2.50000000 0.0 2049 2151 742 2049 2 0 743 2049 0 0 744 20048.0000 47.5406000 0 0 0 02049 3 1 745 0.0 0.0 0 0 1 19992049 3 1 746 1999 2 2049 3 1 747 1.00000E-5 2009.73138 1.02999E-5 1980.25687 1.06087E-5 1951.223692049 3 1 748 1.09269E-5 1922.60288 1.12544E-5 1894.41930 1.15920E-5 1866.632962049 3 1 749 1.19395E-5 1839.26862 1.22976E-5 1812.29119 1.26662E-5 1785.723512049 3 1 750 1.30462E-5 1759.52805 1.34372E-5 1733.73722 1.38403E-5 1708.305382049 3 1 751 1.42552E-5 1683.26438 1.46827E-5 1658.57591 1.51229E-5 1634.260932049 3 1 752 1.55765E-5 1610.28754 1.60434E-5 1586.68408 1.65246E-5 1563.410262049 3 1 753 1.70199E-5 1540.49230 1.75304E-5 1517.89800 1.80559E-5 1495.645292049 3 1 754 1.85975E-5 1473.70747 1.91550E-5 1452.10388 1.97295E-5 1430.805502049 3 1 755 2.03209E-5 1409.83007 2.09305E-5 1389.14928 2.15579E-5 1368.786962049 3 1 756 2.22045E-5 1348.70914 2.28701E-5 1328.93871 2.35561E-5 1309.444792049 3 1 757 2.42622E-5 1290.25054 2.49899E-5 1271.32540 2.57390E-5 1252.688672049 3 1 758 2.65110E-5 1234.31505 2.73057E-5 1216.22033 2.81247E-5 1198.381882049 3 1 759 2.89678E-5 1180.81368 2.98367E-5 1163.49334 3.07311E-5 1146.437792049 3 1 760 3.16528E-5 1129.62253 3.26017E-5 1113.06269 3.35795E-5 1096.736822049 3 1 761 3.45861E-5 1080.65921 3.56235E-5 1064.80817 3.66913E-5 1049.199092049 3 1 762 3.77919E-5 1033.80932 3.89247E-5 1018.65484 4.00923E-5 1003.712822049 3 1 763 4.12941E-5 988.999825 4.25327E-5 974.492808 4.38076E-5 960.2081432049 3 1 764 4.51216E-5 946.123949 4.64742E-5 932.254663 4.78681E-5 918.5808012049 3 1 765 4.93030E-5 905.114984 5.07818E-5 891.839291 5.23041E-5 878.7654142049 3 1 766 5.38729E-5 865.875934 5.54878E-5 853.182952 5.71521E-5 840.6688632049 3 1 767 5.88653E-5 828.345266 6.06310E-5 816.194977 6.24484E-5 804.2306742049 3 1 768 6.43215E-5 792.434617 6.62496E-5 780.818126 6.82368E-5 769.3650402049 3 1 769 7.02822E-5 758.087183 7.23903E-5 746.967754 7.45603E-5 736.0180042049 3 1 770 7.67967E-5 725.222128 7.90987E-5 714.591323 8.14712E-5 704.1100962049 3 1 771 8.39134E-5 693.788436 8.64304E-5 683.612015 8.90212E-5 673.5911842049 3 1 772 9.16913E-5 663.711318 9.44399E-5 653.981935 9.72725E-5 644.3897292049 3 1 773 1.00188E-4 634.943571 1.03193E-4 625.631939 1.06287E-4 616.4594742049 3 1 774 1.09475E-4 607.417023 1.12756E-4 598.513508 1.16139E-4 589.7335362049 3 1 775 1.19620E-4 581.090008 1.23208E-4 572.566413 1.26901E-4 564.1737622049 3 1 776 1.30707E-4 555.899628 1.34626E-4 547.750006 1.38664E-4 539.7149632049 3 1 777 1.42820E-4 531.804402 1.47104E-4 524.004027 1.51513E-4 516.3230292049 3 1 778 1.56058E-4 508.750004 1.60736E-4 501.292375 1.65557E-4 493.9400972049 3 1 779 1.70520E-4 486.699318 1.75635E-4 479.560246 1.80899E-4 472.5311202049 3 1 780 1.86325E-4 465.600923 1.91911E-4 458.775412 1.97667E-4 452.0464302049 3 1 781 2.03592E-4 445.420186 2.09699E-4 438.887010 2.15985E-4 432.4537862049 3 1 782 2.22463E-4 426.111088 2.29132E-4 419.864890 2.36004E-4 413.7070502049 3 1 783 2.43079E-4 407.642510 2.50370E-4 401.663518 2.57875E-4 395.7759772049 3 1 784 2.65610E-4 389.970993 2.73572E-4 384.254932 2.81777E-4 378.6193352049 3 1 785 2.90224E-4 373.069318 2.98929E-4 367.597578 3.07890E-4 362.2093702049 3 1 786 3.17125E-4 356.896757 3.26631E-4 351.665608 3.36428E-4 346.5078032049 3 1 787 3.46513E-4 341.428829 3.56906E-4 336.421300 3.67605E-4 331.4900962049 3 1 788 3.78631E-4 326.628237 3.89981E-4 321.840733 4.01678E-4 317.1204692049 3 1 789 4.13719E-4 312.472318 4.26128E-4 307.889473 4.38901E-4 303.3766712049 3 1 790 4.52066E-4 298.927334 4.65617E-4 294.545855 4.79583E-4 290.2260812049 3 1 791 4.93959E-4 285.972158 5.08775E-4 281.778161 5.24026E-4 277.6480962049 3 1 792 5.39744E-4 273.576191 5.55923E-4 269.566405 5.72598E-4 265.6130562049 3 1 793 5.89762E-4 261.720028 6.07452E-4 257.881743 6.25661E-4 254.1021172049 3 1 794 6.44427E-4 250.375658 6.63744E-4 246.706021 6.83653E-4 243.0880652049 3 1 795 7.04146E-4 239.525283 7.25267E-4 236.012621 7.47007E-4 232.5536382049 3 1 796 7.69413E-4 229.143359 7.92477E-4 225.784996 8.16247E-4 222.4739982049 3 1 797 8.40715E-4 219.213451 8.65932E-4 215.998816 8.91889E-4 212.8332662049 3 1 798 9.18641E-4 209.712227 9.46178E-4 206.638872 9.74558E-4 203.6087472049 3 1 799 .001003771 200.624860 .001033879 197.682965 .001064871 194.7859822049 3 1 800 .001096811 191.929737 .001129689 189.117138 .001163573 186.3441042049 3 1 801 .001198452 183.613383 .001234399 180.921118 .001271402 178.2699122049 3 1 802 .001309537 175.656007 .001348791 173.082058 .001389247 170.5443372049 3 1 803 .001430892 168.045295 .001473810 165.581474 .001517989 163.1552242049 3 1 804 .001563521 160.763120 .001610389 158.407579 .001658691 156.0851842049 3 1 805 .001708412 153.798213 .001759655 151.543453 .001812403 149.3231032049 3 1 806 .001866765 147.133995 .001922723 144.978343 .001980394 142.8530062049 3 1 807 .002039758 140.760140 .002100939 138.696736 .002163917 136.6648122049 3 1 808 .002228823 134.661492 .002295634 132.688784 .002364490 130.7438372049 3 1 809 .002435368 128.828586 .002508415 126.940311 .002583608 125.0808462049 3 1 810 .002661102 123.247563 .002740871 121.442294 .002823082 119.6624272049 3 1 811 .002907706 117.909754 .002994921 116.181760 .003084697 114.4801412049 3 1 812 .003177221 112.802489 .003272461 111.150463 .003370617 109.5216982049 3 1 813 .003471655 107.917812 .003575785 106.336511 .003682973 104.7793672049 3 1 814 .003793441 103.244155 .003907154 101.732387 .004024346 100.2419212049 3 1 815 .004144980 98.7742139 .004269306 97.3271913 .004397283 95.90226402049 3 1 816 .004529177 94.4974184 .004664944 93.1140308 .004804866 91.75013822049 3 1 817 .004948897 90.4070803 .005097336 89.0829508 .005250134 87.77904952049 3 1 818 .005407609 86.4935233 .005569708 85.2276443 .005736768 83.97960092049 3 1 819 .005908733 82.7506374 .006085962 81.5389926 .006268395 80.34586652049 3 1 820 .006456412 79.1695579 .006649949 78.0112324 .006849411 76.86923412049 3 1 821 .007054729 75.7446971 .007266331 74.6360156 .007484147 73.54428222049 3 1 822 .007708630 72.4679433 .007939704 71.4080667 .008177850 70.36313782049 3 1 823 .008422990 69.3341856 .008675632 68.3197512 .008935694 67.32082892049 3 1 824 .009203714 66.3360025 .009479605 65.3662388 .009763940 64.41016112049 3 1 825 .010056625 63.4687091 .010358267 62.5405447 .010668767 61.62658342049 3 1 826 .010988770 60.7255232 .011318170 59.8382535 .011657652 58.96350962049 3 1 827 .012007102 58.1021583 .012367248 57.2529684 .012737969 56.41678232049 3 1 828 .013120036 55.5924068 .013513323 54.7806543 .013918647 53.98037122049 3 1 829 .014335873 53.1923458 .014765869 52.4154567 .015208491 51.65047052049 3 1 830 .015664661 50.8962972 .016134225 50.1536822 .016618162 49.42156652049 3 1 831 .017116308 48.7006745 .017629702 47.9899775 .018158171 47.29017862049 3 1 832 .018702814 46.6002799 .019263450 45.9209634 .019841246 45.25126062049 3 1 833 .020436008 44.5918337 .021048973 43.9417428 .021679938 43.30162882049 3 1 834 .022330215 42.6705813 .022999587 42.0492226 .023689445 41.43666812049 3 1 835 .024399561 40.8335218 .025268741 40.1302456 .025300000 40.10563212049 3 1 836 .026058858 39.5217913 .026840000 38.9469241 .027645049 38.38021152049 3 1 837 .028473738 37.8222129 .029327791 37.2721336 .030206922 36.73051682049 3 1 838 .031112960 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