TENDL-2011 gen. purp. file: proton + Ti- 49 1 MeV - 200 MeV 99 0 0 0 22049.0000 48.5273900 -1 0 0 12234 1451 1 0.0 0.0 0 0 0 62234 1451 2 .998620000 200000000. 1 0 10010 02234 1451 3 0.0 0.0 1 0 268 62234 1451 4 22-Ti- 49 NRG EVAL-OCT11 A.J. Koning 2234 1451 5 TENDL-2011 DIST- REV1- 2234 1451 6 ----TENDL-2011 Material 2234 REVISION 1 2234 1451 7 -----Incident proton data 2234 1451 8 ------ENDF-6 Format 2234 1451 9 2234 1451 10 TENDL-2011 (TALYS Evaluated Nuclear Data Library) 2234 1451 11 2234 1451 12 Charged particle transport library made by TALYS 2234 1451 13 2234 1451 14 Author: A.J. Koning, NRG Petten, The Netherlands 2234 1451 15 2234 1451 16 ************** G E N E R A L I N F O R M A T I O N *************2234 1451 17 2234 1451 18 This evaluated data file is based primarily on the nuclear model 2234 1451 19 code TALYS [kon07], version 1.4. 2234 1451 20 It is part of a large collection of isotopic 2234 1451 21 evaluations, all created by running TALYS with either default or 2234 1451 22 adjusted input parameters. This means that the data in this 2234 1451 23 evaluation have been tested in detail for some isotopes against 2234 1451 24 individual experimental data, while for other isotopes it is 2234 1451 25 only as good as the global quality of TALYS at the present moment.2234 1451 26 The mutual quality of all individual evaluations is however 2234 1451 27 consistent: The same set of nuclear models is used and, equally 2234 1451 28 important, the same ENDF-6 formatting procedures for each isotope.2234 1451 29 The resulting data file provides a complete representation of 2234 1451 30 nuclear data needed for transport, damage, heating, radioactivity,2234 1451 31 and shielding applications over the incident projectile energy 2234 1451 32 range from 1.0E-11 to 200 MeV. 2234 1451 33 2234 1451 34 All transport data for neutrons, other particles, photons and 2234 1451 35 residual nuclides are filed using a combination of MF1,3, 2234 1451 36 and MF6. This includes cross sections, angular distributions, 2234 1451 37 double-differential spectra, production cross sections, 2234 1451 38 residual production (activation) cross sections and recoils. 2234 1451 39 This evaluation can thus be used as both transport and activation 2234 1451 40 library. The data file has been created automatically using the 2234 1451 41 ENDF-6 format generator TEFAL. 2234 1451 42 2234 1451 43 ##### ORIGIN 2234 1451 44 2234 1451 45 All data < 200 MeV : Produced with TALYS code 2234 1451 46 2234 1451 47 *************************** T H E O R Y **************************2234 1451 48 2234 1451 49 TALYS is a computer code system for the prediction and analysis 2234 1451 50 of nuclear reactions. TALYS simulates reactions that involve 2234 1451 51 neutrons, gamma-rays, protons, deuterons, tritons, helions and 2234 1451 52 alpha-particles, in the 1 keV - 200 MeV energy range and for 2234 1451 53 target nuclides of mass 12 and heavier. This is achieved by 2234 1451 54 implementing a suite of nuclear reaction models into a single 2234 1451 55 code system. It enables to evaluate nuclear reactions from 2234 1451 56 the unresolved resonance region up to intermediate energies. This 2234 1451 57 evaluation is based on a theoretical analysis that utilizes the 2234 1451 58 optical model, compound nucleus statistical theory, fission, 2234 1451 59 direct reactions and pre-equilibrium processes, in combination 2234 1451 60 with databases and models for nuclear structure. The following 2234 1451 61 output of TALYS is stored in this data file: 2234 1451 62 2234 1451 63 - Elastic and non-elastic cross sections 2234 1451 64 - Elastic scattering angular distributions 2234 1451 65 - Residual production cross sections 2234 1451 66 - Recoil data 2234 1451 67 - Total particle cross sections, e.g. (p,xn), (p,xp),.. 2234 1451 68 - Total particle energy spectra 2234 1451 69 - Total particle double-differential spectra 2234 1451 70 2234 1451 71 Here follows a short description of the used nuclear models: 2234 1451 72 2234 1451 73 ##### OPTICAL MODEL 2234 1451 74 2234 1451 75 All optical model calculations are performed by ECIS-06 [ray94], 2234 1451 76 in TALYS used as a subroutine. The default optical model 2234 1451 77 potentials (OMP) used are the local and global parameterizations 2234 1451 78 of Koning and Delaroche [kon03]. These are phenomenological OMPs 2234 1451 79 for neutrons and protons which in principle are valid over the 2234 1451 80 1 keV - 200 MeV energy range, though the low energy boundary of 2234 1451 81 validity may differ from nucleus to nucleus. For neutrons and 2234 1451 82 protons, the used parameterization is given in Eq. (7) of 2234 1451 83 [kon03]. Revised versions of these potentials (unpublished) are 2234 1451 84 used in the case of deformed nuclides. 2234 1451 85 To calculate the transmission coefficients and reaction 2234 1451 86 cross sections for deuterons, tritons, helions and alpha 2234 1451 87 particles, we use OMPs that are directly derived from our nucleon 2234 1451 88 potentials using Watanabe's folding approach. 2234 1451 89 2234 1451 90 ##### DIRECT REACTIONS 2234 1451 91 2234 1451 92 The built-in ECIS-06 is used for DWBA or coupled-channels 2234 1451 93 calculations for rotational or vibrational (or a combination of 2234 1451 94 these) nuclides, depending on the information present in the 2234 1451 95 nuclear structure database of TALYS. 2234 1451 96 In addition, a macroscopic, phenomenological model to describe 2234 1451 97 giant resonances in the inelastic channel is used. For each 2234 1451 98 multipolarity an energy weighted sum rule applies and a DWBA 2234 1451 99 calculation with ECIS-06 is performed for each giant resonance 2234 1451 100 state. The cross section is then spread over the continuum with a 2234 1451 101 Gaussian distribution. 2234 1451 102 2234 1451 103 ##### COMPOUND NUCLEUS 2234 1451 104 2234 1451 105 For compound nucleus reactions we use the the Hauser-Feshbach 2234 1451 106 model. The transmission coefficients have been generated 2234 1451 107 with the aforementioned OMPs and the full j,l-dependence of the 2234 1451 108 transmission coefficients in the Hauser-Feshbach model is used. 2234 1451 109 For each nucleus that can be reached through a binary reaction, 2234 1451 110 several discrete levels and a continuum described by level 2234 1451 111 densities are included simultaneously as competing channels. 2234 1451 112 2234 1451 113 For each residual nucleus several discrete states 2234 1451 114 are included as well as a continuum described by level densities. 2234 1451 115 Multiple compound emission is continued until all reaction 2234 1451 116 channels are closed and the population distribution of all 2234 1451 117 residual nuclides is depleted, through gamma decay, until they 2234 1451 118 end up in the ground state or in an isomer. 2234 1451 119 2234 1451 120 For the level density, we take the Constant Temperature Model 2234 1451 121 with level density parameters as given in [kon08]. This employs 2234 1451 122 the temperature law at low energies and a Fermi gas expression at 2234 1451 123 high energies, and takes into account the damping of shell 2234 1451 124 effects at high excitation energy. We have obtained the level 2234 1451 125 density parameters from a simultaneous fit to all experimental 2234 1451 126 discrete levels and D0 values from the RIPL library [rip09]. 2234 1451 127 2234 1451 128 Gamma-ray transmission coefficients are generated with the 2234 1451 129 Kopecky-Uhl generalized Lorentzian for strength functions, with 2234 1451 130 giant dipole resonance parameters taken from the RIPL library 2234 1451 131 [rip09], and normalized with experimental radiative widths. 2234 1451 132 2234 1451 133 ##### PRE-EQUILIBRIUM REACTIONS 2234 1451 134 2234 1451 135 For pre-equilibrium reactions, which become important for 2234 1451 136 incident energies above about 10 MeV, we use the two-component 2234 1451 137 exciton model [kon04], in which the neutron or proton types of 2234 1451 138 particles and holes are followed throughout the reaction. For 2234 1451 139 energies above 20 MeV, multiple pre-equilibrium emission up to 2234 1451 140 any order of particle emission was included in the calculations. 2234 1451 141 A parameterization for the squared matrix element is used that is 2234 1451 142 valid for the whole energy range of this evaluation. 2234 1451 143 2234 1451 144 For deuterons, tritons, helions and alpha-particles, an extra 2234 1451 145 contribution was added from the pick/up and knock-out reaction 2234 1451 146 model by Kalbach [kal05]. 2234 1451 147 2234 1451 148 For photons, the model of Akkermans and Gruppelaar [akk85] was 2234 1451 149 applied, to simulate the direct and semi-direct capture 2234 1451 150 processes. 2234 1451 151 2234 1451 152 The angular distribution systematics by Kalbach [kal88] were used 2234 1451 153 to describe the angular distributions for all continuum 2234 1451 154 particles. An isotopic distribution for photons was adopted. 2234 1451 155 2234 1451 156 ***************** F I L E I N F O R M A T I O N ****************2234 1451 157 2234 1451 158 ##### MF1: GENERAL INFORMATION 2234 1451 159 2234 1451 160 - MT451 : Descriptive data and directory 2234 1451 161 2234 1451 162 This text and the full directory of used MF/MT sections. 2234 1451 163 2234 1451 164 ##### MF3: REACTION CROSS SECTIONS 2234 1451 165 2234 1451 166 All the data present in the following MT-sections have been 2234 1451 167 calculated with TALYS. If the maximal cross section in an 2234 1451 168 excitation function over the whole energy range does not exceed 2234 1451 169 1.e-9 b, the MT-number is not included at all. Cross sections 2234 1451 170 lower than 1.e-20 b are assumed to have no physical meaning and 2234 1451 171 are set to zero. The minor reaction channels are also present 2234 1451 172 but they are stored in MT5 and can be reproduced in combination 2234 1451 173 with MF6. All MT numbers extend up to the highest incident energy.2234 1451 174 The following reaction channels/MT numbers are generally included:2234 1451 175 2234 1451 176 - MT2 : Elastic scattering cross section: nuclear + 2234 1451 177 interference terms 2234 1451 178 2234 1451 179 Obtained by integrating the "nuclear-plus-interference" angular 2234 1451 180 distributions of MF=6. Note that because of the interference 2234 1451 181 effect, the tabulations in both MF=6 and MF=3 can be negative at 2234 1451 182 some energies and angles. 2234 1451 183 2234 1451 184 - MT5 : (p,anything) cross section 2234 1451 185 2234 1451 186 MT5 contains the reactions which can not be stored in any other 2234 1451 187 MT-number. As the incident energy increases, the cross section 2234 1451 188 of MT5 increases as more reaction channels are no longer stored 2234 1451 189 under a specific MT number. The information of MF3/MT5 can be 2234 1451 190 combined with MF6/MT5 to obtain residual production cross 2234 1451 191 sections particle production cross sections and 2234 1451 192 (double-)differential cross sections. 2234 1451 193 2234 1451 194 ##### MF6: PRODUCT ENERGY-ANGLE DISTRIBUTIONS 2234 1451 195 2234 1451 196 In MF6 we store all secondary energy, angle, and energy-angle 2234 1451 197 distributions, as well as all residual and photon production 2234 1451 198 cross sections. All data are generated with TALYS. 2234 1451 199 2234 1451 200 - MT2 : Elastic scattering angular distribution: nuclear + 2234 1451 201 interference terms 2234 1451 202 2234 1451 203 Relative angular distributions are tabulated on an angular grid. 2234 1451 204 They are obtained by using the "nuclear-plus-interference" option 2234 1451 205 in MF=6, which corresponds to LAW=5, LTP=12, and the appropriate 2234 1451 206 integrated cross section is stored in MF=3. Note that because 2234 1451 207 of the interference effect, the tabulations in both MF=6 and 2234 1451 208 MF=3 can be negative at some energies and angles. 2234 1451 209 2234 1451 210 - MT5 : (p,anything) yields and energy-angle distributions 2234 1451 211 2234 1451 212 MT5 contains the production yields of particles and residual 2234 1451 213 products. It also contains the secondary energy-angle 2234 1451 214 distributions for all particles and photons. First, the yields 2234 1451 215 for neutrons are given for the whole energy range. Next, on a 2234 1451 216 secondary energy grid the relative emission spectra are given 2234 1451 217 together with the parameters for the Kalbach systematics for 2234 1451 218 angular distributions. Inelastic scattering cross sections for 2234 1451 219 discrete states have been broadened and added to the continuum 2234 1451 220 spectra. This procedure is repeated for protons, deuterons, 2234 1451 221 tritons, Helium-3, alpha particles and photons. Finally, the 2234 1451 222 residual production yields are given per final product. All these 2234 1451 223 yields and relative distributions can be multiplied with the 2234 1451 224 cross sections given in MF3/MT5 to get the production cross 2234 1451 225 sections and (double-)differential cross sections. 2234 1451 226 2234 1451 227 ***** 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 ****2234 1451 228 2234 1451 229 This file has been checked successfully by the BNL checking 2234 1451 230 codes CHECKR-8.0, FIZCON-8.0 and PSYCHE-8.0 [her08] and has 2234 1451 231 been processed successfully into an MCNP library by the 2234 1451 232 processing code NJOY99.90 [mac00]. 2234 1451 233 2234 1451 234 *********************** R E F E R E N C E S **********************2234 1451 235 2234 1451 236 [akk85] J.M. Akkermans and H. Gruppelaar, Phys. Lett. 157B, 95 2234 1451 237 (1985). 2234 1451 238 [her08] M. Herman, ENDF Utility Codes Release 8.0, (2008). 2234 1451 239 [kal88] C. Kalbach, Phys. Rev. C37, 2350 (1988). 2234 1451 240 [kal05] C. Kalbach, Phys. Rev. C71, 034606 (2005). 2234 1451 241 [kon03] A.J. Koning and J.P. Delaroche, Nucl. Phys. A713, 231 2234 1451 242 (2003). 2234 1451 243 [kon04] A.J. Koning and M.C. Duijvestijn, Nucl. Phys. A744, 15 2234 1451 244 (2004). 2234 1451 245 [kon07] A.J. Koning, S. Hilaire and M.C. Duijvestijn, TALYS-1.0, 2234 1451 246 Proceedings of the International Conference on Nuclear 2234 1451 247 Data for Science and Technology - ND-2007, 2234 1451 248 April 22-27, 2007, Nice, France 2234 1451 249 [kon08] A.J. Koning, S. Hilaire and S. Goriely, ``Global and 2234 1451 250 local level density models'', Nucl Phys. A810, 2234 1451 251 13-76 (2008). 2234 1451 252 [mac00] R.E. Macfarlane, NJOY99 - Code system for producing 2234 1451 253 pointwise and multigroup neutron and photon cross 2234 1451 254 sections from ENDF/B Data, RSIC PSR-480 (2000). 2234 1451 255 [ray94] J. Raynal, Notes on ECIS94, CEA Saclay Report 2234 1451 256 No. CEA-N-2772, 1994. 2234 1451 257 [rip09] R. Capote, M. Herman, P. Oblozinsky, P.G. Young, 2234 1451 258 S. Goriely, T. Belgya, A.V. Ignatyuk, A.J. Koning, 2234 1451 259 S. Hilaire, V. Plujko, M. Avrigeanu, O. Bersillon, 2234 1451 260 M.B. Chadwick, T. Fukahori, S. Kailas, J. Kopecky, 2234 1451 261 V.M. Maslov, G. Reffo, M. Sin, E. Soukhovitskii, 2234 1451 262 P. Talou, H. Yinlu, and G. Zhigang, 2234 1451 263 RIPL - Reference Input Parameter Library for calculation 2234 1451 264 of nuclear reactions and nuclear data evaluation, 2234 1451 265 Nucl. Data Sheets 110, 3107 (2009). 2234 1451 266 2234 1451 267 ************************* C O N T E N T S ************************2234 1451 268 2234 1451 269 *************** PROGRAM ACTIVATE (VERSION 2010-1) ***************2234 1451 270 MF=10 Activation Cross Sections Defined by Combining MF=3 2234 1451 271 Cross Sections and MF=9 Multipliers. MF=9 Deleted. 2234 1451 272 1 451 275 12234 1451 273 3 2 18 12234 1451 274 3 5 18 12234 1451 275 6 2 1401 12234 1451 276 6 5 19387 12234 1451 277 8 5 133 12234 1451 278 2234 1 0 279 2234 0 0 280 22049.0000 48.5273900 0 0 0 02234 3 2 281 0.000000+0 0.000000+0 0 0 1 452234 3 2 282 45 2 2234 3 2 283 1.000000+6-1.889927-5 2.000000+6-1.748030-3 3.000000+6-1.742521-22234 3 2 284 4.000000+6-3.363548-2 5.000000+6-2.587047-2 6.000000+6-3.629324-22234 3 2 285 7.000000+6-9.145897-2 8.000000+6-1.652831-1 9.000000+6-2.357557-12234 3 2 286 1.000000+7-2.936845-1 1.100000+7-3.361326-1 1.200000+7-3.634385-12234 3 2 287 1.300000+7-3.778312-1 1.400000+7-3.823103-1 1.500000+7-3.795639-12234 3 2 288 1.600000+7-3.714927-1 1.700000+7-3.593625-1 1.800000+7-3.441545-12234 3 2 289 1.900000+7-3.267888-1 2.000000+7-3.081370-1 2.200000+7-2.697486-12234 3 2 290 2.400000+7-2.326296-1 2.600000+7-1.979800-1 2.800000+7-1.659722-12234 3 2 291 3.000000+7-1.366613-1 3.500000+7-7.578982-2 4.000000+7-3.166924-22234 3 2 292 4.500000+7-1.030323-3 5.000000+7 1.932475-2 5.500000+7 3.202723-22234 3 2 293 6.000000+7 3.922359-2 6.500000+7 4.256857-2 7.000000+7 4.329771-22234 3 2 294 7.500000+7 4.231684-2 8.000000+7 4.027655-2 9.000000+7 3.470844-22234 3 2 295 1.000000+8 2.877094-2 1.100000+8 2.340923-2 1.200000+8 1.894810-22234 3 2 296 1.300000+8 1.541333-2 1.400000+8 1.271262-2 1.500000+8 1.070034-22234 3 2 297 1.600000+8 9.236224-3 1.800000+8 7.465779-3 2.000000+8 6.645749-32234 3 2 298 2234 3 0 299 2.204900+4 4.852739+1 0 0 0 02234 3 5 300 0.000000+0 0.000000+0 0 0 1 452234 3 5 301 45 2 2234 3 5 302 1.000000+6 4.329000-5 2.000000+6 1.035300-2 3.000000+6 8.950301-22234 3 5 303 4.000000+6 2.592800-1 5.000000+6 4.579900-1 6.000000+6 6.245900-12234 3 5 304 7.000000+6 7.282300-1 8.000000+6 7.904100-1 9.000000+6 8.377801-12234 3 5 305 1.000000+7 8.807001-1 1.100000+7 9.194001-1 1.200000+7 9.519501-12234 3 5 306 1.300000+7 9.781100-1 1.400000+7 9.995701-1 1.500000+7 1.018200+02234 3 5 307 1.600000+7 1.034900+0 1.700000+7 1.049200+0 1.800000+7 1.060100+02234 3 5 308 1.900000+7 1.067400+0 2.000000+7 1.071200+0 2.200000+7 1.071600+02234 3 5 309 2.400000+7 1.067700+0 2.600000+7 1.062400+0 2.800000+7 1.055800+02234 3 5 310 3.000000+7 1.047100+0 3.500000+7 1.018000+0 4.000000+7 9.854500-12234 3 5 311 4.500000+7 9.529901-1 5.000000+7 9.216400-1 5.500000+7 8.921201-12234 3 5 312 6.000000+7 8.647701-1 6.500000+7 8.396000-1 7.000000+7 8.165600-12234 3 5 313 7.500000+7 7.955000-1 8.000000+7 7.763301-1 9.000000+7 7.428500-12234 3 5 314 1.000000+8 7.149200-1 1.100000+8 6.914300-1 1.200000+8 6.715400-12234 3 5 315 1.300000+8 6.545500-1 1.400000+8 6.398901-1 1.500000+8 6.271300-12234 3 5 316 1.600000+8 6.159000-1 1.800000+8 5.969800-1 2.000000+8 5.814800-12234 3 5 317 2234 3 0 318 2234 0 0 319 22049.0000 48.5273900 0 0 133 0223410 5 320 0.0 0.0 1 0 1 45223410 5 321 45 2 223410 5 322 1.000000+6 0.0 2.000000+6 .010170849 3.000000+6 .086220487223410 5 323 4.000000+6 .247236444 5.000000+6 .425503853 6.000000+6 .558724486223410 5 324 7.000000+6 .624375663 8.000000+6 .649456185 9.000000+6 .661461738223410 5 325 1.000000+7 .671081146 1.100000+7 .681317767 1.200000+7 .695265323223410 5 326 1.300000+7 .718312247 1.400000+7 .789162593 1.500000+7 .940443121223410 5 327 1.600000+7 1.08991528 1.700000+7 1.18778883 1.800000+7 1.24179054223410 5 328 1.900000+7 1.26703582 2.000000+7 1.27419240 2.200000+7 1.26543101223410 5 329 2.400000+7 1.24920900 2.600000+7 1.26271552 2.800000+7 1.31970777223410 5 330 3.000000+7 1.37594176 3.500000+7 1.40917668 4.000000+7 1.40217710223410 5 331 4.500000+7 1.41613376 5.000000+7 1.41409990 5.500000+7 1.40778336223410 5 332 6.000000+7 1.40655722 6.500000+7 1.40793364 7.000000+7 1.40846801223410 5 333 7.500000+7 1.41671391 8.000000+7 1.41343316 9.000000+7 1.44764379223410 5 334 1.000000+8 1.50278329 1.100000+8 1.54854046 1.200000+8 1.61557750223410 5 335 1.300000+8 1.67469890 1.400000+8 1.72779925 1.500000+8 1.78263584223410 5 336 1.600000+8 1.83862779 1.800000+8 1.94987399 2.000000+8 2.05970683223410 5 337 0.0 0.0 1001 0 1 45223410 5 338 45 2 223410 5 339 1.000000+6 0.0 2.000000+6 3.12167E-8 3.000000+6 4.00410E-5223410 5 340 4.000000+6 .002344070 5.000000+6 .018110711 6.000000+6 .052082187223410 5 341 7.000000+6 .094246070 8.000000+6 .133971333 9.000000+6 .168086335223410 5 342 1.000000+7 .205490232 1.100000+7 .281872441 1.200000+7 .410894981223410 5 343 1.300000+7 .560022749 1.400000+7 .659025563 1.500000+7 .647143483223410 5 344 1.600000+7 .598420576 1.700000+7 .570163608 1.800000+7 .562436055223410 5 345 1.900000+7 .566059298 2.000000+7 .575114426 2.200000+7 .592878774223410 5 346 2.400000+7 .640394715 2.600000+7 .720037350 2.800000+7 .773357663223410 5 347 3.000000+7 .796609597 3.500000+7 .825240682 4.000000+7 .862655046223410 5 348 4.500000+7 .895975561 5.000000+7 .914324022 5.500000+7 .930873797223410 5 349 6.000000+7 .942158376 6.500000+7 .951476700 7.000000+7 .956461225223410 5 350 7.500000+7 .963899395 8.000000+7 .966298075 9.000000+7 .982218556223410 5 351 1.000000+8 1.00447690 1.100000+8 1.02649006 1.200000+8 1.04521172223410 5 352 1.300000+8 1.06759069 1.400000+8 1.08917614 1.500000+8 1.11015180223410 5 353 1.600000+8 1.14257457 1.800000+8 1.18684400 2.000000+8 1.23701729223410 5 354 0.0 0.0 1002 0 1 45223410 5 355 45 2 223410 5 356 1.000000+6 0.0 2.000000+6 0.0 3.000000+6 0.0 223410 5 357 4.000000+6 0.0 5.000000+6 0.0 6.000000+6 0.0 223410 5 358 7.000000+6 6.9424E-10 8.000000+6 3.44232E-6 9.000000+6 1.21181E-4223410 5 359 1.000000+7 7.28023E-4 1.100000+7 .001914448 1.200000+7 .003864556223410 5 360 1.300000+7 .006246582 1.400000+7 .008994122 1.500000+7 .012156595223410 5 361 1.600000+7 .015526915 1.700000+7 .018906794 1.800000+7 .022111248223410 5 362 1.900000+7 .025252549 2.000000+7 .028297569 2.200000+7 .033872955223410 5 363 2.400000+7 .039237975 2.600000+7 .044219532 2.800000+7 .047443534223410 5 364 3.000000+7 .051496273 3.500000+7 .060034209 4.000000+7 .066477570223410 5 365 4.500000+7 .071878992 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