JENDL-3.3 Rb087 pointwise at 0K 0 0 3.708700+4 8.616260+1 2 0 0 23731 1451 1 0.000000+0 1.000000+0 0 0 0 63731 1451 2 1.000000+0 2.000000+7 0 0 10 33731 1451 3 0.000000+0 0.000000+0 1 0 240 433731 1451 4 37-RB- 87 JNDC EVAL-MAR90 JNDC FP NUCLEAR DATA W.G. 3731 1451 5 DIST-MAR02 REV2-FEB02 20020222 3731 1451 6 ----JENDL-3.3 MATERIAL 3731 3731 1451 7 -----INCIDENT NEUTRON DATA 3731 1451 8 ------ENDF-6 FORMAT 3731 1451 9 3731 1451 10 =========================================================== 3731 1451 11 JENDL-3.2 data were automatically transformed to JENDL-3.3. 3731 1451 12 Interpolation of spectra: 22 (unit base interpolation) 3731 1451 13 (3,251) deleted, T-matrix of (4,2) deleted, and others. 3731 1451 14 =========================================================== 3731 1451 15 3731 1451 16 HISTORY 3731 1451 17 84-10 EVALUATION FOR JENDL-2 WAS MADE BY JNDC FPND W.G./1/ 3731 1451 18 90-03 MODIFICATION FOR JENDL-3 WAS MADE/2/. 3731 1451 19 3731 1451 20 MF = 1 GENERAL INFORMATION 3731 1451 21 MT=451 COMMENTS AND DICTIONARY 3731 1451 22 3731 1451 23 MF = 2 RESONANCE PARAMETERS 3731 1451 24 MT=151 RESOLVED AND UNRESOLVED RESONANCE PARAMETERS 3731 1451 25 RESOLVED RESONANCE REGION (MLBW FORMULA) : BELOW 12.46 KEV 3731 1451 26 RESONANCE PARAMETERS OF JENDL-2 WERE MODIFIED AS FOLLOWS : 3731 1451 27 EVALUATION OF JENDL-2 WAS PERFORMED ON THE BASIS OF THE DATA 3731 1451 28 MEASURED BY OHKUBO ET AL./3/ AMONG 30 LEVELS MEASURED IN THE 3731 1451 29 ENERGY REGION UP TO 49 KEV, 28 LEVELS WERE ASSUMED TO BE 3731 1451 30 S-WAVE, AND REMAINING 2 LEVELS AT 267.1 AND 376.9 EV TO BE 3731 1451 31 P-WAVE. NEUTRON WIDTHS WERE DETERMINED FROM THE 2G*(NEUTRON 3731 1451 32 WIDTH) MEASURED BY OHKUBO ET AL. HOWEVER, THE VALUE OF TOTAL 3731 1451 33 SPIN J FOR EACH RESONANCE LEVEL WAS UNKNOWN EXCEPT ONLY 6 3731 1451 34 LEVELS ASSIGNED BY OHKUBO ET AL. THE TARGET SPIN OF 1.5 WAS 3731 1451 35 ADOPTED FOR THESE UNKNOWN LEVELS INSTEAD OF J. RADIATION 3731 1451 36 WIDTH WAS OBTAINED TO BE 166+-8 MEV FOR ONLY ONE RESONANCE 3731 1451 37 LEVEL AT 376.9 EV FROM THE MEASUREMENT BY OHKUBO ET AL. 3731 1451 38 AVERAGE RADIATION WIDTH WAS ALSO ESTIMATED TO BE 166+-30 MEV 3731 1451 39 BY OHKUBO ET AL., AND WAS ADOPTED FOR THE OTHER LEVELS. 3731 1451 40 3731 1451 41 FOR JENDL-3, THE TOTAL SPIN J OF 24 RESONANCE LEVELS WAS 3731 1451 42 TENTATIVELY ESTIMATED WITH A RANDOM NUMBER METHOD. NEUTRON 3731 1451 43 WIDTHS OF THESE LEVELS WERE MODIFIED ON THE BASIS OF THE 3731 1451 44 ESTIMATED J-VALUES. RADIATION WIDTH OF THE 2ND LEVEL AT 376.93731 1451 45 EV AND AVERAGE RADIATION WIDTH WERE ALSO MODIFIED TO 115.33 3731 1451 46 AND 115.0 MEV, RESPECTIVELY, SO AS TO REPRODUCE THE THERMAL 3731 1451 47 CAPTURE CROSS SECTION OF 120+-30 MB GIVEN BY MUGHABGHAB ET 3731 1451 48 AL./4/ SCATTERING RADIUS WAS TAKEN FROM THE GRAPH (FIG. 1, 3731 1451 49 PART A) GIVEN BY MUGHABGHAB ET AL. 3731 1451 50 3731 1451 51 UNRESOLVED RESONANCE REGION : 12.46 KEV - 100 KEV 3731 1451 52 UNRESOLVED RESONANCE PARAMETERS WERE ADOPTED FROM JENDL-2. 3731 1451 53 THE NEUTRON STRENGTH FUNCTION, S0, WAS TAKEN FROM THE 3731 1451 54 RECOMMENDATION IN REF./5/, AND S1 AND S2 WERE CALCULATED WITH 3731 1451 55 OPTICAL MODEL CODE CASTHY/6/. THE OBSERVED LEVEL SPACING WERE3731 1451 56 DETERMINED TO REPRODUCE THE CAPTURE CROSS SECTION CALCULATED 3731 1451 57 WITH CASTHY. THE EFFECTIVE SCATTERING RADIUS WAS OBTAINED 3731 1451 58 FROM FITTING TO THE CALCULATED TOTAL CROSS SECTION AT 100 KEV.3731 1451 59 THE RADIATION WIDTH GG WAS BASED ON THE COMPILATION OF BNL-3253731 1451 60 (3RD ED.)/5/. 3731 1451 61 3731 1451 62 TYPICAL VALUES OF THE PARAMETERS AT 70 KEV: 3731 1451 63 S0 = 1.600E-4, S1 = 2.920E-4, S2 = 0.650E-4, SG = 0.987E-4, 3731 1451 64 GG = 0.290 EV, R = 6.423 FM. 3731 1451 65 3731 1451 66 CALCULATED 2200-M/S CROSS SECTIONS AND RES. INTEGRALS (BARNS) 3731 1451 67 2200 M/S RES. INTEG. 3731 1451 68 TOTAL 4.479 - 3731 1451 69 ELASTIC 4.359 - 3731 1451 70 CAPTURE 0.1200 2.72 3731 1451 71 3731 1451 72 MF = 3 NEUTRON CROSS SECTIONS 3731 1451 73 BELOW 100 KEV, RESONANCE PARAMETERS WERE GIVEN. 3731 1451 74 ABOVE 100 KEV, THE SPHERICAL OPTICAL AND STATISTICAL MODEL 3731 1451 75 CALCULATION WAS PERFORMED WITH CASTHY, BY TAKING ACCOUNT OF 3731 1451 76 COMPETING REACTIONS, OF WHICH CROSS SECTIONS WERE CALCULATED 3731 1451 77 WITH PEGASUS/7/ STANDING ON A PREEQUILIBRIUM AND MULTI-STEP 3731 1451 78 EVAPORATION MODEL. THE OMP'S FOR NEUTRON GIVEN IN TABLE 1 WERE 3731 1451 79 DETERMINED TO REPRODUCE A SYSTEMATIC TREND OF THE TOTAL CROSS 3731 1451 80 SECTION BY CHANGING R0, RS AND RSO OF IIJIMA-KAWAI POTENTIAL/8/.3731 1451 81 THE OMP'S FOR CHARGED PARTICLES ARE AS FOLLOWS: 3731 1451 82 PROTON = PEREY/9/ 3731 1451 83 ALPHA = HUIZENGA AND IGO/10/ 3731 1451 84 DEUTERON = LOHR AND HAEBERLI/11/ 3731 1451 85 HELIUM-3 AND TRITON = BECCHETTI AND GREENLEES/12/ 3731 1451 86 PARAMETERS FOR THE COMPOSITE LEVEL DENSITY FORMULA OF GILBERT 3731 1451 87 AND CAMERON/13/ WERE EVALUATED BY IIJIMA ET AL./14/ MORE 3731 1451 88 EXTENSIVE DETERMINATION AND MODIFICATION WERE MADE IN THE 3731 1451 89 PRESENT WORK. TABLE 2 SHOWS THE LEVEL DENSITY PARAMETERS USED 3731 1451 90 IN THE PRESENT CALCULATION. ENERGY DEPENDENCE OF SPIN CUT-OFF 3731 1451 91 PARAMETER IN THE ENERGY RANGE BELOW E-JOINT IS DUE TO GRUPPELAAR3731 1451 92 /15/. 3731 1451 93 3731 1451 94 MT = 1 TOTAL 3731 1451 95 SPHERICAL OPTICAL MODEL CALCULATION WAS ADOPTED. 3731 1451 96 3731 1451 97 MT = 2 ELASTIC SCATTERING 3731 1451 98 CALCULATED AS (TOTAL - SUM OF PARTIAL CROSS SECTIONS). 3731 1451 99 3731 1451 100 MT = 4, 51 - 91 INELASTIC SCATTERING 3731 1451 101 SPHERICAL OPTICAL AND STATISTICAL MODEL CALCULATION WAS 3731 1451 102 ADOPTED. THE LEVEL SCHEME WAS TAKEN FROM REF./16/. 3731 1451 103 3731 1451 104 NO. ENERGY(MEV) SPIN-PARITY 3731 1451 105 GR. 0.0 3/2 - 3731 1451 106 1 0.4030 5/2 - 3731 1451 107 2 0.8458 1/2 - 3731 1451 108 3 1.4630 3/2 - 3731 1451 109 4 1.5785 9/2 + 3731 1451 110 5 1.7410 5/2 - 3731 1451 111 6 2.4150 7/2 + 3731 1451 112 7 2.5560 5/2 + 3731 1451 113 LEVELS ABOVE 2.811 MEV WERE ASSUMED TO BE OVERLAPPING. 3731 1451 114 3731 1451 115 MT = 102 CAPTURE 3731 1451 116 SPHERICAL OPTICAL AND STATISTICAL MODEL CALCULATION WITH 3731 1451 117 CASTHY WAS ADOPTED. DIRECT AND SEMI-DIRECT CAPTURE CROSS 3731 1451 118 SECTIONS WERE ESTIMATED ACCORDING TO THE PROCEDURE OF BENZI 3731 1451 119 AND REFFO/17/ AND NORMALIZED TO 1 MILLI-BARN AT 14 MEV. 3731 1451 120 3731 1451 121 THE GAMMA-RAY STRENGTH FUNCTION (1.125E-04) WAS ADJUSTED TO 3731 1451 122 REPRODUCE THE CAPTURE CROSS SECTION OF 30 MILLI-BARNS AT 25 3731 1451 123 KEV MEASURED BY KONONOV ET AL./18/ FINALLY, THE CROSS SECTION 3731 1451 124 WAS MODIFIED BY MULTIPLYING AN ENERGY-DEPENDENT FACTOR SO AS 3731 1451 125 TO REPRODUCE THE EXPERIMENTAL DATA /19,20/ IN THE ENERGY 3731 1451 126 RANGE FROM 100 KEV TO 10 MEV. 3731 1451 127 3731 1451 128 MT = 16 (N,2N) CROSS SECTION 3731 1451 129 MT = 17 (N,3N) CROSS SECTION 3731 1451 130 MT = 22 (N,N'A) CROSS SECTION 3731 1451 131 MT = 28 (N,N'P) CROSS SECTION 3731 1451 132 MT = 32 (N,N'D) CROSS SECTION 3731 1451 133 MT =103 (N,P) CROSS SECTION 3731 1451 134 MT =104 (N,D) CROSS SECTION 3731 1451 135 MT =105 (N,T) CROSS SECTION 3731 1451 136 MT =107 (N,ALPHA) CROSS SECTION 3731 1451 137 THESE REACTION CROSS SECTIONS WERE CALCULATED WITH THE 3731 1451 138 PREEQUILIBRIUM AND MULTI-STEP EVAPORATION MODEL CODE PEGASUS. 3731 1451 139 3731 1451 140 THE KALBACH'S CONSTANT K (= 322.2) WAS ESTIMATED BY THE 3731 1451 141 FORMULA DERIVED FROM KIKUCHI-KAWAI'S FORMALISM/21/ AND LEVEL 3731 1451 142 DENSITY PARAMETERS. 3731 1451 143 3731 1451 144 FINALLY, THE (N,2N), (N,P) AND (N,ALPHA) CROSS SECTIONS WERE 3731 1451 145 NORMALIZED TO THE FOLLOWING VALUES AT 14.5 MEV: 3731 1451 146 (N,2N) 1300.00 MB (RECOMMENDED BY BYCHKOV+/22/) 3731 1451 147 (N,P) 11.80 MB (RECOMMENDED BY FORREST/23/) 3731 1451 148 (N,ALPHA) 3.80 MB (RECOMMENDED BY FORREST) 3731 1451 149 3731 1451 150 MT = 251 MU-BAR 3731 1451 151 CALCULATED WITH CASTHY. 3731 1451 152 3731 1451 153 MF = 4 ANGULAR DISTRIBUTIONS OF SECONDARY NEUTRONS 3731 1451 154 LEGENDRE POLYNOMIAL COEFFICIENTS FOR ANGULAR DISTRIBUTIONS ARE 3731 1451 155 GIVEN IN THE CENTER-OF-MASS SYSTEM FOR MT=2 AND DISCRETE INELAS-3731 1451 156 TIC LEVELS, AND IN THE LABORATORY SYSTEM FOR MT=91. THEY WERE 3731 1451 157 CALCULATED WITH CASTHY. FOR OTHER REACTIONS, ISOTROPIC DISTRI- 3731 1451 158 BUTIONS IN THE LABORATORY SYSTEM WERE ASSUMED. 3731 1451 159 3731 1451 160 MF = 5 ENERGY DISTRIBUTIONS OF SECONDARY NEUTRONS 3731 1451 161 ENERGY DISTRIBUTIONS OF SECONDARY NEUTRONS WERE CALCULATED WITH 3731 1451 162 PEGASUS FOR INELASTIC SCATTERING FROM OVERLAPPING LEVELS AND FOR3731 1451 163 OTHER NEUTRON EMITTING REACTIONS. 3731 1451 164 3731 1451 165 TABLE 1 NEUTRON OPTICAL POTENTIAL PARAMETERS 3731 1451 166 3731 1451 167 DEPTH (MEV) RADIUS(FM) DIFFUSENESS(FM) 3731 1451 168 ---------------------- ------------ --------------- 3731 1451 169 V = 46.0-0.25E R0 = 5.7 A0 = 0.62 3731 1451 170 WS = 7.0 RS = 6.2 AS = 0.35 3731 1451 171 VSO= 7.0 RSO= 5.7 ASO= 0.62 3731 1451 172 THE FORM OF SURFACE ABSORPTION PART IS DER. WOODS-SAXON TYPE. 3731 1451 173 3731 1451 174 TABLE 2 LEVEL DENSITY PARAMETERS 3731 1451 175 3731 1451 176 NUCLIDE SYST A(1/MEV) T(MEV) C(1/MEV) EX(MEV) PAIRING 3731 1451 177 --------------------------------------------------------------- 3731 1451 178 35-BR- 83 1.324E+01 7.830E-01 2.683E+00 6.978E+00 1.460E+00 3731 1451 179 35-BR- 84 * 1.302E+01 7.738E-01 1.393E+01 5.216E+00 0.0 3731 1451 180 35-BR- 85 1.100E+01 7.000E-01 7.248E-01 3.841E+00 9.300E-01 3731 1451 181 35-BR- 86 * 9.718E+00 7.558E-01 1.999E+00 2.830E+00 0.0 3731 1451 182 3731 1451 183 36-KR- 84 9.970E+00 9.600E-01 4.942E-01 8.590E+00 2.630E+00 3731 1451 184 36-KR- 85 1.024E+01 8.900E-01 1.570E+00 6.261E+00 1.170E+00 3731 1451 185 36-KR- 86 9.052E+00 8.686E-01 2.185E-01 5.874E+00 2.100E+00 3731 1451 186 36-KR- 87 9.400E+00 8.860E-01 8.826E-01 5.481E+00 1.170E+00 3731 1451 187 3731 1451 188 37-RB- 85 1.190E+01 8.690E-01 2.827E+00 7.561E+00 1.460E+00 3731 1451 189 37-RB- 86 1.002E+01 8.500E-01 3.954E+00 4.312E+00 0.0 3731 1451 190 37-RB- 87 8.806E+00 9.410E-01 1.125E+00 5.465E+00 9.300E-01 3731 1451 191 37-RB- 88 9.801E+00 8.185E-01 2.880E+00 3.704E+00 0.0 3731 1451 192 --------------------------------------------------------------- 3731 1451 193 SYST: * = LDP'S WERE DETERMINED FROM SYSTEMATICS. 3731 1451 194 3731 1451 195 SPIN CUTOFF PARAMETERS WERE CALCULATED AS 0.146*SQRT(A)*A**(2/3).3731 1451 196 IN THE CASTHY CALCULATION, SPIN CUTOFF FACTORS AT 0 MEV WERE 3731 1451 197 ASSUMED TO BE 5.214 FOR RB- 87 AND 5.0 FOR RB- 88. 3731 1451 198 3731 1451 199 REFERENCES 3731 1451 200 1) AOKI, T. ET AL.: PROC. INT. CONF. ON NUCLEAR DATA FOR BASIC 3731 1451 201 AND APPLIED SCIENCE, SANTA FE., VOL. 2, P.1627 (1985). 3731 1451 202 2) KAWAI, M. ET AL.: PROC. INT. CONF. ON NUCLEAR DATA FOR SCIENCE3731 1451 203 AND TECHNOLOGY, MITO, P. 569 (1988). 3731 1451 204 3) OHKUBO, M., MIZUMOTO, M., AND KAWARASAKI, Y.: 3731 1451 205 NUCL. SCI. TECH. 21, 254 (1984). 3731 1451 206 4) MUGHABGHAB, S.F. ET AL.: "NEUTRON CROSS SECTIONS, VOL. I, 3731 1451 207 PART A", ACADEMIC PRESS (1981). 3731 1451 208 5) MUGHABGHAB, S.F. AND GARBER, D.I.: "NEUTRON CROSS SECTIONS, 3731 1451 209 VOL. 1, RESONANCE PARAMETERS", BNL 325, 3RD ED., VOL. 1(1973).3731 1451 210 6) IGARASI, S.: J. NUCL. SCI. TECHNOL., 12, 67 (1975). 3731 1451 211 7) IIJIMA, S. ET AL.: JAERI-M 87-025, P. 337 (1987). 3731 1451 212 8) IIJIMA, S. AND KAWAI, M.: J. NUCL. SCI. TECHNOL., 20, 77 3731 1451 213 (1983). 3731 1451 214 9) PEREY, F.G: PHYS. REV. 131, 745 (1963). 3731 1451 215 10) HUIZENGA, J.R. AND IGO, G.: NUCL. PHYS. 29, 462 (1962). 3731 1451 216 11) LOHR, J.M. AND HAEBERLI, W.: NUCL. PHYS. A232, 381 (1974). 3731 1451 217 12) BECCHETTI, F.D., JR. AND GREENLEES, G.W.: POLARIZATION 3731 1451 218 PHENOMENA IN NUCLEAR REACTIONS ((EDS) H.H. BARSHALL AND 3731 1451 219 W. HAEBERLI), P. 682, THE UNIVERSITY OF WISCONSIN PRESS. 3731 1451 220 (1971). 3731 1451 221 13) GILBERT, A. AND CAMERON, A.G.W.: CAN. J. PHYS., 43, 1446 3731 1451 222 (1965). 3731 1451 223 14) IIJIMA, S., ET AL.: J. NUCL. SCI. TECHNOL. 21, 10 (1984). 3731 1451 224 15) GRUPPELAAR, H.: ECN-13 (1977). 3731 1451 225 16) MATSUMOTO, J.: PRIVATE COMMUNICATION (1981). 3731 1451 226 17) BENZI, V. AND REFFO, G.: CCDN-NW/10 (1969). 3731 1451 227 18) KONONOV, V.N., ET AL.: AT. ENERG. 5, 514 (1958). 3731 1451 228 19) DOVBENKO, A.G., ET AL.: ATOM. ENERGIJA, 23, 151 (1967). 3731 1451 229 20) DUDEY, N.D., ET AL.: J. NUCL. ENERG., 24, 181 (1970). 3731 1451 230 21) KIKUCHI, K. AND KAWAI, M.: "NUCLEAR MATTER AND NUCLEAR 3731 1451 231 REACTIONS", NORTH HOLLAND (1968). 3731 1451 232 22) BYCHKOV, V.M. ET AL.: INDC(CCP)-146/LJ (1980). 3731 1451 233 23) FORREST, R.A.: AERE-R 12419 (1986). 3731 1451 234 3731 1451 235 ***************** Program LINEAR (VERSION 2000-1) ***************3731 1451 236 For All Data Greater than 1.00000-10 barns in Absolute Value 3731 1451 237 Data Linearized to Within an Accuracy of 0.10000000 per-cent 3731 1451 238 ***************** Program RECENT (VERSION 2000-1) ***************3731 1451 239 for All Data Greater than 1.00000-10 barns in Absolute Value 3731 1451 240 Data Linearized to within an Accuracy of 0.10000000 per-cent 3731 1451 241 ***************** Program LINEAR (VERSION 2000-1) ***************3731 1451 242 For All Data Greater than 1.00000-10 barns in Absolute Value 3731 1451 243 Data Linearized to Within an Accuracy of 0.10000000 per-cent 3731 1451 244 1 451 287 13731 1451 245 2 151 173 13731 1451 246 3 1 773 13731 1451 247 3 2 703 13731 1451 248 3 4 27 13731 1451 249 3 16 9 13731 1451 250 3 17 4 13731 1451 251 3 22 221 13731 1451 252 3 28 112 13731 1451 253 3 32 162 13731 1451 254 3 51 44 13731 1451 255 3 52 40 13731 1451 256 3 53 38 13731 1451 257 3 54 36 13731 1451 258 3 55 37 13731 1451 259 3 56 33 13731 1451 260 3 57 33 13731 1451 261 3 91 20 13731 1451 262 3 102 1414 13731 1451 263 3 103 176 13731 1451 264 3 104 115 13731 1451 265 3 105 213 13731 1451 266 3 107 191 13731 1451 267 4 2 159 23731 1451 268 4 16 10 13731 1451 269 4 17 10 13731 1451 270 4 22 10 13731 1451 271 4 28 10 13731 1451 272 4 32 10 13731 1451 273 4 51 24 13731 1451 274 4 52 24 13731 1451 275 4 53 22 13731 1451 276 4 54 22 13731 1451 277 4 55 22 13731 1451 278 4 56 22 13731 1451 279 4 57 22 13731 1451 280 4 91 22 13731 1451 281 5 16 45 23731 1451 282 5 17 18 23731 1451 283 5 22 109 23731 1451 284 5 28 85 23731 1451 285 5 32 30 23731 1451 286 5 91 100 23731 1451 287 3731 1 099999 3731 0 0 0 3.708700+4 8.616260+1 0 0 1 03731 2151 1 3.708700+4 1.000000+0 0 0 2 03731 2151 2 1.000000-5 1.246000+4 1 2 0 03731 2151 3 1.500000+0 7.100000-1 0 0 2 03731 2151 4 8.616260+1 0.000000+0 0 0 168 283731 2151 5 3.769000+2 2.000000+0 9.553300-1 8.400000-1 1.153300-1 0.000000+03731 2151 6 3.823300+3 2.000000+0 2.283500+1 2.272000+1 1.150000-1 0.000000+03731 2151 7 5.115000+3 1.000000+0 6.144830+1 6.133330+1 1.150000-1 0.000000+03731 2151 8 7.344000+3 2.000000+0 6.035000+0 5.920000+0 1.150000-1 0.000000+03731 2151 9 7.560000+3 1.000000+0 1.294480+2 1.293330+2 1.150000-1 0.000000+03731 2151 10 8.768000+3 2.000000+0 1.721150+2 1.720000+2 1.150000-1 0.000000+03731 2151 11 9.840000+3 2.000000+0 1.859000+0 1.744000+0 1.150000-1 0.000000+03731 2151 12 1.034600+4 2.000000+0 8.350000-1 7.200000-1 1.150000-1 0.000000+03731 2151 13 1.106000+4 2.000000+0 1.947500+1 1.936000+1 1.150000-1 0.000000+03731 2151 14 1.386500+4 2.000000+0 6.915000+0 6.800000+0 1.150000-1 0.000000+03731 2151 15 1.851000+4 2.000000+0 1.643500+1 1.632000+1 1.150000-1 0.000000+03731 2151 16 2.196000+4 2.000000+0 1.243500+1 1.232000+1 1.150000-1 0.000000+03731 2151 17 2.313000+4 1.000000+0 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