coulomb excitation data analysis codes; gosia 2007 - Physics and ...

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RECOMMENDED RELATIVE GE(LI) EFFICIENCIESEXPERIMENT1 0.10E+012 0.10E+013 0.10E+014 0.10E+015 0.10E+016 0.10E+017 0.10E+018 0.10E+019 0.10E+0110 0.10E+0111 0.10E+0112 0.10E+0113 0.10E+0114 0.10E+0115 0.10E+0116 0.10E+0117 0.10E+0118 0.10E+0119 0.10E+0120 0.10E+0121 0.10E+0122 0.10E+0123 0.10E+0124 0.10E+0125 0.10E+0126 0.10E+0127 0.10E+01Initial (NI) and final (NF) states ofthe gamma-decay transition.Gamma-decay yields calculated from finalmatrix elements at chi-squared minimum(YCAL) and “corrected” experimental yields(YEXP). Note that these are pointapproximations.CALCULATED AND EXPERIMENTAL YIELDS EXPERIMENT 1 DETECTOR 1NI NF II IF ENERGY(MEV) YCAL YEXP PC. DIFF. (YE-YC)/SIGMA5 4 8.0 6.0 0.4268 .2884E+00 .3088E+00 6.6 1.34 3 6.0 4.0 0.3256 .3843E+01 .3937E+01 2.4 0.53 2 4.0 2.0 0.2134 .2372E+02 .2588E+02 8.4 1.72 1 2.0 0.0 0.0932 .2082E+02 .2230E+02 6.6 1.3Initial and final spin of the transition.CHISQ SUBTOTAL = 0.637868E+01CALCULATED AND EXPERIMENTAL YIELDS EXPERIMENT 2 DETECTOR 1NI NF II IF ENERGY(MEV) YCALPercent discrepancyYEXP PC. DIFF. (YE-YC)/SIGMA6 5 10.0 8.0 0.5120 .1007E+00 .9742E-01 -3.4 -0.75 4 8.0 6.0 0.4268 .9732E+00 between .9889E+00 calculated and 1.6 0.34 3 6.0 4.0 0.3256 .7974E+01 experimental .7896E+01 yields. -1.0 -0.23 2 4.0 2.0 0.2134 .3017E+02 .3249E+02 7.2 1.42 1 2.0 0.0 0.0932 .1643E+02 .1627E+02 -1.0 -0.2Discrepancy expressedas a fraction of the errorin the experimentalvalues.CHISQ SUBTOTAL = 0.265775E+01182
CALCULATED AND EXPERIMENTAL YIELDS EXPERIMENT 3 DETECTOR 1NI NF II IF ENERGY(MEV) YCAL YEXP PC. DIFF. (YE-YC)/SIGMA6 5 10.0 8.0 0.5120 .3698E+00 .3562E+00 -3.8 -0.85 4 8.0 6.0 0.4268 .2393E+01 .2507E+01 4.5 0.94 3 6.0 4.0 0.3256 .1281E+02 .1357E+02 5.6 1.23 2 4.0 2.0 0.2134 .3196E+02 .3402E+02 6.0 1.22 1 2.0 0.0 0.0932 .1203E+02 .1214E+02 0.9 0.2CHISQ SUBTOTAL = 0.428679E+01CALCULATED AND EXPERIMENTAL YIELDS EXPERIMENT 4 DETECTOR 1NI NF II IF ENERGY(MEV) YCAL YEXP PC. DIFF. (YE-YC)/SIGMA7 6 12.0 10.0 0.5800 .1370E+00 .1303E+00 -5.2 -1.16 5 10.0 8.0 0.5120 .9888E+00 .9104E+00 -8.6 -1.75 4 8.0 6.0 0.4268 .4513E+01 .4739E+01 4.8 0.94 3 6.0 4.0 0.3256 .1652E+02 .1704E+02 3.0 0.63 2 4.0 2.0 0.2134 .2907E+02 .3226E+02 9.9 2.12 1 2.0 0.0 0.0932 .8517E+01 .8516E+01 0.0 0.0CHISQ SUBTOTAL = 0.968194E+01The agreement between the calculated gamma-ray yields and the experimental values (at the chisquaredminimum) is tabulated by logical experiment number (first) and detector number (second).Note that these are the result of point approximations that have been scaled by correction factors toapproximate integrated values. The yields should be integrated again using the final set of matrixelements in order to make an accurate comparison with the original experimental data and toensure that the point approximation remains valid at the chi-squared minimum. (In some cases asecond iteration of the fit may be required. Refer to the tutorial in this chapter.)Experiments 4-26 skipped for brevity.CALCULATED AND EXPERIMENTAL YIELDS EXPERIMENT 27 DETECTOR 1NI NF II IF ENERGY(MEV) YCAL YEXP PC. DIFF. (YE-YC)/SIGMA10 9 18.0 16.0 0.6850 .1738E+00 .2005E+00 13.3 2.89 8 16.0 14.0 0.6580 .4521E+00 .4482E+00 -0.9 -0.28 7 14.0 12.0 0.6270 .8240E+00 .8760E+00 5.9 1.37 6 12.0 10.0 0.5800 .1071E+01 .1142E+01 6.2 1.36 5 10.0 8.0 0.5120 .1283E+01 .1262E+01 -1.7 -0.35 4 8.0 6.0 0.4268 .1556E+01 .1562E+01 0.4 0.14 3 6.0 4.0 0.3256 .1681E+01 .1735E+01 3.1 0.73 2 4.0 2.0 0.2134 .1651E+01 .1616E+01 -2.2 -0.42 1 2.0 0.0 0.0932 .4006E+00 .3747E+00 -6.9 -1.3CHISQ SUBTOTAL = 0.138775E+02183
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COULOMB EXCITATION DATA ANALYSIS CO
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10 MINIMIZATION BY SIMULATED ANNEAL
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1 INTRODUCTION1.1 Gosia suite of Co
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104 Ru, 110 Pd, 165 Ho, 166 Er, 186
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Figure 1: Coordinate system used to
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Cλ E =1.116547 · (13.889122) λ (
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Figure 2: The orbital integrals R 2
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2.2 Gamma Decay Following Electroma
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where :d 2 σ= σ R (θ p ) X R kχ
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Formula 2.49 is valid only for t mu
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Ã XK(α) =exp−iτ i (E γ )x i (
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important to have an accurate knowl
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3 APPROXIMATE EVALUATION OF EXCITAT
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with the reduced matrix element M c
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q (20)s (0 + → 2 + ) · M 1 ζ (2
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esults of minimization and error ru
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adjustment of the stepsize accordin
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approximation reliability improves
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Zd 2 σ(I → I f )Y (I → I f )=s
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4.5 MinimizationThe minimization, i
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X(CC k Yk c − Yk e ) 2 /σ 2 k =m
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However, estimation of the stepsize
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It can be shown that as long as the
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een exceeded; third, the user-given
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where f k stands for the functional
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x i + δx i Rx iexp ¡ − 1 2 χ2
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method used for the minimization, i
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OP,ERRO (ERRORS) (5.6):Activates th
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-----OP,SIXJ (SIX-j SYMBOL) (5.25):
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5.3 CONT (CONTROL)This suboption of
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I,I1 Ranges of matrix elements to b
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CODE DEFAULT OTHER CONSEQUENCES OF
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5.4 OP,CORR (CORRECT )This executio
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5.6 OP,ERRO (ERRORS)ThemoduleofGOSI
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5.7 OP,EXIT (EXIT)This option cause
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M AControls the number of magnetic
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5.10 OP,GDET (GE DETECTORS)This opt
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5.12 OP,INTG (INTEGRATE)This comman
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¡ dE¢dx1 ..¡ dEdx¢Stopping powe
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NI1, NI2 Number of subdivisions of
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5.13 LEVE (LEVELS)Mandatory subopti
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5.15 ME (OP,COUL)Mandatory suboptio
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Figure 10: Model system having 4 st
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ME =< INDEX2||E(M)λ||INDEX1 > The
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When entering matrix elements in th
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There are no restrictions concernin
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5.18 OP,POIN (POINT CALCULATION)Thi
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5.20 OP,RAW (RAW UNCORRECTED γ YIE
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5.21 OP,RE,A (RELEASE,A)This option
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5.25 OP,SIXJ (SIXJ SYMBOL)This stan
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5.27 OP,THEO (COLLECTIVE MODEL ME)C
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2,5,1,-2,23,5,1,-2,23,6,1,-2,2Matri
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5.29 OP,TROU (TROUBLE)This troubles
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to that of the previous experiment,
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To reduce the unnecessary input, on
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OP,STAR or OP,POIN under OP,GOSI. N
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5.31 INPUT OF EXPERIMENTAL γ-RAY Y
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6 QUADRUPOLE ROTATION INVARIANTS -
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*½P 5 (J) = s(E2 × E2) J ×¯h¾
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The expectation value of cos3δ can
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where ē is an arbitratry vector. D
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achieved using “mixed“ calculat
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TAPE9 Contains the parameters neede
Page 131 and 132: TAPE18 Input file, containing the i
Page 133 and 134: 7.4.4 CALCULATION OF THE INTEGRATED
Page 135 and 136: OP,EXITInput: TAPE4,TAPE7,TAPE9Outp
Page 137 and 138: OP,ERRO0,MS,MEND,1,0,RMAXand the fi
Page 139 and 140: 8 SIMULTANEOUS COULOMB EXCITATION:
Page 141 and 142: 4, 3, 1kr88.corKr corrected yields
Page 143 and 144: 0 Correction for in-flight decay ch
Page 145 and 146: OP, ERRO Estimation of errors of fi
Page 147 and 148: 9 COULOMB EXCITATION OF ISOMERIC ST
Page 149 and 150: configurations with a probability e
Page 151 and 152: The average range covered by each m
Page 153 and 154: SFX,NTOTI1(1),I2(1),RSIGN(1)I1(2),I
Page 155 and 156: 11.2 LearningtoWriteGosiaInputsThe
Page 157 and 158: (1.6 MeV)1.1 MeV0.75 MeV0.4 MeV0.08
Page 159 and 160: Define the germaniumdetector geomet
Page 161 and 162: Figure 15: Flow diagram for Gosia m
Page 163 and 164: gosia < 2-make-correction-factors.i
Page 165 and 166: Issue the commandgosia < 9-diag-err
Page 167 and 168: At this point, it is suggested to c
Page 169 and 170: calculation.) In this case, a copy
Page 171 and 172: 4,-4, -3.705, 3,44,5, 4.626, 3.,7.5
Page 173 and 174: 90145901459014590145901459014590145
Page 175 and 176: .10.028921.10.026031.10.023431.10.0
Page 177 and 178: 5,5,634,650,82.000,84.000634,638,64
Page 179 and 180: ***********************************
Page 181: *** CHISQ= 0.134003E+01 ***MATRIX E
Page 185 and 186: 11.7 Annotated excerpt from a Coulo
Page 187 and 188: 11.8 Accuracy and speed of calculat
Page 189 and 190: 18,10.056,0.068,0.082,0.1,0.12,0.15
Page 191 and 192: line 152 Eu 182 Tanumber (keV) (keV
Page 193 and 194: 1.6 Normalization between data sets
Page 195 and 196: 13 GOSIA 2007 RELEASE NOTESThese no
Page 197 and 198: Matrix elements 500(April 1990, T.
Page 199 and 200: 14 GOSIA Manual UpdatesDATE UPDATE2
Page 201 and 202: [KIB08]T.Kibédi,T.W.Burrows,M.B.Tr
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