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

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are available using positive and negative values of ∆M k . In addition, J ki can be evaluated using the i-thcomponent of the gradient at perturbed M k or using the k-th component of the gradient with perturbedM i . Since the quadratic approximation 6.1 is not fully adequate, the averaging procedure must be used tocancel the difference between various estimates and to preserve the symmetry of J. Furthermore, for thematrix elements M k for which the full error calculation was not performed only the diagonal element J kk isassumed to be non-zero, i.e., the correlation is neglected. The estimate of J kk is this case results from:∆S =1= 1 2 J kk∆M k (6.42)where ∆M k is the average diagonal error of M k , i.e., the mean value of the negative and positive deviations.The method presented above allows to estimate the errors of the collective parameters and their distributionswith the reasonable efficiency. However, one must be aware of the scope of the approximationsused, which do not allow treating the estimated errors very rigorously, providing only a crude estimate ofthe determined accuracy the sum rules.6.2.3 INPUT INSTRUCTIONSSIGMA reads in the input file, which must be called SIGMA.INP and in addition three permanent filescreated by GOSIA, referred to in SIGMA as filename.err [TAPE11], filename.smr [TAPE12] and sixj.tab[TAPE3].The input file selects the mode of calculation and should be given as:ILNSTI(1)I(2)filename.smr corresponding to SIGMA TAPE12filename.err corresponding to SIGMA TAPE11sixj.tab corresponding to SIGMA TAPE3· only if 0< NST ≤ 75I(NST)That is, the input file comprises two switches, three filenames, followed by the list of states for which allerrors are to be calculated (NST records) where:IL may be either 0 or 1. IL =1will cause the printout of the matrix elements (by their indices)involved in the evaluation of 14 invariants calculated for each state. The invariants are numbered from 1 to14 according to the sequence they appear in the first column of the output table (see the sample output atthe end of this chapter). IL =0will cause no compilation of this list.NST selects the mode of error calculation. Three special values of NST: NST = −1, NST =0orNST =99require no further input. NST = −1 is used if only the invariants and the resulting statisticalmoments (given in the second column of the output table) are to be calculated and no error estimation isrequested. In this mode SIGMA can be used independently of GOSIA and the information concerning thelevel scheme and coupling scheme, normally produced by GOSIA, must be provided by the user (see thedescription of the TAPE files below). NST =0implies that the error calculation is to be performed onlyfor Q 2 ,threevaluesofv(Q 2 ) and four values of cos3δ for all states, while NST =99specifies the errors tobe estimated for every statistical moment for all states. The reason for this distinction is that the statisticalmoments based on the sixth-order invariants are usually not meaningful due to the number of the matrixelements involved and the resulting error propagation. Also, calculation of these invariants is most timeconsuming.Usually, it is practical to calculate all the errors only for the few lowest-lying states. This can be126
achieved using “mixed“ calculation mode, specified by 0< NST ≤ 75. Inthiscase,NST has the meaning ofthe number of states for which the “full“ calculation is to be done, while for the remaining states the “fast“mode, corresponding to NST =0will be used. In this mode the list of state indices (NST records) mustfollow.Note that the errors quoted are the errors of the statistical moments (column 2 of the output table), notof the invariants listed in the first column.An example is:00nd.smrnd150.errsixj.tabPermanent Files:TAPE11 This file contains the errors of the matrix elements and is written by GOSIA as TAPE15. Itis not required if NST = −1. Usethefilename explicitly in the input, e.g. nd150.errTAPE3 Contains the table of the 6-j symbols used for the calculation of the invariants. This table can becreated by GOSIA with OP,SIXJ (see 5.25). GOSIA writes the table on TAPE14.TAPE12 This file is written by GOSIA during full error calculation on TAPE3 if the CONT switchSMR, is set. TAPE12 contains the level scheme, the coupling scheme and the set of gradients used toevaluate the J matrix. Use filename explicitly in th einput, e.g.nd150.smr. If SIGMA is to be usedindependently of GOSIA, (i.e., only if NST = −1) apartofthisfile must be prepared by the user.The format of this portion of TAPE12 should be the following:NS, NME, NI, NFwhereNS = number of statesINDEX(1), SPIN(1), ENERGY(1)· Level scheme· NS recordsNME =number of matrix elementsNI =index of a first E2 matrix elementNF =index of a last E2 matrix elementINDEX(NS), SPIN(NS), ENERGY(NS)IME(1), INI(1), INF(1) Coupling scheme. IME is the index of matrix element,· INI is the index of an initial state· INF is the index of a final state.· The GOSIA convention applies to the ordering of the matrix elements (see 5.15).IME(NME), INI(NME), INF(NME)IME(1), ME(1)· NME records·IME(NME), ME(NME)Values of the matrix elements.0, 0 Two zeros terminate the input.NME records.127
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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
Page 75 and 76: M AControls the number of magnetic
Page 77 and 78: 5.10 OP,GDET (GE DETECTORS)This opt
Page 79 and 80: 5.12 OP,INTG (INTEGRATE)This comman
Page 81 and 82: ¡ dE¢dx1 ..¡ dEdx¢Stopping powe
Page 83 and 84: NI1, NI2 Number of subdivisions of
Page 85 and 86: 5.13 LEVE (LEVELS)Mandatory subopti
Page 87 and 88: 5.15 ME (OP,COUL)Mandatory suboptio
Page 89 and 90: Figure 10: Model system having 4 st
Page 91 and 92: ME =< INDEX2||E(M)λ||INDEX1 > The
Page 93 and 94: When entering matrix elements in th
Page 95 and 96: There are no restrictions concernin
Page 97 and 98: 5.18 OP,POIN (POINT CALCULATION)Thi
Page 99 and 100: 5.20 OP,RAW (RAW UNCORRECTED γ YIE
Page 101 and 102: 5.21 OP,RE,A (RELEASE,A)This option
Page 103 and 104: 5.25 OP,SIXJ (SIXJ SYMBOL)This stan
Page 105 and 106: 5.27 OP,THEO (COLLECTIVE MODEL ME)C
Page 107 and 108: 2,5,1,-2,23,5,1,-2,23,6,1,-2,2Matri
Page 109 and 110: 5.29 OP,TROU (TROUBLE)This troubles
Page 111 and 112: to that of the previous experiment,
Page 113 and 114: To reduce the unnecessary input, on
Page 115 and 116: OP,STAR or OP,POIN under OP,GOSI. N
Page 117 and 118: 5.31 INPUT OF EXPERIMENTAL γ-RAY Y
Page 119 and 120: 6 QUADRUPOLE ROTATION INVARIANTS -
Page 121 and 122: *½P 5 (J) = s(E2 × E2) J ×¯h¾
Page 123 and 124: The expectation value of cos3δ can
Page 125: where ē is an arbitratry vector. D
Page 129 and 130: 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
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5,5,634,650,82.000,84.000634,638,64
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***********************************
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*** CHISQ= 0.134003E+01 ***MATRIX E
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CALCULATED AND EXPERIMENTAL YIELDS
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11.7 Annotated excerpt from a Coulo
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11.8 Accuracy and speed of calculat
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18,10.056,0.068,0.082,0.1,0.12,0.15
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line 152 Eu 182 Tanumber (keV) (keV
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1.6 Normalization between data sets
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13 GOSIA 2007 RELEASE NOTESThese no
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Matrix elements 500(April 1990, T.
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14 GOSIA Manual UpdatesDATE UPDATE2
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[KIB08]T.Kibédi,T.W.Burrows,M.B.Tr
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