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

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5.17 OP,MINI (MINIMIZE)This command causes execution of the least-squares fitting of matrix elements to the experimental data.Refer to Section 4.5 for an explanation of the procedures used for the least-square search. The startingset of matrix elements used by OP,MINI depends on the other option commands specified. If OP,RANDis specified then OP,MINI uses the set of random numbers generated by OP,RAND as the set of startingmatrix elements. If OP,REST is specified, then the starting set of matrix elements is read from TAPE2. Ifneither OP,RAND nor OP,REST are specified then the matrix elements input using the suboption ME areused as a starting set. Completion of an OP,MINI command causes the set of matrix elements resulting fromminimization to be written onto TAPE2. This current set can be used as a new starting point for continuedminimization.The OP,MINI command provides various switches to allow those matrix elements satisfying certaincriteria to be locked during the current minimization procedure. This reduction of the number of freevariables can greatly speed up the minimization procedure. The FIX command in the suboption CONTprovides another mechanism for fixing matrix elements (see Section 5.3). Sections 7.4.6 and 7.4.7 show thecorrect location of OP,MINI in the input stream.The input to OP,MINI comprises the title plus one record, i.e.OP,MINIIMODE,NPTL,CHILIM,CONV,TEST,LOCKF,NLOCK,IFBL,LOCKS,DLOCKwhere:IMODEMode selector. IMODE should be defined as a four-digit number IJKL where:I= 1or 2I =1specifies that the fast approximation will be used to calculate both S (Eq.4.24) and its partialderivatives.I =2implies that S will be calculated using the full Coulomb excitation formalism while its derivativesstill will be estimated using the fast approximation.Use of I =1is recommended for almost all applications. The time required to complete the minimizationstep using I =2is about an order of magnitude greater than when using I =1. The use of I =2should be reserved for small cases or for cases requiring extreme accuracy in locating the minimum.The TEST switch, described below, provides a more efficient way of retaining high accuracy thanusing I =2.J =0or 1J =0selects the simple steepest descent minimization while J =1selects the gradient and gradientderivative method (see Section 4.5).K =0or 1K =0 implies that the absolute changes in matrix elements will be used to improve the minimumwhile K =1requests the use of the relative changes. To first order K =1corresponds to using thelogarithms of matrix elements as independent variables instead of the matrix elements themselves, aswhen K =0.L =0or 1L =0specifies that the experimental yields, branching ratios etc. will be used as dependent variablesto construct the S function while L =1requests that a logarithmic scale will be used for dependentvariables.94
There are no restrictions concerning the selection of the above switches and any combination can beused. Proper selection of IMODE can speed up the minimization procedure appreciably and is casedependentNPTLCHILIMThe maximum number of steps of minimization allowed.The S criterion to stop minimization. That is, the minimization terminates if S< CHILIM.CONV The convergence criterion to stop minimization when | ¯M i+1 − ¯M i |
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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
Page 43 and 44: 4.5 MinimizationThe minimization, i
Page 45 and 46: X(CC k Yk c − Yk e ) 2 /σ 2 k =m
Page 47 and 48: However, estimation of the stepsize
Page 49 and 50: It can be shown that as long as the
Page 51 and 52: een exceeded; third, the user-given
Page 53 and 54: where f k stands for the functional
Page 55 and 56: x i + δx i Rx iexp ¡ − 1 2 χ2
Page 57 and 58: method used for the minimization, i
Page 59 and 60: OP,ERRO (ERRORS) (5.6):Activates th
Page 61 and 62: -----OP,SIXJ (SIX-j SYMBOL) (5.25):
Page 63 and 64: 5.3 CONT (CONTROL)This suboption of
Page 65 and 66: I,I1 Ranges of matrix elements to b
Page 67 and 68: CODE DEFAULT OTHER CONSEQUENCES OF
Page 69 and 70: 5.4 OP,CORR (CORRECT )This executio
Page 71 and 72: 5.6 OP,ERRO (ERRORS)ThemoduleofGOSI
Page 73 and 74: 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: When entering matrix elements in th
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 and 126: where ē is an arbitratry vector. D
Page 127 and 128: achieved using “mixed“ calculat
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
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OP, ERRO Estimation of errors of fi
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9 COULOMB EXCITATION OF ISOMERIC ST
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configurations with a probability e
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The average range covered by each m
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SFX,NTOTI1(1),I2(1),RSIGN(1)I1(2),I
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11.2 LearningtoWriteGosiaInputsThe
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(1.6 MeV)1.1 MeV0.75 MeV0.4 MeV0.08
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Define the germaniumdetector geomet
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Figure 15: Flow diagram for Gosia m
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gosia < 2-make-correction-factors.i
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Issue the commandgosia < 9-diag-err
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At this point, it is suggested to c
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calculation.) In this case, a copy
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4,-4, -3.705, 3,44,5, 4.626, 3.,7.5
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90145901459014590145901459014590145
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.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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