· in- <strong>and</strong> interb<strong>and</strong> couplings for the first multipolarity are exhausted·0, 0 Ends first multipolarity definitionλ 2Second multipolarityNB i , NB jQ1, Q2, Q3···0, 0 Ends second multipolarity definition···0 Ends multipolarity loop <strong>and</strong> the input to OP, THEOExample:Assume an even-even nucleus X with two b<strong>and</strong>s - a ground state b<strong>and</strong> <strong>and</strong> a gamma-vibrational b<strong>and</strong>.The LEVE <strong>and</strong> ME setup is as follows:LEVE1,1,0,02,1,.2,.2 Levels 1,2,3 form the ground-state b<strong>and</strong>, while 4,5,6 form the gamma b<strong>and</strong>3,1,4,.54,1,2,.75,1,3,1.16,1,4,1.50,0,0,0ME2,0,0,0,01,2,1,-2,21,4,1,-2,22,2,1,-2,22,3,1,-2,22,5,1,-2,22,6,1,-2,23,3,1,-2,23,5,1,-2,23,6,1,-2,24,4,1,-2,24,5,1,-2,24,6,1,-2,25,6,1,-2,26,6,1,-2,27,0,0,0,02,4,1,-2,2106
2,5,1,-2,23,5,1,-2,23,6,1,-2,2Matrix elements on the restart file can be generated by OP, THEO using the following sequence:OP, THEO2 Two b<strong>and</strong>s0,3 K of the gsb, # of levels1,2,3 Level list for the gsb2,3 K of the gamma b<strong>and</strong>, # of levels4,5,6 Level list for the gamma b<strong>and</strong>2 Multipolarity E21,1 In-b<strong>and</strong>, gsb1,0,0 Q1, two zeros irrelevant1,2 Interb<strong>and</strong> E21,1,0 Q1,Q2- Mikhailov formula, none of the K’s=1/2, so Q3 irrelevant2,2 In-b<strong>and</strong>, gamma b<strong>and</strong>1,0,0 In-b<strong>and</strong> Q1, Q2 <strong>and</strong> Q3 irrelevant0,0 Ends E2 loop7 M1 loop1,2 Interb<strong>and</strong> M11,1,0 Q1 <strong>and</strong> Q2 for Mikhailov formula2,2 In-b<strong>and</strong> M11,0,0 Q1 for in-b<strong>and</strong> transitions0,0 Ends M1 loop0 Ends multipolarity loop <strong>and</strong> OP, THEO inputAs a result, the restart file will be created overriding the values of matrix elements as given in ME input.If the first entry, NBANDS, is changed to -2 OP, THEO will become inactive.107
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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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à 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
- 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 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: 5.27 OP,THEO (COLLECTIVE MODEL ME)C
- 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 ׯh¾
- 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
- 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
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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