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

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Note that the definition of reduced matrix element does not include the i λ term for the Eλ matrixelements used in the original Winther-deBoer semiclassical Coulomb excitation code (WI66). The Eλ matrixelements are given in units of e.barns λ/2 i.e., e (10 −28 m 2 ) λ/2 .TheMλ matrix elements are given in units ofμ n barns (λ−1)/2 . Within a given multipolarity, only matrix elements in the upper triangle, i.e. INDEX2 ≥INDEX1, should be given. Matrix elements in the lower triangle are set by the program. Within a givenmultipolarity both INDEX1 and INDEX2 columns must appear in increasing order (odometer ordering).The header of the next multipolarity ends input for a given multipolarity. A single record of 3 zeros endsthe input to ME.RESTRICTIONS:Note that the sequence of matrix elements is uniquely set by the input conventions. An error messagewill be printed and the job aborted if any of the following restrictions are violated.a. Multipolariaties must appear in order from lowest to highest starting with Eλ and then Mλ.b. Matrix elements must belong to the upper triangle, i.e., INDEX2 ≥ INDEX1.c. INDEX values must be in increasing order, i.e. odometer order.MATRIX ELEMENT PHASES:Note that the phase of a wavefunction is arbitrary. However, to facilitate comparison with models itis best to fix the relative phases of states. Choosing one matrix element between two states to be positivecouples the relative phases of the wavefunctions of these two states to be the same. Then the phases of anyother matrix elements coupling these two states, relative to the phase of the positive one, are observables.Consequently for typical collective bands it is convenient to choose the primary ∆I =2,E2 transitions inthe band to have a positive phase locking the state wavefunctions of the band to have the same phase. Inaddition the phase of one strong matrix element connecting two separate collective bands locks the relativephase between these collective bands.When entering matrix elements in the upper triangle be careful to enter the correct phase rememberingthat time reversal invariance relates the time-reversed matrix elements by=(−) J1−J2−λ Thus the phase of the matrix elements in the lower triangle is related to the upper triangle phase bythe (−) J 1−J 2 −λ phase term. Similar care must be taken comparing the observed relative phases with modelpredictions.88
Figure 10: Model system having 4 states with E2 and M1 coupling. The 2 + 1 − 2+ 2 coupling is assumed to beof mixed M1 and E2 character.EXAMPLE:An example of the use of the suboptions LEVE and ME for a OP,COUL calculation is given below.Consider the definition for the following nuclear level scheme shown in the figure.OP,TITLExample of definition of nucleusOP,COULLEVE1, 1, 0, 0 - Ground state is given index “1“.2, 1, 2, 0.5003, 1, 4, 1.0004, 1, 2, 0.7500, 0, 0, 0 - Ends LEVE input.ME2, 0, 0 E2 - matrix elements. All E2 matrix elements1, 2, 1.0 equal to 1.0 e.barns.1, 4, 1.02, 2, 1.0 INDEX1 and INDEX2 - in increasing order.2, 3, 1.02, 4, 1.03, 3, 1.04, 4, 1.07, 0, 0 - Terminates input for E2. Starts input for2, 4, 1 M1 - matrix element equal to 1mN.0, 0, 0 End ME input.89
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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
Page 37 and 38: adjustment of the stepsize accordin
Page 39 and 40: approximation reliability improves
Page 41 and 42: 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: 5.15 ME (OP,COUL)Mandatory suboptio
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 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
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8 SIMULTANEOUS COULOMB EXCITATION:
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4, 3, 1kr88.corKr corrected yields
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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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