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

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5.8 EXPT (Mandatory suboption of OP,COUL and OP,GOSI)This suboption provides input of the experimental conditions used for the various experiments to be analyzed.Theexperimentsaredefined by mean values of projectile energy and scattering angle, which are used for“point“ excitation/deexcitation calculations. The realistic approach must include integration of γ-ray yieldsover finite ranges of bombarding energy and scattering angles. This feature is provided by OP,INTG whichshould be used to reproduce observed γ yields. As described in Chapter 4, GOSIA uses “point“ energyand scattering angles to execute all modules except for the integration module activated by OP,INTG. Theoptions OP,INTG and OP,CORR are used to convert experimental γ yields to “point“ values. Mean valuesof bombarding energy and scattering angle used by OP,CORR are the ones given in the EXPT input. EXPTshould follow LEVE in OP,GOSI or OP,COUL.The input to EXPT is as follows:EXPTNEXP,Z 1 ,A 1±Z n ,±A n ,E p ,±θ LAB ,M c ,M a ,IAX,φ 1 ,φ 2 ,IKIN,LN··There needs to be NEXP records equal to the number of experiments. The experiments will be numberedby the code according to the sequence of these records from 1 to NEXP. A detailed explanation of entries isgiven below.NEXP The number of experiments defined in the input. Each experiment corresponds to a particularcombination of bombarding energy, scattering angle, experimental detector arrangement and (Z, A)of the nucleus exciting the nucleus being investigated. (NEXP ≤ 50).Z 1A 1Charge number of the investigated nucleus (Integer format).Mass (in units of amu) of the investigated nucleus.Z n Charge number of the uninvestigated nucleus. A positive value signifies target excitation, i.e.,Z n =Z projecticle . A negative value signifies projectile excitation, i.e., Z n = Z t arg et (Integer format).A nE PMass (in the units of amu) of the uninvestigated nucleus. A n will thus correspond to the projectilemass if Z n is positive and target mass if Z n is negative. A negative sign appended to A n signifies thatthis is a “thick“ target experiment, that is, the beam is completely stopped in the target. This latteroption has the time saving feature of switching off some irrelevant calculations such as the deorientationeffect and recoil velocity correction.The mean projectile bombarding energy, in the laboratory frame of reference, to be used for calculatingthe Coulomb excitation yields for the particular experiment. Input in units of MeV.θ LABThe mean scattering angle must be positive if the projectile is detected. A negative sign shouldbe given with the true value of the projectile scattering angle if the recoiling target nucleus has beendetected to ensure the selection of the proper kinematics. Note that by definition θ LAB is alwayspositive, the sign being only used by the code to set appropriate flags.M CControls the number of magnetic substates to be included in the full Coulomb excitation calculations.For a given ground state polarization M o , the magnetic substates in the range (M o − M c ,M o + M c ) will be included for each level. The code takes care of the obvious limitations in magneticsubstates set by the spins of the states. M c =0corresponds to the conservation of magnetic quantumnumber as occurs for backscattering.74
M AControls the number of magnetic substates to be included in the approximate Coulomb excitationcalculation. The meaning of M A isthesameasforM C , namely magnetic substates in the range(M o − M a , M o + M a ) will be included for all states for a given ground state polarization M o ). Theonly allowed values of M a are 0 or 1.IAXThe axial symmetry flag which can take values of 0 or 1 only. Zero defines axial symmetry of theparticle detector, in which case further input is simplified and the calculations are speeded up. Unityimplies that axial symmetry is not assumed.φ 1 , φ 2 The azimuthal angular limits of the particle detector (in degrees). The coordinate system usedhas the z axis in the direction of the incoming beam. The x and y axes can be definedinanyconvenientway provided that the angles of all detectors are given relative to the same cooordinate system. Notethat φ 2 must be larger than φ 1 .IKIN The kinematics flag which can take values of 0 and 1 only. If A Pr ojectile >A T arg et, IKINspecifies which of the two possible kinematic solutions to choose. IKIN =0implies that the solutionhaving the larger center-of-mass scattering angle is chosen. Redundant if A Pr ojectile
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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
Page 23 and 24: Formula 2.49 is valid only for t mu
Page 25 and 26: Ã XK(α) =exp−iτ i (E γ )x i (
Page 27 and 28: important to have an accurate knowl
Page 29 and 30: 3 APPROXIMATE EVALUATION OF EXCITAT
Page 31 and 32: with the reduced matrix element M c
Page 33 and 34: q (20)s (0 + → 2 + ) · M 1 ζ (2
Page 35 and 36: 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: 5.7 OP,EXIT (EXIT)This option cause
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
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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
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TAPE18 Input file, containing the i
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7.4.4 CALCULATION OF THE INTEGRATED
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OP,EXITInput: TAPE4,TAPE7,TAPE9Outp
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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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