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

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do not include σ R (θ p ) · sin(θ p ). Y Point (I → I f ) is given by equation 4.16. See also section 5.18, OP.POINThe experimental values are compared to the calculated Y Mini (I → I f ) which do include the σ R (θ p ) ·sin(θ p ) term. Thus these missing terms in Y Mini (I → I f ) are absorbed into the normalization constants foreach experiment.96
5.18 OP,POIN (POINT CALCULATION)This option command causes execution of a calculation of the γ-ray yields for one scattering angle andone bombarding energy as specified for each experiment in EXPT. OP,POIN can be used to simulate’corrected’ experimental γ yields. In this mode OP,POIN also generates a ’corrected experimental yieldsfile’ on TAPE4, which can be used subsequently for simulating the real experiments (e.g. to analyze theinfluence of the matrix elements on the supposedly observed yields). Note: when executing OP,POIN oneshould set the experimental yields file selector (NTAP in OP,YIEL input) to 0 - see 5.29. Section 7.4.3 showsthe correct location of OP,POIN in the input stream.The input to OP,POIN is as follows:OP, POINIFL, YLIM IFL =0 specifies the normal calculation, IFL =1 the ’simulation’ calculation. YLIMis redundant if IFL =0,whereasifIFL =1 it specifies that all transitions whose yield divided bythe yield of the normalizing transition (defined in OP,YIEL) exceeds YLIM will be treated as ’experimentallyobservables’ and will be included in the TAPE4 file. OP,POIN will also produce a filecontaining the γ detector efficiency information if OP,RAW was executed and PRT, flag 20 was set to1 (TAPE23). Note that the decay energies in TAPE23 output are Doppler-shifted.Note that OP.POIN evaluates the point γ-ray yield in the laboratory frame for transition I → I f that isdefined by equation 4.16. That is:ZY Point d 2 σ(I → I f )(I → I f )=sin(θ p )dφφ pdΩ γ dΩ p (4.16)pwhere the integrand is given byd 2 σ(I → I f )dΩ p dΩ γ= σ R (θ p ) X R kχ (I,I f ; θ p )P kχ (θ γ )(2 cos χ(φ p − φ γ ) − δ χ0 ) (4.13)kχ≥0Note that Y Point (I → I f ) includes the Rutherford cross section, the sin(θ p ) term, integration over theprojectile φ p angle, the deorientation effect and γ-detector Q K attenuation coefficients.The total number of coincident γ-raysdetectedthenisgivenbyCounts =10 −27 ·∙ Qˆqe¸·∙NAA¸· [ρdx] · Y Point (I → I f ) · ∆θ p · ε p · ε γ · ∆Ω γwhere:Q is the integrated beam charge [C]ˆq the average charges state of the beame the proton charge [1.602 × 10 −19 C]N A Avogadro number [6.022 × 10 23 atoms/mol]A Target mass number [g/mol]ρdx areal target thickness in [g/cm 2 ]Y Point mb(I → I f ) OP.POIN output in [sr·rad ]∆θ p Projectile scattering angle range [rad]ε p particle detection efficiency per unit solid angleε γ γ-ray detector efficiency excluding the geometrical solid angle∆Ω γ geometrical solid angle of the γ-ray detector. Note that usually one only knows the productε γ · ∆Ω γ97
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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
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 and 94: When entering matrix elements in th
Page 95: There are no restrictions concernin
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
Page 145 and 146: 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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