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

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11.3.2 Fitting Matrix Elements to Gamma-Ray Yield DataThis section describes the use of a series of sample inputs to fit matrix elements to experimental data. Thesimplest possible case is examined: fitting one parameter (two E2 reduced matrix elements coupled as oneparameter) to a few experimental gamma-ray yields (from the lowest 4 excited states in a fictitious nucleus).The level scheme is the same as the one in the previous demonstration, that is Fig 13, but in this case,matrix elements 3 and 5 will be adjusted to find the chi-squared minimum in the calculated yields.This “toy” problem can be used as a model for the basic procedure used to analyze real data, eventhough a real problem might involve more sophistication, such as, axially asymmetric particle detectors (ofarbitrary shape), data from user-defined Ge detector “clusters,” choices regarding the normalization of onedata subset to another, data from multiple beam and target combinations, data from unresolved doublets,inverse scattering kinematics, etc. A flowchart of the general procedure to define the germanium detector(s),fit matrix elements to the data and estimate the errors in the fitted matrix elements is given in Fig 15 plus16.The demonstration is run using a set of inputs and related files in the toyfit.tar archive on the Gosiawebsite. Each step of the demonstration is run with a different *.inp file. In practice it is probably betterto use the same input file for all or most steps to prevent accidental inconsistencies between steps. The filesshould be modified for each step in a text editor such as emacs or vi, paying attention to delimiters, spacingand capitalization. The second fitting demonstration (section 11.4) uses this method of editing one inputfile between steps and fits more matrix elements. However, the present demonstration can be run withoutany modification to each input file.Eachstepintheprocedureisexecutedbytypinggosia < *.inpAt each step, the relevant portion of the input is described, but the novice user should refer to the manualentry in Chapter 5 for complete details of the records and fields required for a particular Gosia option, e.g.OP,GOSI or OP,INTG etc. This demonstration includes two iterations of the fitting procedure to makesure that the correction factors for the point approximations used in the fit weresufficiently accurate at thestarting point in the chi-squared surface (steps 5 - 7).A set of simulated gamma-ray yield data is provided for the user in the file ge-data.yld. In practice, thisfile would be typed by the user according to the format in section 5.31.1. Define the Ge detector(s) (1-make-detector.inp)In Gosia, detectors are considered to be “physically different” if they have different geometry (crystal length,crystal radius, etc.), if they are placed at different distances from the target position, or if they are fittedwith different absorbers. Two identical Ge detectors placed at different distances from the target would needto be defined separately, but two identical detectors that only differ by their angular position in space (andtheir efficiencies) should be defined as the same “type.” In this demonstration, one detector type is definedand named type “1.”Refer to the file “1-make-detector.inp”. In OP,FILE the three necessary files for OP,GDET are defined.The general output will be written to 1-make-detector.out, but the coefficients for the angular attenuation(Sections 5.10 and 2.2.3) will be written to “det.gdt” for use by Gosia in steps 2 - 10.OP,GDET has three lines. The first line is the detector type, 1. The second line0.1,2.5,10.,15.defines a Ge crystal with an inactive core of radius 0.1 cm, outer radius of 2.5 cm and length 10. cm, placed15. cm from the target. The angular position(s) in space of all detectors of this type will be definedinthenext step.To execute the input, issue the commandgosia < 1-make-detector.inpThe output file 1-make-detector.out contains verbose output, some of which is selected by the user in thesub-option PRT of CONT. Error messages will also be written to file 22 (*.out in this demonstration). TheGe detector file det.gdt is created with the following records.160
Figure 15: Flow diagram for Gosia matrix element fitting procedure, [part A]161
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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
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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
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x i + δx i Rx iexp ¡ − 1 2 χ2
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method used for the minimization, i
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OP,ERRO (ERRORS) (5.6):Activates th
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-----OP,SIXJ (SIX-j SYMBOL) (5.25):
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5.3 CONT (CONTROL)This suboption of
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I,I1 Ranges of matrix elements to b
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CODE DEFAULT OTHER CONSEQUENCES OF
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5.4 OP,CORR (CORRECT )This executio
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5.6 OP,ERRO (ERRORS)ThemoduleofGOSI
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5.7 OP,EXIT (EXIT)This option cause
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M AControls the number of magnetic
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5.10 OP,GDET (GE DETECTORS)This opt
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5.12 OP,INTG (INTEGRATE)This comman
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¡ dE¢dx1 ..¡ dEdx¢Stopping powe
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NI1, NI2 Number of subdivisions of
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5.13 LEVE (LEVELS)Mandatory subopti
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5.15 ME (OP,COUL)Mandatory suboptio
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Figure 10: Model system having 4 st
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ME =< INDEX2||E(M)λ||INDEX1 > The
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When entering matrix elements in th
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There are no restrictions concernin
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5.18 OP,POIN (POINT CALCULATION)Thi
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5.20 OP,RAW (RAW UNCORRECTED γ YIE
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5.21 OP,RE,A (RELEASE,A)This option
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5.25 OP,SIXJ (SIXJ SYMBOL)This stan
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5.27 OP,THEO (COLLECTIVE MODEL ME)C
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2,5,1,-2,23,5,1,-2,23,6,1,-2,2Matri
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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
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
Page 157 and 158: (1.6 MeV)1.1 MeV0.75 MeV0.4 MeV0.08
Page 159: Define the germaniumdetector geomet
Page 163 and 164: gosia < 2-make-correction-factors.i
Page 165 and 166: Issue the commandgosia < 9-diag-err
Page 167 and 168: At this point, it is suggested to c
Page 169 and 170: calculation.) In this case, a copy
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Page 175 and 176: .10.028921.10.026031.10.023431.10.0
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Page 181 and 182: *** CHISQ= 0.134003E+01 ***MATRIX E
Page 183 and 184: CALCULATED AND EXPERIMENTAL YIELDS
Page 185 and 186: 11.7 Annotated excerpt from a Coulo
Page 187 and 188: 11.8 Accuracy and speed of calculat
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Page 191 and 192: line 152 Eu 182 Tanumber (keV) (keV
Page 193 and 194: 1.6 Normalization between data sets
Page 195 and 196: 13 GOSIA 2007 RELEASE NOTESThese no
Page 197 and 198: Matrix elements 500(April 1990, T.
Page 199 and 200: 14 GOSIA Manual UpdatesDATE UPDATE2
Page 201 and 202: [KIB08]T.Kibédi,T.W.Burrows,M.B.Tr
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