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

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11 LEARNING GOSIAGOSIA is capable of performing accurate calculations for a wide range of Coulomb excitation experiments.Consequently, precise definitions of the experimental parameters, data and the variables to be fit requirecareful attention. Chapter 5 of this manual covers the details of each section of the user input (the “input”),while the present chapter will help reduce the time required to install and learn GOSIA.Section 1 of this chapter gives compiling instructions.Section 2 is a description of the basic components of the typical GOSIA input required by the noviceuser.Section 3 is a tutorial that introduces the user to the basic operations involved in simulating an experimentand fitting matrix elements to data with the help of flow diagrams.Section 4 is a second tutorial that demonstrates a fit of 10 adjustable parameters to simulated data. Thetutorial guides the user through editing a Gosia input in a text editor to perform each step of the fittingprocedure. Understanding this tutorial is aided by the annotated version in Section 5.Sections 6 and 7 explain important features of a Gosia output file.Section 8 details the situations in which accuracy problems might arise and describes how they can beavoided.Lastly, Section 9 gives a brief set of suggestions to help the novice debug syntax errors and physics-relatedproblems.11.1 Compiling GOSIA 2007GOSIA 2007 has been updated significantly from previous versions: The code is now explicitly 64-bit andno longer allows the user the option of compiling in 32-bit mode, because of the danger of serious accuracyproblems using 32-bit math. Because of these and other changes, GOSIA 2007 is much more portable, andthe source is easily compiled to produce an object that gives high-accuracy results. Proper alignment of thecommon blocks is now handled in the source of GOSIA 2007, so it is no longer necessary for the user to setthe alignment for 64-bit accuracy.We recommend running GOSIA 2007 on a true 64-bit processor using the GNU g77 compiler with thefollowing command:g77 -o gosia gosia.fThis will produce a functional object on most modern Unix-like machines. The user may find improvementsin speed by using compiler optimization switches. When experimenting with compiler optimization,the accuracy should be tested using the sample inputs and outputs provided on the Gosia website.154
11.2 LearningtoWriteGosiaInputsThe fastest way to learn to write GOSIA inputs is to begin with one of the sample inputs on the GOSIAwebsite and modify it in stages. The meaning of each line in the sample input can be understood bycomparing it with the manual entry for the relevant section (e.g. OP,YIEL or OP,INTG), while Chapter 5gives a listing of the options that are required for each of the functions of GOSIA. Each function is controlledby an “option” labeled in the input as “OP,XXXX”, where XXXX is a four-letter identifier. The subsectionsof each option are referred to in this manual as “sub-options,” and have a two- to four-letter identifier. Ingeneral, the physical problem is defined in several sections (“options”) of the code in the order that follows,with other sections being optional.OP,FILE Assigns file names to the input and output files. The OP,FILE entry is optional but recommended,because descriptive file names prevent confusion that can arise from the default names fort.1, fort.2,etc.OP,TITL The user’s choice of a description of the input.OP,GOSI This block defines, among other parameters, the nuclear system and a brief description of theexperimental situation. (OP,COUL can be used instead, if the user desires only to calculate gamma-rayyields, not to fit matrixelements.)LEVE This is the level scheme of the nucleus to be studied (either projectile or target).ME The starting values of the EM matrix elements are given here. The desired coupling of fit parametersand boundaries for the fit are entered if OP,GOSI was specified.EXPT This sub-option defines the experimental setup briefly, including particle detector geometry andspecifications for the point-approximations used to increase the speed of the fit. The mean beamenergy (as the beam traverses the target) is specified here, along with the projectile and target species.Up to 50 “experiments” may be specified, where each experiment may be defined as merely a range ofprojectile scattering angles, or as a truly distinct experiment with a different projectile, target, etc.CONT A number of accuracy controls are given here. Several other switches in this sub-option allow theuser to quickly fix or release matrix elements in the fit. The user may also choose output options inCONT.END, This entry marks the end of the CONT sub-option and should be followed by a single blank line.[Blank line]OP,YIEL This option defines internal conversion coefficents, gamma-ray detector types and angular coverages,normalization of the particle detectors (if necessary), normalization of calculated gamma-rayyields, detector sensitivity (for the calculation of chi-squared). Optionally, a set of lifetime, matrix element,gamma-ray branching ratio and mixing ratio datacanbeenteredandincludedinthechi-squaredfit.OP,INTG This option defines the particle scattering angle ranges over which the yields are to be integratedfor each experiment. This consists of defining the particle detector shape (if necessary), angular limitsand meshpoints for the integration. Stopping powers and beam energy ranges effectively define thetarget thickness here.The input is generally run several times to perform the fit, with minor changes to the input at each stage,as demonstrated in the tutorials in this chapter. It is recommended that the user begin analysis of real databy running an integration (OP,INTG) based on one of the inputs used in the tutorials. When the physicalsystem is satisfactorily defined (beam, target, level scheme, initial guesses at the matrix elements, beamenergies and scattering angles), the integrated yields can be compared to the data. A fit toexperimentaldata can then be accomplished by following the steps that are described in the fitting tutorials.155
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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
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
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: SFX,NTOTI1(1),I2(1),RSIGN(1)I1(2),I
Page 157 and 158: (1.6 MeV)1.1 MeV0.75 MeV0.4 MeV0.08
Page 159 and 160: Define the germaniumdetector geomet
Page 161 and 162: Figure 15: Flow diagram for Gosia m
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
Page 171 and 172: 4,-4, -3.705, 3,44,5, 4.626, 3.,7.5
Page 173 and 174: 90145901459014590145901459014590145
Page 175 and 176: .10.028921.10.026031.10.023431.10.0
Page 177 and 178: 5,5,634,650,82.000,84.000634,638,64
Page 179 and 180: ***********************************
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
Page 189 and 190: 18,10.056,0.068,0.082,0.1,0.12,0.15
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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