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12 GAMMA DETECTION EFFICIENCY CODE: GREMLINAlexander KavkaUniversity of RochesterThe FORTRAN program GREMLIN (“Gamma-Ray Efficiency Measurement and Line INtensity calculation”)was developed at Rochester in 1987 by Alexander Kavka. The purpose is to simplify the routineprocedure of γ-ray detector efficiency calibration and detection efficiency correction of measured peak areasfor deexcitation γ-ray yields following Coulomb excitation.GREMLIN can perform two separate tasks:1) Least-squares fit ofaγ-ray detection efficiency-calibration function to a set of peak areas from γ-raycalibration spectra.2) Calculation of detection-efficiency corrected γ-ray intensities from peak areas, using the fitted efficiencyfunction for the Doppler shift corrected γ-ray energy.The functional form of the dependence of detection efficiency on γ-ray energy is factored into terms thatseparately account for γ-ray absorption, high and low energy dependence, and electronic thresholds in orderto obtain well-behaved functions that do not exhibit pathological behaviour such as at K-edges.GREMLIN is an essential component of the GOSIA suite of Coulomb excitation analysis codes and canbe used in either of two modes. One approach is to use GREMLIN to correct the raw peak areas of theobserved deexcitation γ-rays to account for the γ-ray detector efficiency at the appropriate Doppler-shiftedenergy. These corrected yields then are input as the data to be fit by GOSIA. The second approach is to usethe GOSIA option OP,RAW which allows input to GOSIA of the raw, i.e. not detector efficiency corrected,γ-ray yields. The parameters for the γ-ray detection efficiency function, as determined by the GREMLINleast-squares fit, are used by OP,RAW to detector-efficiency correct the raw yields input to GOSIA.The code GREMLIN is interactive, and its prompts and questions are hopefully sufficient to guide theuser. Therefore, this memo provides no real input instructions, with one exception: it describes the structureof the input files containing the calibration points.12.1 Option 1: EFFICIENCY CALIBRATION1.1 Input of calibration pointsA maximum of 500 calibration points can be entered, grouped in up to 9 independently normalized datasets. Typically, these will originate from runs with different calibration sources, but there can just as wellbe several sets from the same source. If there is more than one data set, the code will automatically fitnormalization parameters.GREMLIN will ask for calibration points for each data set separately. For each set the input can befrom a disk file or from the keyboard, and consists of one record for each calibration line. A record looks asfollows:E, I, ∆I, A, ∆Awhere E is the γ-ray energy, I ± ∆I the tabulated relative intensity, and A ± ∆A the measured peak area.Note that two data sets cannot be in one file.However, the input is simplified in the case of 152 Eu or 182 Ta sources, because the energies and intensitiesof major 152 Eu and 182 Ta transitions are stored in DATA statements in the program. These values weretaken from R.A. Meyer: Multigamma-Ray Calibration Sources (Lawrence Livermore Laboratory 1978). Therecord format is thenA, ∆AIf keyboard input was chosen, the code will display each tabulated energy and intensity and ask for the areaand error. In an input file, the 152 Eu or 182 Ta lines must be given according to the following table:190
line 152 Eu 182 Tanumber (keV) (keV)1 121.783 31.7372 244.692 65.7223 295.939 67.7504 344.276 84.6805 367.789 100.1066 411.115 113.6737 443.967 116.4218 488.661 152.4309 564.021 156.39010 586.294 179.39711 688.678 198.35012 778.903 222.10813 867.388 229.32214 964.131 264.07815 1005.279 927.98316 1085.914 1001.69617 1112.116 1113.41418 1212.950 1121.29919 1299.124 1157.50520 1408.011 1189.05121 1528.115 1221.40622 1231.01923 1257.42124 1273.73525 1289.158Any unobserved line that is to be excluded from the fit mustbeenteredasA = ∆A =0, at the keyboard aswell as in a file.Data for other sources than 152 Eu and 182 Ta easily can be added to the code in the future, should theneed arise. Similarly it is trivial to include additional 152 Eu and 182 Ta lines in the lists.1.2 Experimental and theoretical efficiencyFor each calibration line GREMLIN calculates the relative efficiency and root-mean-square error:s µ∆Aε = A 2 µ 2 ∆I∆ε = ε +IA Iand makes a transformation to the variables which are then internally used for the fit, i.e.x ≡ log E E 0y ≡ log ε ∆y = ∆εεThe logarithms are of base e and E 0 =50keV.The functional form used by GREMLIN is factored into four functions that separately account for γ-rayabsorption, higher energy, lower energy detection efficiencies, and electronic thresholds in order to obtainwell-behaved functions that do not exhibit pathological behaviour such as at K-edges etc. That is, thefunctional form of the detection efficiency used isε(E) =A(E)P (E; a 1 ...a n )F (E; f)W (E; b, c)with the parameters a 1 ...a n , f, b, andc to be determined. The separate terms are discussed below.1.3 Attenuation factor191
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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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5.29 OP,TROU (TROUBLE)This troubles
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to that of the previous experiment,
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To reduce the unnecessary input, on
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OP,STAR or OP,POIN under OP,GOSI. N
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5.31 INPUT OF EXPERIMENTAL γ-RAY Y
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6 QUADRUPOLE ROTATION INVARIANTS -
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*½P 5 (J) = s(E2 × E2) J ×¯h¾
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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
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 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
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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 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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