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

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etween meshpoints. When starting a new calculation it is wise to halve or double the number of subdivisionsat least once to make sure that convergence is achieved. Refer to the troubleshooting section in this chapter.In this example, the Ge detector definitions file det.gdt has already been provided. (The fitting tutorialin this section gives an example of how to create a detector file.) In order to produce simulated yields, Gosiaonly needs to be told to execute the simulate.inp input file using the commandgosia < simulate.inpThe following output should be generatedOPENED simulate.outIO-num = 22 UNKNOWN FORMATTEDetcWhen the system prompt is returned, an output file simulate.out will be present. Among other data, thesimulated, integrated yields appear at the end of the input. The yield output looks like the following.INTEGRATED RUTHERFORD CROSS SECTION=.9472E+03 FOR EXP. 1INTEGRATED YIELDSEXPERIMENT 1 DETECTOR 1ENERGY RANGE 230.000--- 250.000 MEV SCATTERING ANGLE RANGE 60.000--- 80.000 DEGNI NF II IF YIELD NORMALIZED YIELD5 4 8.0 6.0 0.12033E-08 0.12681E-094 3 6.0 4.0 0.14781E-04 0.15576E-053 2 4.0 2.0 0.64335E-01 0.67797E-022 1 2.0 0.0 0.94893E+01 0.10000E+01********* END OF EXECUTION **********First, the Rutherford cross section is given, integrated over the target thickness as well as the solid angle,in mb•mg/cm 2 . To obtain the usual Rutherford cross section, it is necessary to divide this number by thetarget thickness, givingσ R =(0.9472E +03mb•mg/cm 2 )/(0.62mg/cm 2 ) = 1528mb. The cross section for measuring the gammaraytransition from state 2 to state 1 in a perfect (blackbody) detector can be obtained from the finalline of output. In the YIELD column, Gosia gives a differential cross section, which is integrated over theparticle detector solid angle and the energy range in the target, but not over the Ge detector solid angle.In the present example, this quantity is dσ/dΩ γ =(0.94893E + 01)mb•(mg/cm2)(1/sr). The det.gdt filethat came with simulate.inp represents a Ge detector of 5 cm diameter placed with its face 15 cm from thetarget position. Hence, it subtends a solid angle of 0.087sr. (Refer to the second demo on fitting matrixelements for an example that shows how to define a Ge detector.) The absolute cross section for scatteringof the beam into the particle detector and emission of the 2 + to 0 + γ−ray into the Ge detector is thenσ pγ =0.94893E +01mb•(mg/cm2)(1/sr) × 0.087sr ÷ 0.62mg/cm 2 =1.33mb. Note that this is not a pointcalculation of the mean cross section at the mean beam energy, but rather, it is integrated over the energyrange of the beam in the target. Refer to section 5.12.5 of this manual to convert this cross section toabsolute counts.158
Define the germaniumdetector geometry(OP,GDET)Integrate the gamma‐ray yields(OP,INTG). This should be done withNTAP set to 0 in OP,YIEL to indicatethat no experimental data are to beread.Convert GOSIA yield toabsolute counts using the“yield” output (not“normalized yield”) asdescribed at the end of theOP,INTG section.Adjust experimentalparameters (e.g. beam ortarget species, targetthickness, placement ofGe or particle detectors,beam energy) to optimizecross sections as desired.Figure 14: Gosia simulation flow diagram159
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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
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 and 154: SFX,NTOTI1(1),I2(1),RSIGN(1)I1(2),I
Page 155 and 156: 11.2 LearningtoWriteGosiaInputsThe
Page 157: (1.6 MeV)1.1 MeV0.75 MeV0.4 MeV0.08
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
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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