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

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Figure 17: Initial guesses (squares) of transition matrix elements in g1demo.inp and final values (+) comparedto the true values used to simulate the data (circles).*** CHISQ= 0.277172E+02 ****** CHISQ= 0.965818E+01 ****** CHISQ= 0.594594E+01 ****** CHISQ= 0.403621E+01 ***...*** CHISQ= 0.100057E+01 ****** CHISQ= 0.999197E+00 ****** CHISQ= 0.995206E+00 ****** CHISQ= 0.984981E+00 ***In this case, the fit converged after 34 steps with chi-squared=0.98. Additional output is given in theg1demo.out file, which can be compared with the example found in g1demo.tar.The final values of the matrix elements after the fit are compared with the “true” values used to simulatethe data in Figure 17. For the assumed data set the multiple-step Coulomb excitation is insensitive to themagnitudes of the lowest transition matrix elements, while the matrix elements for I=10...14 agree betterwith the true values. The calculated yields are not sensitive enough to the matrix element toobtain a fit.Obviously, the quantity of data in this example is marginally sufficient to fit 10 matrix elements separatelyand find a unique minimum. Note that only data from a single Ge detector are represented in this fit! It iseducational to experiment with the couplings of the matrix elements (e.g. coupling the E2 matrix elementsfor several states to one intrinsic quadrupole moment), changing the weight and value of the lifetime of state3, changing the OP,MINI controls, etc. In many cases, a more accurate fit of the matrix elements couplingthe lower-spin states can be achieved by fixing the matrix elements for high-spin states (e.g. with the FIXoption in the CONT block). Alternatively, new logical experiments and new gamma-ray detectors can beadded to the input. If new experiments or detectors are added, it will be necessary to generate new simulateddata. This can be done using OP,INTG and inserting the data from the YIELD column into the g1demo.yldfile (see section 5.31) or by using OP,POIN (Section 5.18).A second iteration of steps II to IV will be necessary in some cases, especially if the matrix elementsvary greatly in the first fit. (See section 4.2 for details regarding when it is necessary to re-run the map168
calculation.) In this case, a copy of the g1demo.bst file (tape 12) which was written by OP,MINI must bekept in the working directory and re-read by inserting OP,REST in the appropriate place in the input, asshown in step 5 below. Note that unit 12 will be overwritten when OP,MINI is run again.5. Reproduction of the Experimental YieldsFollowing the minimization, gamma-ray data can be compared to the calculated (expected) values bymaking the following changes to the input and running one last time.RemovetheOP,MINIcommandwhereitwasinsertedinstepIVabove,andinserttheOP,RESTcommandso that the final values of the matrix elements will be read from the g1demo.bst file. Set NTAP to 0, so thatexperimental data are not read from a file.1.10.012370 !NTAP0,01,1.0 !lifetime data3,112.,1.0,00,0OP,REST0,0OP,INTG5,7,634,650,22.000,26.000 !4 deg exptsAtthebottomofOP,INTG,removeOP,CORR.010,10010,10OP,EXITThe input can now be run with the usual command. Gamma-ray yields will be integrated using thefinal matrix elements in TAPE 12 (TAPE 2 in older versions of GOSIA) and given in the g1demo.out file.The experimental yields should be compared with these integrated yields, rather than the output given byOP,MINI, since the latter are corrected point calculations and may be normalized on a different scale.169
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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
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 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: At this point, it is suggested to c
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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