4, 4,.2, −1, 17, 0, 0, 0, 0 E2 exhausted, now M1. Firstentry=6+M multipolarity (1 <strong>and</strong> 2 allowed).2, 4,.5, −2, 20, 0, 0, 0, 0 First entry= 0means that ME setup is completeEXPTDefinition of experiments at mean values of scattering angle <strong>and</strong> energy2, 36, 88 Two experiments, Z,A of investigated nucleus−6, 12, 194, −4, 3, 1, 0, 0, 360, 0, 1 First experiment −Z of uninvestigated nucleus (minus appendedmeans projectile <strong>excitation</strong>, i.e. Kr is projectile). A of uninvestigated nucleus. Bombarding energy(MeV) Projectile scattering angle(deg). Appended minus sign tells that actually target was detected.Number of magnetic substates from the starting m of the ground state to be used in the calculation usingthe full COULEX formalism, number of magnetic substates to be included in the fast approximation(0 or 1). Particle detector axial symmetry flag, 0 means axial symmetry, φ range of particle detector,redundant for axial symmetry. Kinematics flag −0 means larger CMS solution if projectile is heavierthan target, 1 otherwise. Coupling of experiment normalizations, for the first experiment it is coupledto itself.−6, 12, 194, −6.4, 3, 1, 0, 0, 360, 0, 1 As above, differs by scattering angle. Last entry specifies commonnormalization with experiment 1 (see OP,YIEL).CONTAs in GOSIA. Some print defaults changed, so to custom-make your input use PRT,END, END, concludes CONT, End must be followed by a blank line. Empty record is the end ofOP,GOSI input.BeforeOP,YIEL,OP,GDETmustbeexecutedonlyoncetocreateafile (Unit9). Remove the OP,GDETsequence after executing OP,GDET.Assuming that all gamma detectors are physically identical one inserts:OP, GDET1 One physical detector (geometry).0001, 3.5, 10, 10 Radius of inactive core (historical), radius of the crystal, length of the crystal, distancefrom target to the detector face —all in cm.0, 0, 0, 0, 0, 0, 0 Thicknesses of Al.,C,Fe,Cu,Ag/Cd/sn, Ta <strong>and</strong> Pb absorbers in front of the detector.Here no absorbers are specified.OP, EXITEnd of execution, the remainder of the input ignored.Note that the Coulex amplitudes <strong>and</strong> level populations can be calculated using:OP, STAROP, EXITThe gamma-yields related portion of the input starts:OP, YIEL142
0 Correction for in-flight decay changing the geometry of gamma detectors. 0 means no correction, 1tells the code to apply it.5, 2 Number of energy meshpoints <strong>and</strong> multipolarities to define internal conversion coefficients for Kr..05,.1,.4,.8, 1. Energy meshpoints (MeV)2 E21, 1, 1, 1, 1 ICC’s for E2 (here of course not real7 M11, 1, 1, 1, 1 As above2, −2 Number of gamma detectors for each experiment. Here two detectors are defined. Minus signappended to the second entry signifies that gamma detector setup is identical to this defined for previousexperiment (common situation)1, 1 Definition of the „physical” detectors as they appear in OP,GDET. There we assumed that alldetectors are physically identical <strong>and</strong> we defined only one, so for experiment 1 both detectors are thesame, as well as for experiment 2.5, 90 θ angles of the gamma detectors0, 0 φ angles of the gamma detectorsIn the case of a non-identical detector setup the above sequence should be defined for each experiment.2, 1 Normalization transition (level #2 to level#1). Used only for printout <strong>and</strong> simulation of experimentalyields by OP,POIN.2 Number of <strong>data</strong> sets, usually equal to the number of detectors unless clusters were formed by OP,RAW.Given for experiment 1, experiment 2 assumed to have identical setup.1000, 1000 Upper limits of the transition intensities relative to the normalization transition for bothdetectors. If exceeded for the transitions not given as observed the contribution to least-squares functionis added. Here this feature is practically switched off.1, 1 Relative normalization constants of gamma detectors. The values should be the same for efficiencycorrectedspectra or if OP,RAW is used.4 Defines the file experimental „corrected” yields reside on. See also OP,POIN.0, 0 Numbers <strong>and</strong> weigths of available spectroscopic <strong>data</strong> — branching ratios,0, 0 lifetimes, mixing ratios <strong>and</strong> known matrix elements.0, 0 First 0 means no <strong>data</strong> available, otherwise the input is like in GOSIA.0, 0OP, POIN0, 0 or 1,limit, Optional, 0,0 — calculation of „point” yields just for printout. 1,limit causes additionallycreation of the simulated experimental yields file containing all transitions of intensities exceeding thevalue of limit with respect to the normalization transition specified in OP,YIEL. This file will be writtenon unit 4. When executing OP,POIN the unit selector in OP,YIEL (in this example =4 should be setto 0. )OP, INTGPerforms integration over target thickness <strong>and</strong> particle detectors ranges143
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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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à 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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- Page 119 and 120: 6 QUADRUPOLE ROTATION INVARIANTS -
- Page 121 and 122: *½P 5 (J) = s(E2 × E2) J ׯh¾
- Page 123 and 124: The expectation value of cos3δ can
- Page 125 and 126: where ē is an arbitratry vector. D
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- Page 135 and 136: OP,EXITInput: TAPE4,TAPE7,TAPE9Outp
- Page 137 and 138: OP,ERRO0,MS,MEND,1,0,RMAXand the fi
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- Page 141: 4, 3, 1kr88.corKr corrected yields
- Page 145 and 146: OP, ERRO Estimation of errors of fi
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- Page 149 and 150: configurations with a probability e
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- Page 153 and 154: SFX,NTOTI1(1),I2(1),RSIGN(1)I1(2),I
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- 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
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- Page 181 and 182: *** CHISQ= 0.134003E+01 ***MATRIX E
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1.6 Normalization between data sets
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13 GOSIA 2007 RELEASE NOTESThese no
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Matrix elements 500(April 1990, T.
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14 GOSIA Manual UpdatesDATE UPDATE2
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[KIB08]T.Kibédi,T.W.Burrows,M.B.Tr