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

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5.30 OP,YIEL (YIELDS)This option is mandatory if it is desired to calculate the yields of deexcitation γ-rays following Coulombexcitation. The first part of this option is used to input the internal conversion coefficients and the descriptionof the γ-ray detectors. This first section is used in conjunction with either OP,COUL or OP,GOSI. The secondpart of this option is used in conjunction with OP,GOSI to input additional information required for theleast-squares fitting such as normalization constants, γ-ray branching ratios, lifetimes, E2/M 1 mixing ratios,and diagonal or transitional E2 matrix element data to be included in the fit. The input to OP,YIEL mustbe complete and consistent with the option of the code selected. Section 7.4 shows the correct position ofOP,YIEL in the input stream for various calculations.OP,YIEL defines the “logical“ γ detectors, which are referred to everywhere in the input except inOP,GDET. Different logical detectors may be in fact the same “physical“ ones. This distinction allows toreduce the number of experiments defined in all cases where the setup used is symmetric with respect tothe beam axis. As an example, let us consider the experiment in which two particle detectors are placedsymmetrically about the beam axis at angles (θ, φ) and(θ, φ, +π), respectively. Gamma rays are detectedin coincidence with scattered particles in one Ge detector placed at position (θ g ,φ g ), so the scan of eventby-eventdata yields two γ spectra. A straightforward approach is to define two experiments, differing onlyby the placement of the Ge detector with respect to the scattered particles. Instead, one can define onlyone experiment (keeping in mind that the Coulomb excitation depends on θ, but not on φ) and two logicaldetectors, one at (θ g ,φ g ), and another at (θ g ,φ g +π). Both are identified as the same “physical“ detector, butdifferent sets of γ yields (both spectra resulting from the scan) are assigned to them. Such a manipulationsaves almost 50% of CPU time since evaluation of deexcitation γ yields requires negligible computation timecompared to the excitation calculation.GOSIA allows also to define logical detector clusters (see OP,RAW-5.20), i.e. sets of γ yields which resultfrom summing the raw spectra, therefore the number of experimental data sets is not always equal to thenumber of logical detectors. Further description will refer to the “logical“ detectors simply as γ detectors,which should be distinguished from either “physical“ detectors or data sets.Brief resumé of the input to OP,YIEL:OP, YIELIFLAG Assumes the values of 0 or 1. IFLAG =1means that the correction to the angular distributionof the γ-rays due to a finite distance traveled by the decaying nucleus will be included in the calculation(see Section 4.3). IFLAG =0switches off this correction.N1, N2 Number of energies (N1 ≤ 50) and multipolarities (N2) todefine the internal conversion coefficients.E 1 , E 2 , ..., E N1 Energy meshpoints for the internal conversion coefficients (in MeV), common for allmultipolarities for the nucleus of interest. The code uses four point interpolation between meshpoints.Note that the large discontinuities in the internal conversion coefficients at the K and L edges can betaken into account correctly by ensuring that there are at least two mesh points between the transitionenergy of interest and the nearest discontinuity; that is, so that the four point interpolation does notdoes straddle any discontinuity.I1 Multipolarity I1.CC(I1, 1)..CC(I1, N1) Internal conversion coefficients for multipolarity I1 at each energy meshpoint(N1 entries). Note that internal conversion coefficients can be obtained from the NNDC (US NationalNuclear Data center) at http://www.nndc.bnl.gov/bricc/.I2This sequence should be repeated for all multipolarities defined, i.e. N2 times.CC(I2, 1)..CC(I2, N1)NANG(I)..NANG(NEXP) Number of γ-ray detectors for each of the NEXP experiments. NANG(I)can be entered as its true value with a negative sign, which means that the γ detector setup is identical110
to that of the previous experiment, for example if the experiments differ only by the scattering angle.In this case the next three records need not be entered.IP(1)..IP(NANG(I)) Identifies the γ detectors used in a given experiment according to the sequencethe “physical“ detectors were defined in the input to OP,GDET (Section 5.10). For example, ifIP(L) =K, then it is understood that the L-th detector used in the current experiment is the K-th detector defined in the OP,GDET input. This assignment of “physical“ detectors to the “logical“ones is the only instance the “physical“ detectors are referred to. Everywhere else the γ detectors arethe “logical“ detectors.θ 1 ,...θ NANG(I) θ angles for γ detectors used in experiment I.φ 1 ,...φ NANG(I 0 ) φ angles for γ detectors used in experiment I.The above sequence, starting from the definition of IP should be repeated for each of NEXP experimentsdefined, except of the experiments for which NANG is negative. The experiments must be ordered accordingto the sequence they appear in EXPT input.NS1, NS2 The transition from NS1 to NS2 to be used as the normalization transition where NS1and NS2 are the state indices.End of input for OP,COUL. The remainder of the input is required only if OP,GOSI was specified.NDST Number of data sets in experiment 1. Usually equal to NANG(1), unless detector clusters weredefinedinOP,RAW.UPL 1 ...UPL n Upper limits for all γ detectors used in experiment 1.YNRM 1 ....YNRM n Relative normalization factors of γ detectors used in experiment 1.The above three records should be repeated for all experiments according to the sequence of EXPT, exceptfor those assigned the negative value of NANG. Subscript n = NDST denotes the number of data sets.NTAP Specifies file containing experimental yields. NTAP=0 is used when this file is not necessary,e.g. when running OP,STAR or OP,POIN under OP,GOSI. Otherwise NTAP=3 or 4 corresponding tofile TAPE3 or TAPE4, respectively. NTAP must equal 3 if OP,CORR is executed and must equal 4 ifOP,ERRO is executed.NBRA, WBRANumber and weight of branching ratios.I1, I2, I3, I4, B, DB... NBRA records of branching ratios.· (I1 → I2)/(I3 → I4) = B/DB where I 1 ≡ I 3 and· where I1,I2,I3,I4 are state indices, B is the branching ratio with error DB. Note I1 =I3 is theinitial state that γ decays and I2,I4 are the final states.NL, WLNumber and weight of mean lifetimes.INDEX, T, DTT/DT is the mean lifetime of level INDEX.··· NL records, lifetimes in picosecondsNDL, WDLNumber and weight of E2/M1 multipole mixing ratios.IS, IF, DELTA, ERROR··· NDL recordsδ E2M1(IS → IF)=DELTA ± ERRORNAMX, WAMXNumber and weight of known EM matrix elements.111
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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
Page 59 and 60: OP,ERRO (ERRORS) (5.6):Activates th
Page 61 and 62: -----OP,SIXJ (SIX-j SYMBOL) (5.25):
Page 63 and 64: 5.3 CONT (CONTROL)This suboption of
Page 65 and 66: I,I1 Ranges of matrix elements to b
Page 67 and 68: CODE DEFAULT OTHER CONSEQUENCES OF
Page 69 and 70: 5.4 OP,CORR (CORRECT )This executio
Page 71 and 72: 5.6 OP,ERRO (ERRORS)ThemoduleofGOSI
Page 73 and 74: 5.7 OP,EXIT (EXIT)This option cause
Page 75 and 76: M AControls the number of magnetic
Page 77 and 78: 5.10 OP,GDET (GE DETECTORS)This opt
Page 79 and 80: 5.12 OP,INTG (INTEGRATE)This comman
Page 81 and 82: ¡ dE¢dx1 ..¡ dEdx¢Stopping powe
Page 83 and 84: NI1, NI2 Number of subdivisions of
Page 85 and 86: 5.13 LEVE (LEVELS)Mandatory subopti
Page 87 and 88: 5.15 ME (OP,COUL)Mandatory suboptio
Page 89 and 90: Figure 10: Model system having 4 st
Page 91 and 92: ME =< INDEX2||E(M)λ||INDEX1 > The
Page 93 and 94: When entering matrix elements in th
Page 95 and 96: There are no restrictions concernin
Page 97 and 98: 5.18 OP,POIN (POINT CALCULATION)Thi
Page 99 and 100: 5.20 OP,RAW (RAW UNCORRECTED γ YIE
Page 101 and 102: 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: 5.29 OP,TROU (TROUBLE)This troubles
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 and 158: (1.6 MeV)1.1 MeV0.75 MeV0.4 MeV0.08
Page 159 and 160: Define the germaniumdetector geomet
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Figure 15: Flow diagram for Gosia m
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gosia < 2-make-correction-factors.i
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Issue the commandgosia < 9-diag-err
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At this point, it is suggested to c
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calculation.) In this case, a copy
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4,-4, -3.705, 3,44,5, 4.626, 3.,7.5
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90145901459014590145901459014590145
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.10.028921.10.026031.10.023431.10.0
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5,5,634,650,82.000,84.000634,638,64
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***********************************
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*** CHISQ= 0.134003E+01 ***MATRIX E
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CALCULATED AND EXPERIMENTAL YIELDS
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11.7 Annotated excerpt from a Coulo
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11.8 Accuracy and speed of calculat
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18,10.056,0.068,0.082,0.1,0.12,0.15
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line 152 Eu 182 Tanumber (keV) (keV
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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
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