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

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are three to four orders of magnitude shorter than the lifetimes of nuclear states for which internal conversionis important. Consequently the reduction of the internal conversion coefficients due to partial ionization andexcitation of the atomic shells is expected to be small. The database tabulates coefficients calculated for allatomic shells, for transition energies between 1 − 6000keV, and for atomic numbers 5
important to have an accurate knowledge of the absolute bombarding energy of the incident beam and agood measure of the energy loss in the target. Most accelerator facilities quote the bombarding energy tomany significant digits, but it behoves the experimenter to ascertain what absolute reference was used tocalibrate the absolute beam energy.The classical Rutherford trajectory is perturbed slightly by atomic screening, vacuum polarization andrelativistic effects. These effects slightly change the distance of closest approach which can be taken intoaccount by making a small change in the bombarding energy used in the Gosia calculations. Since theseeffects are small, and tend to cancel, the net correction to the bombarding energy typically is < 0.3% whichis unimportant for most experiments[ALD75, KAV90]d) Virtual excitation of unobserved statesIt is important to include explicitly, in the coupled-channel calculations, all states in the yrast domainthat are likely to influence the results significantly. Unobserved states with excitation probabilities exceeding0.1% canhavemeasurableinterferenceeffects on the calculated population of observed states. Also thetruncation of the coupled equations results in errors in the calculated cross section for the uppermost statein any collective band. Thus it is necessary to extend all collective bands by adding at least two bufferstates beyond what is observed to ensure that virtual excitation and coupled-channel truncation effects aretaken into account. The virtual excitation effects are reasonably insensitive to the exact excitation energiesassumed for these unobserved states.Moderate strength matrix elements coupling two nearly degenerate states can lead to appreciable effectseven though there is no observable γ-ray deexcitation between them. Experience has shown that, in mostnuclei, virtual excitation effects due to low-lying states can be estimated reliably and thus do not significantlyadd to the uncertainties in the final results.Virtual excitation of the giant E1 resonance can decrease the population of high-spin states by up to 12%[CLI86]. Fortunately this can be estimated reliably by adding a polarization term to the interaction[ALD75].e) Mutual excitationBoth the target and projectile can be excited simultaneously influencing the cross sections for Coulombexcitation of a given state. Normally one of the two interacting nuclei is chosen to be a closed-shell nucleus,such as 208 Pb, to minimize such mutual excitation effects. Fortunately the multipole-multipole interactionterm does not interfere with either monopole-multipole term, thus the corrections are small even for caseswhen mutual excitation is appreciable. For example, for the case of 76 Se excited by 48 Ti the predicted mutualexcitation changes the 76 Se crossections by only 0.7%.[KAV90]f) Gamma-ray angular distributionsThe hyperfine interaction of the excited nuclei recoiling in vacuum, that is the deorientation effect,contributes the largest uncertainty in predicting the angular distributions of the deexcitation γ-rays. Themagnitude of the deorientation effect depends sensitively of the lifetimes of the deexciting states. Use ofbest-fit global parameters, within the framework of the Brenn and Spehl two-state model of the hyperfineinteraction, has been shown to give a reasonable prediction of the deorientation effect [BOS77, BRE77].Fortunately the uncertainty in our knowledge of the deorientation effect usually contributes less than a 2%error in the final extracted matrix elements, in part because the many γ-ray detectors used in modern γ-raydetector arrays average over the γ-ray angular distribution.The assumption of cylindrical symmetry in evaluating the attenuation factors Q λ , used to account forthe finite size of the γ-ray detectors, is not applicable for clover-detector geometry used by some Ge detectorarrays. However, use of the cylindrical symmetry assumption in general will introduce errors that are smallerthan the uncertainties inherent in predicting the hyperfine interactions.States having lifetimes in the nanosecond range can decay while displaced significantly from the targetspot due to the recoil. In most cases the first-order correction for this effect available in Gosia is adequateto correct for this displacement.g) Absolute normalization of cross sectionsComparison with the well-known Rutherford cross section for elastic scattering can be used to determineabsolute Coulomb excitation cross sections. Although this approach is easy using the magnetic spectrometertechnique[CLI69a], it is difficult when the higher sensitivity particle-γ coincidence method is employed forheavy-ion Coulomb excitation work[CLI86]. The γ-ray detection efficiency typically is measured to an accuracyof ≈ 5% using well-known γ-ray sources. However, it is necessary to take ino account the coincidencedetection efficiency which can be significantly reduced due to dead time and pile up rejection. An extreme27
Page 1: COULOMB EXCITATION DATA ANALYSIS CO
Page 4 and 5: 10 MINIMIZATION BY SIMULATED ANNEAL
Page 6 and 7: 1 INTRODUCTION1.1 Gosia suite of Co
Page 8 and 9: 104 Ru, 110 Pd, 165 Ho, 166 Er, 186
Page 13 and 14: Figure 1: Coordinate system used to
Page 15 and 16: Cλ E =1.116547 · (13.889122) λ (
Page 17 and 18: Figure 2: The orbital integrals R 2
Page 19 and 20: 2.2 Gamma Decay Following Electroma
Page 21 and 22: where :d 2 σ= σ R (θ p ) X R kχ
Page 23 and 24: Formula 2.49 is valid only for t mu
Page 25: Ã XK(α) =exp−iτ i (E γ )x i (
Page 29 and 30: 3 APPROXIMATE EVALUATION OF EXCITAT
Page 31 and 32: with the reduced matrix element M c
Page 33 and 34: q (20)s (0 + → 2 + ) · M 1 ζ (2
Page 35 and 36: esults of minimization and error ru
Page 37 and 38: adjustment of the stepsize accordin
Page 39 and 40: approximation reliability improves
Page 41 and 42: Zd 2 σ(I → I f )Y (I → I f )=s
Page 43 and 44: 4.5 MinimizationThe minimization, i
Page 45 and 46: X(CC k Yk c − Yk e ) 2 /σ 2 k =m
Page 47 and 48: However, estimation of the stepsize
Page 49 and 50: It can be shown that as long as the
Page 51 and 52: een exceeded; third, the user-given
Page 53 and 54: where f k stands for the functional
Page 55 and 56: x i + δx i Rx iexp ¡ − 1 2 χ2
Page 57 and 58: 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
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¡ dE¢dx1 ..¡ dEdx¢Stopping powe
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NI1, NI2 Number of subdivisions of
Page 85 and 86:
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
Page 101 and 102:
5.21 OP,RE,A (RELEASE,A)This option
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5.25 OP,SIXJ (SIXJ SYMBOL)This stan
Page 105 and 106:
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
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8 SIMULTANEOUS COULOMB EXCITATION:
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4, 3, 1kr88.corKr corrected yields
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0 Correction for in-flight decay ch
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OP, ERRO Estimation of errors of fi
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9 COULOMB EXCITATION OF ISOMERIC ST
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configurations with a probability e
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The average range covered by each m
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SFX,NTOTI1(1),I2(1),RSIGN(1)I1(2),I
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11.2 LearningtoWriteGosiaInputsThe
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(1.6 MeV)1.1 MeV0.75 MeV0.4 MeV0.08
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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
Page 201 and 202:
[KIB08]T.Kibédi,T.W.Burrows,M.B.Tr
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