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

are available using positive and negative values of ∆M k . In addition, J ki can be evaluated using the i-thcomponent of the gradient at perturbed M k or using the k-th component of the gradient with perturbedM i . Since the quadratic approximation 6.1 is not fully adequate, the averaging procedure must be used tocancel the difference between various estimates and to preserve the symmetry of J. Furthermore, for thematrix elements M k for which the full error calculation was not performed only the diagonal element J kk isassumed to be non-zero, i.e., the correlation is neglected. The estimate of J kk is this case results from:∆S =1= 1 2 J kk∆M k (6.42)where ∆M k is the average diagonal error of M k , i.e., the mean value of the negative and positive deviations.The method presented above allows to estimate the errors of the collective parameters and their distributionswith the reasonable efficiency. However, one must be aware of the scope of the approximationsused, which do not allow treating the estimated errors very rigorously, providing only a crude estimate ofthe determined accuracy the sum rules.6.2.3 INPUT INSTRUCTIONSSIGMA reads in the input file, which must be called SIGMA.INP and in addition three permanent filescreated by GOSIA, referred to in SIGMA as filename.err [TAPE11], filename.smr [TAPE12] and sixj.tab[TAPE3].The input file selects the mode of calculation and should be given as:ILNSTI(1)I(2)filename.smr corresponding to SIGMA TAPE12filename.err corresponding to SIGMA TAPE11sixj.tab corresponding to SIGMA TAPE3· only if 0< NST ≤ 75I(NST)That is, the input file comprises two switches, three filenames, followed by the list of states for which allerrors are to be calculated (NST records) where:IL may be either 0 or 1. IL =1will cause the printout of the matrix elements (by their indices)involved in the evaluation of 14 invariants calculated for each state. The invariants are numbered from 1 to14 according to the sequence they appear in the first column of the output table (see the sample output atthe end of this chapter). IL =0will cause no compilation of this list.NST selects the mode of error calculation. Three special values of NST: NST = −1, NST =0orNST =99require no further input. NST = −1 is used if only the invariants and the resulting statisticalmoments (given in the second column of the output table) are to be calculated and no error estimation isrequested. In this mode SIGMA can be used independently of GOSIA and the information concerning thelevel scheme and coupling scheme, normally produced by GOSIA, must be provided by the user (see thedescription of the TAPE files below). NST =0implies that the error calculation is to be performed onlyfor Q 2 ,threevaluesofv(Q 2 ) and four values of cos3δ for all states, while NST =99specifies the errors tobe estimated for every statistical moment for all states. The reason for this distinction is that the statisticalmoments based on the sixth-order invariants are usually not meaningful due to the number of the matrixelements involved and the resulting error propagation. Also, calculation of these invariants is most timeconsuming.Usually, it is practical to calculate all the errors only for the few lowest-lying states. This can be126