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

5.27 OP,THEO (COLLECTIVE MODEL ME)Coulomb excitation is the preemminent probe of collective modes in nuclear structure. Consequently frequentlyit is convenient to calculate Coulomb excitation cross sections assuming a set of matrix elementsrelated by a collective model. OP,THEO generates matrix elements according to the geometrical modelfollowing Bohr-Mottelson prescription ( General Structure of Matrix Elements, paragraph 4-3d in NuclearStructure) (BOH69).OP, THEO generates only the matrix specified in the ME input and writes them to the REST file.Therefore it should be used after OP, COUL or OP, GOSI, but before OP, REST command is executed.Fixing, coupling and releasing of the matrix elements is controlled by the ME and CONT commands, theonly function of OP,THEO being to create numerical values and write them to the restart file. This allowsmaking model-dependent analyses by specifying the coupling scheme, generating a set of matrix elements and,keeping the values coupled, performing the minimization, thus effectively fitting only geometrical intrinsicmoments which can greatly reduce the number of fitted variables. To define the OP,THEO input the usermust divide the levels specified in the LEVE input into bands of definite values of K quantum number. Thefirst entry under OP, THEO is the number of bands, which, as an input-saver feature, can be given as anegative integer, in which case the remainder of the input to OP, THEO will be ignored and the contents ofthe restart file not affected. This is helpful if some matrix elements are added or removed using ME option- OP, THEO then can be easily reactivated.OP,THEO input is divided into two loops. The first one is the definition of the bands and the levelsascribed to be band members. As usual, LEVE-defined state indices are used to identify the levels. Thesecond loop is the multipolarity loop, which should exhaust all couplings defined in the ME input. Herefor each band-to-band coupling ( band indices being either identical for inband matrix elements or differentfor interband matrix elements ) one should specify relevant intrinsic moments for a given multipolarity. Ingeneral there are three intrisic moments that could be involved. For in-band or equal-K interband transitionsonly one of them, marked Q1 is relevant. For non-equal K values generally two moments with the projectionsequal to the sum and difference of K’s are required (Q1 and Q2), unless one of the K’s is zero, when againonly Q1 is needed. For the K-forbidden transitions a three parameter Mikhailov formula is used. Thus,in general, three Q-values are to be input for each band-to-band coupling. Note that Q3 - a decouplingparameter - is irrelevant if none of the K-values assumes the value of 1/2 and Q2 is irrelevant for in-bandtransitions and for K-allowed, one K =0interband couplings. Nevertheless, three numbers are required foreach band-to-band coupling.The specification of multipolarities follows the general convention of GOSIA - E1 through E6 are labeledjust by 1 through 6, whileM1 is labeled as 7 and M2 as 8. Definition of bands and multipolarities shouldexhaust all couplings included in ME scheme. It is important that calculated matrix elements fit within theuser-specified limits.The structure of the input to OP, THEO is:NBANDSNumber of user-defined bands. If negative OP,THEO is ignoredK, NLEV Band definition - K of a band, number of levels in band #1N1, N2......, NNLEV Indices of levels forming band #1·· The above two records should be repeated NBANDS times to define all bands·λ 1Start of multipolarity loop - first multipolarityNB i , NB jBand indicesQ1, Q2, Q3 Intrinsic moments· The above sequence should be repeated until all possible105