Five-Dimensional Quasispin. The N, T-Dependence of Shell Model Matrix Elements in the Seniority Scheme

摘要

The five-dimensional quasispin formalism is used to factor out the n, T-dependent parts of shell model matrix elements in the seniority scheme and derive reduction formulae which make it possible to express matrix elements for states of definite isospin T in the configuration j exp. n in terms of the corresponding matrix elements for the configuration j exp. v. The n, T-dependent factors for one and two nucleon c.f.p.'s, and for the matrix elements of one-body operators and the two-body interaction are expressed in terms of generalized R(5) Wigner coefficients. The needed R(5) Wigner coefficients are calculated in the form of general algebraic expressions for the seniorities v and reduced isospins t corresponding to the simpler R(5) irreducible representations. In this first contribution the R(5) representations (omega sub 1 t) = (j+1/2-1/2v, t) are restricted to (omega sub 1 O), (omega sub 1 1/2), (tt), and the states of (omega sub 1 l) with n-v = 4k-2T, (k = integer). Explicit expressions are given for the diagonal matrix elements of the general charge independent two-body interaction and the iso-vector and iso-tensor parts of the Coulomb interaction for seniorities v = 0 and 1, and the v = 2 states with n = 4k+2-2T. (Author)