Five-dimensional quasi-spin the n, T dependence of shell-model matrix elements in the seniority scheme

Abstract

The five-dimensional quasi-spin 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 jn in terms of the corresponding matrix elements for the configuration jv. The n, T dependent factors for one- and two-nucleon c.f.p. 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 are restricted to ([omega]10), (), (tt), and the states of ([omega]11) with n-v = 4k-2T, (k is an integer). Explicit expressions are given for the diagonal matrix elements of the general, charge-independent, two-body interaction and the isovector and isotensor parts of the Coulomb interaction for seniorities v = 0 and 1, and the v = 2 states with n = 4k +2-2T.