Generalized quasi-spin in neutron-proton systems

Abstract

Using the fact that, in a j n configuration, the nucleon number and isospin dependence for neutrons and protons in a seniority representation is incorporated in a R(5) quasi-spin group, the allowed values of isospin and the number of times it occurs for a given symplectic symmetry (seniority s and reduced isospin t) and nucleon number is derived. Also closed form experessions for the R(5) Clebsch-Gordan coefficients are derived in which one of the irreducible representations is the four-dimensional representation and the others have a) reduced isospin one-half and zero and b) reduced isospine qual 1 2 (2j+1−s) . All others needed for j ≦ 7 2 are calculated numerically. It is shown that these Clebsch-Gordan coefficients give the n, T dependence of the spectroscopic factors. A generalization is made immediately to mixed configurations.