On the Wigner Supermultiplet Scheme

Abstract

Calculation of Wigner and Racah coefficients for the group SU(4)⊃[SU(2)×SU(2)] make it possible to perform the spin—isospin sums in the cfp (fractional parentage coefficients) expansion of the matrix elements of one‐ and two‐body operators in the Wigner supermultiplet scheme. The SU(4) coefficients needed to evaluate one‐ and two‐particle cfp's, the matrix elements of one‐body operators, and the diagonal matrix elements of two‐body operators are calculated in general algebraic form for many‐particle states characterized by the SU(4) irreducible representations [yy0], [y y − 1 0], [yy1], [y11], [y y − 1 y − 1], [y10], [yy y − 1], [y00], and [yyy], whose states are specified completely by the spin and isospin quantum numbers (y = arbitrary integer). Applications are made to the calculation of the matrix elements of the complete space‐scalar part of the Coulomb interaction and the space‐scalar part of the particle‐hole interaction for nucleons in different major oscillator shells.