Theoretical studies in nuclear structure IV. wave functions for the nuclear p -shell. Part B. ( p n | p n-2< gt;

Abstract

The totally antisymmetric states for the p -shell nuclei previously given (part IV A, Jahn & van Wieringen 1951) arc transformed into the form of linear combinations of antisymmetric states for n - 2 particles vector-coupled to antisymmetric states of particles n and n - 1. The coefficients of the combinations, the ( n | n -2, 2) fractional parentage coefficients, are shown to be products of weight factors, orbital factors and charge-spin factors which are tabulated separately, the tabulation being simplified by use of the special unitary group. This form of the wave functions is the most suitable for the evaluation of any two-body interaction and has been used in a series of investigations (J. P. Elliott 1952, 1953; Robinson 1953) relating to the effect of tensor and spin-orbit forces on the levels of p -shell nuclei. The complete p -shell charge-symmetric central force matrix given by Racah (1950) with unspecified phases is recalculated with the standard (amended) phases of part IV A, with the help of the coefficients here tabulated.