Theoretical studies in nuclear structure IV. Wave functions for the nuclear p -shell Part A. ‹ p n │ p n-1 p › fractional parentage coefficients

Abstract

A complete set of wave functions is constructed for the whole of the nuclear p-shell (from p$^{3}$ to p$^{12}$). Following Racah, the wave functions for p$^{n}$ are expressed as linear combinations of totally antisymmetric wave functions for p$^{n-1}$, vector-coupled to the wave functions of the remaining particle. The coefficients in the linear combination are expressed as the product of an orbital coefficient, a charge-spin coefficient and a weight factor equal to the square root of the ratio of the dimensions of two irreducible representations of permutation groups. Using the Young-Yamanouchi orthogonal representation of the permutation group, the orbital and charge-spin coefficients may be calculated independently. Specialization of the new method to the atomic p-shell and an alternative direct method of calculating the total parentage coefficients are described in the appendices. A reciprocal relation for the special unitary group, simplifying the calculation of both the orbital and the charge-spin coefficients, is described in an Addendum.