Studies in jj -coupling - II. Fractional parentage coefficients and the central force energy matrix for equivalent particles

Abstract

Jahn's method of fractional parentage coefficients is adapted to obtain fully antisymmetric wave functions for the configurations j$^{n}$ of neutrons and protons, where j = $\frac{3}{2}$, $\frac{5}{2}$, $\frac{7}{2}$, and n = 3 and 4. Invariant theory is used to obtain linear combinations of Slater integrals which have special transformation properties with respect to the unitary and symplectic groups. In this way it is shown how the ordering of levels in jj-coupling with short-range central interactions is determined by the eigenvalues of Casimir's operator.