Theoretical studies in nuclear structure V. The matrix elements of non-central forces with an application to the 2 p -shell

Formulae are derived for the matrix elements of a non-central force in a configuration of N particles, involving fractional parentage coefficients for a reduction by two particles. The case when this configuration contains a number of closed shells and one unfilled shell is considered, although the methods used are applicable to less simple configurations. Specializing to the single 2 p -shell configurations (1 s ) 4 (2 p ) m for which the necessary coefficients have been derived, the matrices of central, tensor and two-body spin-orbit forces are given in terms of their two-particle elements. The determination of these two-particle elements is discussed and values are given for the 2 p -shell. Finally, the matrices derived are used in an attempt to derive the spins and moment data of certain 2 p -shell nuclei from a two-body charge symmetric interaction containing central, tensor and spin-orbit forces.