A unified shell model description of mass 13-20 nuclei

Abstract

A C¹² core and a (1p1/2, ld5/2, 2s1/2) shell-model basis are used to provide a unified account of A=13-20 nuclei. All possible configurations of the (A-12) active particles are allowed. The residual two-body interactions and single particle energies are reduced to linear expressions in 33 one and two-body matrix elements. These matrix elements are then treated as parameters and varied until a best fit to approximately 100 known energy levels is obtained. From the values of these 33 parameters, the energies and wavefunctions of over 1000 positive and negative parity levels in this region are derived. The resulting wavefunctions are then used to calculate spectroscopic factors for stripping and pickup reactions and M1 and E2 electromagnetic transition rates. Tables and figures containing results of each of these calculations are presented along with the corresponding experimental values. In general, the results are in good agreement for each type of observable and would indicate that both typical single-particle and collective (rotational) phenomena emerge from the assumed shell-model basis.