Triton and alpha-particle cluster states in43Sc

Abstract

A cluster-model calculation of the properties of triton and alpha-particle cluster states in 43Sc is presented. For the triton cluster states, the 40Ca core is assumed to be in its ground state. An effective, local, cluster-core potential containing central and spin-orbit terms, obtained from a simple folding procedure, is used to generate the cluster-state energies and wavefunctions from a single-particle Schrodinger equation. For the alpha-particle cluster states, the 39K core is assumed to be in its ground or first excited state, which is treated as a d3/2 or s1/2 hole in an inert 40Ca core. In addition to a central folded potential, obtained in the same way as for the triton cluster states, a tensor force between cluster and core is calculated microscopically, using an alpha-nucleon scattering potential. This produces a significant splitting of the ground-state band of alpha-particle cluster states into quadruplets, and also mixes members of the bands based on the two different core states. In both triton and alpha-particle cases an orthogonality condition is used to reject redundant states. A comparison of the theoretically calculated spectra and electromagnetic properties of these cluster states with the equivalent measured quantities of some likely experimental counterparts casts doubt on the existence of the triton cluster states. There is good agreement for the alpha-particle cluster states, which appear to be related to similar states in 40Ca and 44Ti, and contain some members with high spins.