Semi-microscopic calculation of trinucleon cluster states in 18F and 18O

A strikingly successful phenomenological model which treated a number of low-lying negative-parity states in 18F and 18O as having the structure of an (A=3) cluster orbiting an (A=15) core is considered. An attempt is made to justify the assumptions inherent in this model on more microscopic grounds. To do this, an effective, local, cluster-core potential containing central, spin-orbit, spin-spin and tensor-spin components is derived from the shell-model approximation to the ground state of the (A=15) core and a nucleon-trinucleon potential. This latter potential would ideally be obtained from a phase-shift analysis of nucleon-trinucleon scattering data, but in the absence of sufficiently detailed experiments to do this, a family of such potentials, whose non-central terms are taken to have Gaussian geometries of various widths and strengths chosen by considering some of the excited states of the A=4 nuclei, is derived and used. Many of the phemomenological assumptions are then semi-microscopically vindicated, and quite reasonable quantitative agreement with the free parameters of the phenomenological model and the measured energies of the trinucleon cluster states in 18F and 18O is obtained. (author)