Simple potential model for cluster states in light nuclei

Abstract

We present a simple model for three and four particle cluster states in light nuclei. These states are considered as bound states and single particle resonances of a cluster-core potential, which is obtained by folding the cluster and core mass densities. We calculate some properties of these states in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, such as the rms radii, $B\left(E2\mathrm{}\right)\mathrm{}$ values, $\alpha$-decay widths, and energy spectra. Good agreement with available data is obtained and some predictions are made for $B\left(E2\mathrm{}\right)\mathrm{}$ values in the $K^{\pi }=0^{-}$ bands in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. This model is also used to interpret recent heavy ion three particle transfer data. Dynamical support is offered for high spin assignments in ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ previously based on kinematical considerations.