Cluster Model Calculation on the Energy Levels of the Lithium Isotopes

A variational procedure is adopted to determine the energies of the levels of the highest space symmetry type in ${\mathrm{Li}}^6$ and ${\mathrm{Li}}^7$. The trial wave functions employed take into consideration the existence of cluster structures in those nuclei. With a simple two-body force, it is shown that the computed energies of the various states are in reasonable agreement with experiment. The ${}_{}{}^2{}_{}{}^{}F_{\frac{5}{2}}^{}{}_{}{}^{}$ level in ${\mathrm{Li}}^7$, as yet undetermined experimentally, is found to have an excitation energy of about 5.6 Mev and a rather large level width. The calculation also indicates that to explain the splitting of levels in those nuclei, a constant two-body spin-orbit force of the pure neutral form is inadequate.