Three-body model of light nuclei with microscopic nonlocal interactions

Abstract

A three-body cluster model involving microscopic nonlocal interactions is developed and compared with a fully microscopic cluster model. The energy-independent nonlocal interactions are obtained from a renormalization of the energy-dependent kernels of the resonating-group method. Such interactions are derived for the $\ensuremath{\alpha}\ensuremath{\alpha}$ and $\ensuremath{\alpha}n$ systems. The role and importance of nonlocality are discussed. These interactions are employed in three-body studies of the $\ensuremath{\alpha}\mathit{nn},\ensuremath{\alpha}\ensuremath{\alpha}n$, and $3\ensuremath{\alpha}$ descriptions of the $^{6}\mathrm{He}$, $^{9}\mathrm{Be}$, and $^{12}\mathrm{C}$ nuclei. A comparison with fully microscopic calculations provides a measure of the importance of three-cluster exchanges in those states. The differences between both cluster-model calculations are in general small, except in the densities at short distances.