Peculiar properties of the cluster-cluster interaction induced by the Pauli exclusion principle

Abstract

The role of the Pauli principle in the formation of both the discrete spectrum and multichannel states of the two-cluster nuclear systems is studied in the algebraic version of the resonating-group method. Solutions of the Hill-Wheeler equations in the discrete representation of a complete basis of the Pauli-allowed states are discussed for the $^{4}\mathrm{He}+n$, $^{3}\mathrm{H}+^{3}\mathrm{H}$, and $^{4}\mathrm{He}+^{4}\mathrm{He}$ binary systems. An exact treatment of the antisymmetrization effects related to the kinetic energy exclusively is shown to result in either an effective repulsion or attraction of the clusters. It also yields a change in the intensity of the centrifugal potential. Both factors significantly affect the scattering phase behavior. Special attention is paid to the $^{6}\mathrm{He}+^{6}\mathrm{He}$ multichannel two-cluster system as well as to the coupled-channel calculation of the $^{12}\mathrm{Be}$ nucleus (provided that $^{6}\mathrm{He}+^{6}\mathrm{He}$ and $^{4}\mathrm{He}+^{8}\mathrm{He}$ clusterings are taken into account). In the latter case, the cluster-cluster interaction derived from the kinetic-energy operator modified by the Pauli principle leads to inelastic processes and ensures the existence of both the bound state and a resonance in the $^{12}\mathrm{Be}$ compound nucleus.