Correlated-basis description ofα-cluster and delocalized0+states in16O

Abstract

A five-body calculation of ${}^{12}$C$\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}n+n+p+p$ is performed to take a step towards solving an outstanding problem in nuclear theory: the simultaneous and accurate description of the ground and first excited 0${}^{+}$ states of ${}^{16}$O. The interactions between the constituent particles are chosen consistently with the energies of bound subsystems, especially ${}^{12}$C$\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}n$, ${}^{12}$C$\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}p$, and the $\ensuremath{\alpha}$ particle. The five-body dynamics is solved with the stochastic variational method on correlated Gaussian basis functions. No restriction is imposed on the four-nucleon configurations except for the Pauli principle excluding the occupied orbits in ${}^{12}$C. The energies of both the ground and first excited states of ${}^{16}$O are obtained in excellent agreement with experiment. Analysis of the wave functions indicates a spatially localized $\ensuremath{\alpha}$-particle-like cluster structure for the excited state and a shell-model-like delocalized structure for the ground state.