Correlated-basis description of $\alpha$-cluster and delocalized $0^{+}$ states in ${}^{16}$O

Abstract

A five-body calculation of ${}^{12}$C+$n$+$n$+$p$+$p$ 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$+n$, ${}^{12}$C$+p$, and $\alpha$-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 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 spatially localized $\alpha$-particle-like cluster structure for the excited state and shell-model-like delocalized structure for the ground state.

Comments: 6 pages, 4 figures, to appear in Phys. Rev. C