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

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.