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

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 the $\alpha$ 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 $\alpha$-particle-like cluster structure for the excited state and a shell-model-like delocalized structure for the ground state.

Figure 1

Energies from ${}^{12}$C$+n+n+p+p$ threshold for the ground and first excited $0^{+}$ states of ${}^{16}$O. The ${}^{12}$C$+\alpha$ threshold and experimental energies are shown by thin dotted lines.

Figure 2

Top: Distributions of the relative distance between the ${}^{12}$C core and the c.m. of $4N$. Bottom: Density distributions of the valence nucleon measured from the $4N$ c.m. The nucleon density distribution of the $\alpha$ particle is calculated using the MN potential.

Figure 3

${}^{12}$C$+\alpha$ spectroscopic amplitudes for the ground and first excited $0^{+}$ states of ${}^{16}$O.

Figure 4

Decomposition of the $0^{+}$ states of ${}^{16}$O and ${}^{16}$C into $Q\hslash \omega$ components with $\hslash \omega =16.0$ MeV.