Alpha cluster model and the spectrum of O-16

The structure of $^{16}\mathrm{O}$ is studied in the alpha cluster model with parity and angular-momentum projection for several nucleon-nucleon interactions. The method differs from previous studies in that the states of positive and negative parity are determined without the customary restriction of the variational space to cluster positions with certain assumed symmetries. It turns out that a number of variational results in the literature are spurious under unrestricted variations. We demonstrate that the alpha cluster model of $^{16}\mathrm{O}$ is capable of explaining most of the experimental $T=0$ levels up to about 15 MeV excitation. In particular, the 6.05 MeV rotational band is reproduced remarkably well. A shell-model analysis of the excited cluster-model states shows the necessity of including a very large number of shells. The evidence for the recently proposed tetrahedral symmetry of some excited states is also discussed.