Alpha-cluster structure ofS32

The ground state and the first excited states of ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ have been studied within the alpha-cluster model for two standard soft-core forces. We discuss the approximations resulting from variation without projection, variation after parity projection, angular momentum projection after variation, and possible $K$ mixing. In contrast to earlier calculations in lighter nuclei a free variation of all parameters has been performed without forcing the alpha clusters to be arranged in configurations with prescribed symmetry. In all approximations and for both forces the intrinsic ground state turns out to be triaxial with $C_{2v}$ symmetry. The resulting binding and excitation energies, rms radii, and quadrupole moments are given. In comparable cases a close agreement is found with Hartree-Fock results for the same forces.