2s1/2occupancies in30Si,31P, and32S

Elastic electron scattering off ${}^{30}$Si and ${}^{31}$P was studied in an effective momentum-transfer range of 1.8–3.0 fm${}^{-1}$. The form-factor data were analyzed together with existing data sets for these nuclei and for ${}^{32}$S in a model-independent Fourier-Bessel expansion. For ${}^{31}$P the $M1\mathrm{}$ contribution was subtracted following an established parametrization. Results of Hartree-Fock (HF) calculations, performed for these three nuclei in a spherical basis and in an axially deformed basis, are compared to experiment. Occupancies have been determined which, when used in the spherical-basis HF calculations, lead to a good description of the elastic form-factor data. The deformed-basis calculations have been used to study the influence of the deformation on the calculated binding energies and ground-state charge densities. In all calculations the influence of using different effective nucleon-nucleon interactions was investigated. The resulting differences in ${2s}_{1/2}$ in occupancy are combined with results from previous existing ${(e,e}^{\prime }p)$ experiments to yield “absolute occupancies” for the ${2s}_{1/2}$ orbital. The deduced ${2s}_{1/2}$ occupancies for ${}^{30}$Si and ${}^{32}$S are 0.24(4) and 1.35(19), respectively.