Valence $1s-0d$ proton vacancy of the ${}^{32}$Si ground state

Abstract

The ${}^{32}$Si(${}^3$He,$d$)${}^{33}$P reaction was studied in inverse kinematics at 6.3~MeV/$u$. States in ${}^{33}$P corresponding to the proton $1s-0d$ single-particle orbitals were identified up to $\sim$4.5 MeV in excitation energy. The (${}^3$He,$d$) spectroscopic factors were determined from Distorted Wave Born Approximation calculations. When combined with complementary neutron-adding data, the $1s-0d$ proton vacancies in the ${}^{32}$Si ground state were extracted. In conjunction with a re-analysis of data from previous single-particle measurements, the trends in proton and neutron vacancy were explored across the ${}^{28,30,32,34}$Si isotopes. Both proton and neutron vacancy data show gradual changes in their occupancies. The proton $1s_{1/2}$ orbitals in ${}^{32}$Si and ${}^{34}$Si are both consistent with being empty. The ground-state nucleon distributions are described by shell-model calculations constrained to the $1s-0d$ model space.

9 pages, 5 figures