Valence 1s-0d proton vacancy of the ³²Si ground state

The ³²Si(³He,d) ³³P reaction was studied in inverse kinematics at 6.3 MeV/u. States in ³³P corresponding to the proton 1s-0d single-particle orbitals were identified up to ≈ 4.5 MeV in excitation energy. The (³He,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 ³²Si ground state were extracted. In conjunction with a reanalysis of data from previous single-particle measurements, the trends in proton and neutron vacancy were explored across the ^28,30,32,34Si isotopes. Both proton and neutron vacancy data show gradual changes in their occupancies. The proton 1s_1/2 orbitals in ³²Si and ³⁴Si are both consistent with being empty. The ground-state nucleon distributions are described by shell-model calculations constrained to the 1s-0d model space.