Valence $1s-0d$ proton vacancy of the $^{32}$Si ground state
N. Watwood, C. R. Hoffman, B. P. Kay, I. A. Tolstukhin, J. Chen, T. L. Tang, D. Bazin, Y. Ayyad, S. Beceiro-Novo, S. J. Freeman, L. P. Gaffney, R. Garg, H. Jayatissa, A. N. Kuchera, P. T. MacGregor, A. J. Mitchell, A. Muñoz-Ramos, C. Müller-Gatermann, F. Recchia, C. Santamaria, M. Z. Serikow, D. K. Sharp, G. L. Wilson, A. H. Wuosmaa, J. C. Zamora
公開日: 2025/10/6
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.