The Structure of ${}^{33}$Si and the magicity of the N=20 gap at Z=14

Abstract

The structure of ${}^{33}$Si was studied by a one-neutron knockout reaction from a ${}^{34}$Si beam at 98.5 MeV/u incident on a ${}^9$Be target. The prompt ${\hat{I}}^3$-rays following the de-excitation of ${}^{33}$Si were detected using the GRETINA ${\hat{I}}^3$-ray tracking array while the reaction residues were identified on an event-by-event basis in the focal plane of the S800 spectrometer at NSCL (National Superconducting Cyclotron Laboratory). The presently derived spectroscopic factor values, $C^{2}S$, for the 3/2${}^{+}$ and 1/2${}^{+}$ states, corresponding to a neutron removal from the $0d_{3/2}$ and $1s_{1/2}$ orbitals, agree with shell model calculations and point to a strong $N=20$ shell closure. Three states arising from the more bound $0d_{5/2}$ orbital are proposed, one of which is unbound by about 930 keV. The sensitivity of this experiment has also confirmed a weak population of 9/2${}^{-}$ and 11/2${}_{1,2}^{-}$ final states, which originate from a higher-order process. This mechanism may also have populated, to some fraction, the 3/2${}^{-}$ and 7/2${}^{-}$ negative-parity states, which hinders a determination of the $C^{2}S$ values for knockout from the normally unoccupied $1p_{3/2}$ and $0f_{7/2}$ orbits.