Measurements of the $N=28$ isotones ${}^{42}\mathrm{Si}$, ${}^{43}\mathrm{P}$, and ${}^{44}\mathrm{S}$ using one- and two-proton knockout reactions from the radioactive beam nuclei ${}^{44}\mathrm{S}$ and ${}^{46}\mathrm{Ar}$ are reported. The knockout reaction cross sections for populating ${}^{42}\mathrm{Si}$ and ${}^{43}\mathrm{P}$ and a 184 keV γ-ray observed in ${}^{43}\mathrm{P}$ establish that the $d_{3/2}$ and $s_{1/2}$ proton orbits are nearly degenerate in these nuclei and that there is a substantial $Z=14$ subshell closure separating these two orbits from the $d_{5/2}$ orbit. The increase in the inclusive two-proton knockout cross section from ${}^{42}\mathrm{Si}$ to ${}^{44}\mathrm{S}$ demonstrates the importance of the availability of valence protons for determining the cross section. New calculations of the two-proton knockout reactions that include diffractive effects are presented. In addition, it is proposed that a search for the $d_{5/2}$ proton strength in ${}^{43}\mathrm{P}$ via a higher statistics one-proton knockout experiment could help determine the size of the $Z=14$ closure.

• Received 27 February 2006

DOI:https://doi.org/10.1103/PhysRevC.74.034313