$d_{5/2}$ proton hole strength in neutron-rich ${}^{43}\mathrm{P}$: Shell structure and nuclear shapes near $N=28$

We report on the use of the one-proton knockout reaction from ${}^{44}\mathrm{S}$ to determine the location of $d_{5/2}$ proton strength in neutron-rich ${}^{43}\mathrm{P}$. The results are used to test two shell-model frameworks with different pictures of the evolution of single-proton energies along the $N=28$ isotones near the neutron dripline. We observe a concentration of $d_{5/2}$ proton hole strength near 1 MeV in excitation energy. This result favors the recent shell-model interaction of Utsuno et al. [Eur. Phys. J. Spec. Top. 150, 187 (2007)] and provides additional evidence for an oblate shape for ${}^{42}\mathrm{Si}$.

Figure 1

Doppler-corrected spectrum of γ rays measured in coincidence with recoiling ${}^{43}\mathrm{P}$ particles. The solid curve is the GEANT3 fit described in the text.

Figure 2

Gamma-ray spectra measured in coincidence with the 184-keV (top panel) and 825-keV (bottom panel) γ rays.

Figure 3

Proposed level scheme of ${}^{43}\mathrm{P}$ based on the present work. Gamma-ray intensities from the fitting process, relative to that of the 184-keV transition, appear in italics.

Figure 4

Parallel momentum distributions of states of ${}^{43}\mathrm{P}$ populated in one-proton knockout from ${}^{44}\mathrm{S}$. The curves are theoretical distributions, described in the text, for $l=0$ (dashed) and $l=2$ (solid).

Figure 5

Measured partial knockout cross sections to $J^{\pi }=5/2^{+}$ states below the neutron separation energy (top left panel) in 250-keV bins compared with theoretical cross sections (two bottom right panels) described in the text. The numerical values in the two bottom left panels are the shell-model spectroscopic factors $C^{2}S$. The plots on the left show spectroscopic factors summed as a function of excitation energy up to 6 MeV for each spin.