Spectroscopy of ${}^{35}\mathrm{P}$ using the one-proton knockout reaction

The structure of ${}^{35}\mathrm{P}$ was studied with a one-proton knockout reaction at 88 MeV/u from a ${}^{36}\mathrm{S}$ projectile beam at NSCL. The $\gamma$ rays from the depopulation of excited states in ${}^{35}\mathrm{P}$ were detected with GRETINA, while the ${}^{35}\mathrm{P}$ nuclei were identified event-by-event in the focal plane of the S800 spectrograph. The level scheme of ${}^{35}\mathrm{P}$ was deduced up to 7.5 MeV using $\gamma \text{−}\gamma$ coincidences. The observed levels were attributed to proton removals from the $sd$ shell and also from the deeply bound $p_{1/2}$ orbital. The orbital angular momentum of each state was derived from the comparison between experimental and calculated shapes of individual $(\gamma$-gated) parallel momentum distributions. Despite the use of different reactions and their associate models, spectroscopic factors, $C^{2}S$, derived from the ${}^{36}\mathrm{S}(-1p)$ knockout reaction agree with those obtained earlier from ${}^{36}\mathrm{S}\left(d,{}^3\mathrm{He}\right)$ transfer, if a reduction factor $R_s$, as deduced from inclusive one-nucleon removal cross sections, is applied to the knockout transitions. In addition to the expected proton-hole configurations, other states were observed with individual cross sections of the order of 0.5 mb. Based on their shifted parallel momentum distributions, their decay modes to negative parity states, their high excitation energy (around 4.7 MeV), and the fact that they were not observed in the $\left(d,{}^3\mathrm{He}\right)$ reaction, we propose that they may result from a two-step mechanism or a nucleon-exchange reaction with subsequent neutron evaporation. Regardless of the mechanism, that could not yet be clarified, these states likely correspond to neutron core excitations in ${}^{35}\mathrm{P}$. This newly identified pathway, although weak, offers the possibility to selectively populate certain intruder configurations that are otherwise hard to produce and identify.

Figure 1

Singles (first line) and $\gamma$-gated (second to fourth lines) $\gamma$-ray Doppler-corrected spectra of ${}^{35}\mathrm{P}$.

Figure 2

Energies (with uncertainties of $\sigma =2$ keV) and population fractions, $b_f$ (in $\%)$ of the states fed in ${}^{35}\mathrm{P}$ during our experiment, by the one proton-knockout reaction (in black), or possibly by a two-step reaction mechanism (right part, in red), see text for details. The reported spins and parities of states, taken from Ref. [25], are confirmed by the present work.

Figure 3

Experimental parallel momentum distributions for the most populated states in ${}^{35}\mathrm{P}$ (black crosses) are compared to calculations assuming a $\ell =0$ (red curves), $\ell =1$ (dashed blue), $\ell =2$ (blue), and $\ell =3$ (green) proton removal from the ${}^{36}\mathrm{S}$ ground state.

Figure 4

Measured parallel momentum distributions for the ground state and the states at 4382, 4766, 4960, and 5096 keV (displayed in red in the level scheme) of ${}^{35}\mathrm{P}$. The bottom panel shows that for ${}^{36}\mathrm{P}$ nucleus, as produced from ${}^{36}\mathrm{S}$. The vertical dashed line, crossing all panels, represents the centroid of the momentum distribution of ${}^{36}\mathrm{P}$ nucleus, $p_0$, shifted by the evaporation of a neutron, i.e., $p_1=(A-1)/A{p}_0$. It is seen that the distributions for all states labeled red in the level scheme are shifted relative to that of the ${}^{35}\mathrm{P}$ ground state, that is produced via direct one-proton knockout.

Figure 5

Doppler-corrected $\gamma$-decay spectrum for the ${}^{36}\mathrm{P}$ nucleus populated from ${}^{36}\mathrm{S}$ in a nucleon-exchange reaction.