Spectroscopic study of the exotic nucleus ${}^{25}\mathrm{P}$

Motivated by the importance of ${}^{25}\mathrm{P}$ for the two-proton decay of ${}^{26}\mathrm{S}$ and for searches of the mirror analog of the island of inversion near $N=16$, we present the first predictions for the spectroscopy of the exotic isotope ${}^{25}\mathrm{P}$ obtained in the shell model, a potential model, and a microscopic-cluster model. All models predict ${}^{25}\mathrm{P}$ to be unbound, with an energy in the range $0.78–1.03$ MeV, which favors previous mass systematics over more recent revisions. We show that ${}^{25}\mathrm{P}$ possesses a rich low-lying spectrum that should be accessible by experimental studies. All of the predicted states below 7 MeV, except one, are narrow. Many of them are built on the excited-core states of ${}^{24}\mathrm{Si}$ for which the Coulomb barrier is raised. For decays into the ${}^{24}\mathrm{Si}\left(\text{g.s.}\right)+p$ channel we determined the proton widths based on their link to the asymptotic normalization coefficients (ANCs) of their mirror analogs in ${}^{25}\mathrm{Ne}.$ We determine these ANCs from the analysis of the transfer reaction ${}^{24}\mathrm{Ne}{(d,p)}^{25}\mathrm{Ne}$. The proton widths for decay into excited-state channels are obtained in model calculations. The only broad state is the intruder $3/2{}^{-}$, the mirror analog of which has been recently observed in ${}^{25}\mathrm{Ne}.$ The ${}^{25}\mathrm{P}(3/2^{-})$ energy is lower than that in ${}^{25}\mathrm{Ne}$, suggesting that the island of inversion may persist on the proton-rich side. All excited states of ${}^{25}\mathrm{P}$ have at least two decay modes and are expected to populate variously the $2_{1,2}^{+}$ and $4^{+}$ states in ${}^{24}\mathrm{Si}$, which then decay electromagnetically.

Figure 1

Experimental level scheme of ${}^{25}\mathrm{Ne}$ compared to shell-model calculations using the WBB and WBP-m interactions (see text for definitions). Dashed lines correspond to states observed experimentally for which no spin and parity is available. The dotted line shows the neutron separation energy, ${\mathrm{S}}_n$, of ${}^{25}\mathrm{Ne}$.

Figure 2

Energies ${\epsilon }_p$ of the resonance states in ${}^{25}\mathrm{P}$ calculated in the potential model using either experimental energies from its mirror analog ${}^{25}\mathrm{Ne}$ (EMA) or shell-model energies (SM) and in the microscopic-cluster model (MCM). The channels with excited cores and the one-, two-, and three-proton decay thresholds are shown by dashed lines.

Figure 3

Spectroscopic factors and ANCs for the observed states of ${}^{25}\mathrm{Ne}$ obtained for various radii of transferred neutron Woods-Saxon potential well and shown as ratios to the values obtained with the radius parameter $r_0=1.25$ fm.