Widths of ${}^{26}\mathrm{P}\left(1^{+}\right)$ and mass of ${}^{26}\mathrm{P}\left(\mathrm{g}.\mathrm{s}.\right)$

For the $1^{+}$ first-excited state of ${}^{26}\mathrm{P}$, the lifetime and the upper limit on the proton width have been combined with shell-model spectroscopic factors to place an upper limit on the proton single-particle (sp) width. With a potential model, this limit on sp width allows an upper limit on the $1^{+}$ resonance energy of $E_{\mathrm{r}}<124\mathrm{keV}$. Combining with the known $1^{+}$ excitation energy provides a limit on the proton separation energy of ${}^{26}\mathrm{P}\left(\mathrm{g}.\mathrm{s}.\right)$ of $S_{\mathrm{p}}>40\mathrm{keV}$, considerably better than a recent result of $S_{\mathrm{p}}>-135\mathrm{keV}$ from a similar procedure that used $R$-matrix sp widths.

Figure 1

Single-particle width for ${}^{25}\mathrm{Si}+p, \ell =2$, computed in a Woods-Saxon well, is plotted vs resonance energy. The horizontal line is at the upper limit deduced from shell-model spectroscopic factors and the upper limit on the proton width for the $1^{+}$ state.