Proton emission from deformed nuclei

The half-lives $T_{1/2}$ for proton decay from the nuclei ${}_{53}^{109}\mathrm{I},$ ${}_{63}^{131}\mathrm{Eu},$ and ${}_{67}^{141}\mathrm{Ho}$ are evaluated exactly, assuming that the emitted proton moves in a deformed single particle Nilsson level. The calculated values of $T_{1/2},$ consistent with experiments, suggest a deformation of $\beta \approx 0.14$ for ${}_{53}^{109}\mathrm{I}$ and $\beta \approx 0.3–0.4$ for ${}_{63}^{131}\mathrm{Eu}$ and ${}_{67}^{141}\mathrm{Ho}.$ The corresponding most likely candidate states as ground states are ${K=1/2\mathrm{}}^{+},$ ${K=5/2\mathrm{}}^{+},$ and ${K=7/2\mathrm{}}^{-}$ for the above three nuclei, respectively. The recently found isomeric state in ${}_{67}^{141}\mathrm{Ho}$ is interpreted as a ${K=1/2\mathrm{}}^{+}$ state.