Di-proton decay of the $6.15\hspace{0.5em}\mathrm{MeV}\hspace{0.5em}{1}^{-}$ state in ${}^{18}\mathrm{Ne}$

The widths for one- and two-proton decay of the $1_2^{-}$ state in ${}^{18}\mathrm{Ne}$ are calculated. Shell-model wave functions are used to obtain the spectroscopic factors. The R-matrix theory of Barker which incorporates the final-state interaction between the two protons is used for the di-proton decay model. The calculated widths for both one- and two-proton decay are in qualitative agreement with experiment. We find that the decay width for sequential two-proton decay through the ghost of the ${1/2}^{+}$ bound state in ${}^{17}\mathrm{F}$ is comparable to the width of the direct di-proton decay.