$\gamma$-ray spectroscopy of ${}^{42}\mathrm{K}$ and ${}^{43}\mathrm{K}$

Excited states of ${}^{42}\mathrm{K}$ and ${}^{43}\mathrm{K}$ were investigated using the reactions ${}^9\mathrm{Be}{(}^{36}\mathrm{S}{,2np)}^{42}\mathrm{K}$ and ${}^9\mathrm{Be}{(}^{36}\mathrm{S}{,np)}^{43}\mathrm{K}$. Three methods of selective $\gamma$-ray spectroscopy were employed: recoil-nuclei-$\gamma$, proton-$\gamma$, and $\gamma$-$\gamma$ coincidence measurements. Thirty-eight electromagnetic transitions were observed originally, 22 belonging to ${}^{42}\mathrm{K}$ and 16 belonging to ${}^{43}\mathrm{K}$. Eight new levels are suggested for ${}^{42}\mathrm{K}$ and four for ${}^{43}\mathrm{K}$. Shell-model calculations were performed in the ${\mathrm{}\left(\mathrm{sd}\right)\mathrm{}}^{-1}{\mathrm{}\left(\mathrm{fp}\right)\mathrm{}}^3$ space to obtain negative-parity states of ${}^{42}\mathrm{K}$ and ${\mathrm{}\left(\mathrm{sd}\right)\mathrm{}}^{-1}{\mathrm{}\left(\mathrm{fp}\right)\mathrm{}}^4$ space for positive-parity states of ${}^{43}\mathrm{K}$. The calculated energies are in good agreement with the experimental values, but some systematic differences indicate that the collectivity of the actual levels is not completely accounted for by the configuration space used in the calculations.