In this paper, we have investigated the interactions of ${K}^{\ensuremath{-}}$ in a ${}^{4}\mathrm{He}$ target using a quantum mechanical approach. For this purpose, we have used time-dependent perturbation theory and Fermi's golden rule to calculate the capture rate of ${K}^{\ensuremath{-}}$ by the ${}^{4}\mathrm{He}$ atom and the rate of internal Auger effect in the $K\ensuremath{\alpha}e$ atom. The initial distribution of $n,\ensuremath{\ell}$ states in the $K{\ensuremath{\alpha}}^{+}$ ion is also calculated. Some detailed analytical and numerical quantum mechanical calculations are performed for several transitions. Our results for the $n,\ensuremath{\ell}\phantom{\rule{0.16em}{0ex}}$ distributions in $K{\ensuremath{\alpha}}_{}^{+}$ ions are necessary to begin a Monte Carlo simulation of the cascade processes in kaonic helium atoms.