Towards producing ultracold CaNa$^+$ molecular ions in the ground electronic state

We present a theoretical analysis of optical pathways for the formation of cold Ca($^1$S)Na$^+$($^1$S) molecular ions, based on accurate potential energy curves and transition dipole moments calculated using effective-core-potential methods of quantum chemistry. In the proposed approach, starting from a mixture of trapped laser-cooled Ca$^+$ ions immersed into an ultracold gas of Na atoms, the (NaCa)$^+$ are photoassociated in the excited $E ^{1}\Sigma^+$ electronic state, followed by spontaneous radiative charge transfer and emission through an intermediate state. We find the optimal formation pathway and report radiative charge-exchange cross sections and vibrational distributions of participating electronic states.