  Experiments with cold ion-atom mixtures have recently opened the way for the
production and application of ultracold molecular ions. Here, in a comparative
study, we theoretically investigate ground and several excited electronic
states and prospects for the formation of molecular ions composed of a calcium
ion and an alkali-metal atom: CaAlk$^{+}$ (Alk=Li, Na, K, Rb, Cs). We use a
quantum chemistry approach based on non-empirical pseudopotential, operatorial
core-valence correlation, large Gaussian basis sets, and full configuration
interaction method for valence electrons. Adiabatic potential energy curves,
spectroscopic constants, and transition and permanent electric dipole moments
are determined and analyzed for the ground and excited electronic states. We
examine the prospects for ion-neutral reactive processes and the production of
molecular ions via spontaneous radiative association and laser-induced
photoassociation. After that, spontaneous and stimulated blackbody radiation
transition rates are calculated and used to obtain radiative lifetimes of
vibrational states of the ground and first-excited electronic states. The
present results pave the way for the formation and spectroscopy of
calcium--alkali-metal-atom molecular ions in modern experiments with cold
ion-atom mixtures.
