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We present a theoretical analysis of optical pathways for formation of coldCa($^1$S)Na$^+$($^1$S) molecular ions via an intermediate state. The formationschemes are based on ab initio potential energy curves and transition dipolemoments calculated using effective-core-potential methods of quantum chemistry.In the proposed approach, starting from a mixture of cold trapped Ca$^+$ ionsimmersed into an ultracold gas of Na atoms, (NaCa)$^+$ molecular ions arephotoassociated in the excited E$^{1}\Sigma^+$ electronic state and allowed tospontaneously decay either to the ground electronic state or an intermediatestate from which the population is transferred to the ground state via anadditional optical excitation. By analyzing all possible pathways, we find thatthe efficiency of a two-photon scheme, via either B$^{1}\Sigma^+$ orC$^{1}\Sigma^+$ potential, is sufficient to produce significant quantities ofground state (NaCa)$^+$ molecular ions. A single-step process results in lowerformation rates that would require either a high density sample or a veryintense photoassociation laser to be viable.

Production of NaCa$^+$ molecular ions in the ground state from cold atom-ion mixtures by photoassociation via an intermediate state