A nonadiabatic theory of photoassociation spectra and spontaneous emission processes in diatomic molecules is presented. This theory was applied in nearly exact nonadiabatic calculations of the photoassociation intensities to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ manifold of states for two colliding calcium atoms at ultralow temperatures and of the spontaneous emission coefficients to the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ electronic state. The calculations were based on most recent state-of-the-art ab initio results for the potential energy curves for the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ and excited $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{1}S+1\phantom{\rule{0.2em}{0ex}}^{1}D),\phantom{\rule{0.2em}{0ex}}c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$, and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}(1\phantom{\rule{0.2em}{0ex}}^{3}P+1\phantom{\rule{0.2em}{0ex}}^{1}S)$ states, for the spin-orbit and nonadiabatic coupling matrix elements, and for the transition dipole moment governing the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}\ensuremath{\leftarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transitions. The computed photoassociation spectrum shows several transitions in the detuning frequency range up to $\ensuremath{-}3000\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. This frequency range corresponds to vibrational levels of the ${J}^{\ensuremath{'}}=1$ state of
Ca2 that can mostly be assigned to the $c\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{u}$ state. The two by far most intense lines at a detuning frequency around $\ensuremath{-}800\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ correspond to the last two bound rovibrational levels lying below the
13P+11S asymptote which are heavily mixed and can partly be assigned to the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state. The corresponding lifetimes and Franck-Condon factors suggest that these levels can be detected experimentally and should show a relatively efficient spontaneous emission to the ground state. An analysis of the branching ratios describing the probability of the decay from these two levels to bound vibrational levels of the ground electronic state shows that the decay will end in the levels with the vibrational quantum number between 10 and 16 with a total probability well over 90%.
We apply the relativistic configuration-interaction valence-bond method to calculate various characteristics of the alkali-metal RbCs dimer. These include the electronic potentials and transition dipole moments between the ground and first excited states and permanent dipole moments of the X 1sigma+ and a 3sigma+ states of the ground configuration. In addition, we estimate the lifetime of the rovibrational levels of the X state due to blackbody radiation. These data can help experimentalists to optimize photoassociative formation of ultracold RbCs molecules and their longevity in a trap or in an optical lattice. Extended basis sets, constructed from Dirac-Fock and Sturm's orbitals, have been used to ensure convergence of our calculations. We compare our data with other theoretical and experimental results when they were available.