  Tiny radiative losses below the 0.1% level can prove ruinous to the effective
laser cooling of a molecule. In this paper the laser cooling of a hydride is
studied with rovibronic detail using ab initio quantum chemistry in order to
document the decays to all possible electronic states (not just the vibrational
branching within a single electronic transition) and to identify the most
populated final quantum states. The effect of spin-orbit and associated
couplings on the properties of the lowest excited states of BaH are analysed in
detail. The lifetimes of the A$^2{\Pi}_{1/2}$, H$^2{\Delta}_{3/2}$ and
E$^2{\Pi}_{1/2}$ states are calculated (136 ns, 5.8 {\mu}s and 46 ns
respectively) for the first time, while the theoretical value for
B$^2{\Sigma}^+_{1/2}$ is in good agreement with experiments. Using a simple
rate model the numbers of absorption-emission cycles possible for both one- and
two-colour cooling on the competing electronic transitions are determined, and
it is clearly demonstrated that the A$^2{\Pi}$ - X$^2{\Sigma}^+$ transition is
superior to B$^2{\Sigma}^+$ - X$^2{\Sigma}^+$, where multiple tiny decay
channels degrade its efficiency. Further possible improvements to the cooling
method are proposed.
