Formation of Be$_2^+$ molecules in the metastable B$^2\Sigma_g^+$ state by ultracold photoassociation

We suggest a photoassociation (PA) scheme to form ultracold Be$_2^+$ molecules in the long-range outer well of the B$^2\Sigma_g^+$ state. In our previous work \footnote{S. Banerjee \textit{et al.} Chem. Phys. Lett. 496 (2010) 208.}, we have calculated the ground states of Be$_2^+$ dimer and have analyzed in detail the double well nature of the B$^2\Sigma_g^+$ state. We also note that the vibrational levels in the outer well of the B$^2\Sigma_g^+$ state have significantly longer radiative lifetimes ($\sim$ ms) than the ones in the inner well ($\sim$ $\mu$s). Using similar \textit{ab initio} methods (valence full CI), we have now calculated the excited $^2\Pi_{u/g}$ and $^2\Sigma_{u/g}$ states. For the proposed PA scheme, we populate the A$^2\Pi_u$ state and radiatively decay into the B$^2\Sigma_g^+$ state of Be$_2^+$. We also calculate transition dipole moment, Frank-Condon factors between the A$^2\Pi_u$ and B$^2\Sigma_g^+$ states.