In experiments on multiphoton ionization of a series of atoms of alkaline-earth and lanthanide elements, an anomalously large yield of doubly charged ions has been observed. The formation of doubly charged ions may occur either by ionization of singly charged ions or with the simultaneous stripping of two electrons from an atom. The excited-state energies of the barium atom are calculated by the Hartree-Fock-Dirac method in the frozen-core approximation. Two-electron states are considered.