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Potential-energy curves for the 1 Σg+ states of Ba2++ are exhibited. The ground-state curve shows a local minimum lying 0.0562 a.u. above the energy at infinite separation, and a local maximum lying at 0.0618. These features form a potential well in which metastable vibrational states can exist. The lifetimes are estimated as high as 10197 sec, using the WKB method. Considerations regarding experimental formation and detection of bound Ba2++ are discussed.