Nonexistence of Resonances inH2−

The controversy of the existence of resonances in ${\mathrm{H}}^{2-}$ ions is revisited. We calculate the hyperspherical adiabatic potential curves for ${\mathrm{H}}^{2-}$. For ${}_{}{}^4{}_{}{}^{}S_{}^0{}_{}{}^{}$ symmetry all the potential curves are repulsive, and thus no bound or resonance states exist. This conclusion contradicts the recent calculations of Sommerfeld et al. [Phys. Rev. Lett. 77, 470 (1996); Phys. Rev. A 55, 1903 (1997)], where a ${}_{}{}^4{}_{}{}^{}S_{}^0{}_{}{}^{}$ resonance has been predicted. We also calculate the potential curves for several values of the nuclear charge $Z$ ranging between 1 and 2 and show that no resonance or bound state can exist for $Z$ less than about 1.6. Based on the general ordering of energies of intrashell states, we show the conclusion of Sommerfeld et al. is in contradiction with experiment.