Multichannel quantum-defect theory of double-minimumΣg+1states inH2. I. Potential-energy curves

Multichannel quantum-defect theory is applied to the highly accurate ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$ ab initio excited-state potential-energy curves calculated by Wolniewicz and Dressler [J. Chem. Phys. 82, 3262 (1985); and (private communication)]. We show that the three double-minimum states, EF, GK, and HH¯, can be represented to within 8 ${\mathrm{cm}}^{\mathrm{-}1}$ by a smooth R-dependent 3×3 nondiagonal quantum-defect matrix. This quantum-defect matrix corresponds to a collision of the Rydberg electron with the ${\mathrm{H}}_2^{+}$ target, which may be in either the 1${\mathrm{\sigma }}_{\mathit{g}}$ or 1${\mathrm{\sigma }}_{\mathit{u}}$ state. Also discussed is the use of this quantum-defect matrix to calculate diabatic states, more highly excited Born-Oppenheimer states, and the electronic ionization width of the superexcited (1${\mathrm{\sigma }}_{\mathit{u}}$ ${)}^2$ doubly excited state.