Doubly excited autoionizing states of H2 above the second ionization threshold: the Q2 resonance series

We report extensive calculations of energy positions, autoionization widths and branching ratios for the $Q_2$ doubly excited states of ${\mathrm{H}}_2$ lying above the second ionization threshold ${}^2{\Sigma }_u^{+}.$ We present results for 60 doubly excited states of the ${}^{\text{1,3}}{\Sigma }_{\mathrm{g,u}}^{+},$ ${}^{\text{1,3}}{\Pi }_{\mathrm{g,u}},$ and ${}^{\text{1,3}}{\Delta }_{\mathrm{g,u}}$ symmetries in the range of internuclear distances $\text{0⩽R⩽6}$ a.u. The resonance parameters have been obtained using the Feshbach theory and an $L^2$ representation of the nonresonant continuum with B-spline functions. Our results are compared with previous theoretical data. We have found significant discrepancies for states of the ${}^1{\Sigma }_g^{+}$ and ${}^1{\Sigma }_u^{+}$ symmetries.