The R-matrix method for electron-molecule collisions has been applied to autoionizing doubly excited adiabatic states of ${\mathrm{H}}_2$ with ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$ symmetry for internuclear distances from 1 to 5 a.u. Above the previously known three states we have found many other doubly excited states for the first time. These states are classified into two Rydberg series, namely, (1${\mathrm{\sigma }}_{\mathit{u}}$)(npσ) and (1${\mathrm{\sigma }}_{\mathit{u}}$)(nfσ) series up to n=10. They are characterized by their complex quantum defect, the imaginary part corresponding to the width of each Rydberg state. For the smaller internuclear distances R these Rydberg states are isolated resonances, but for R>4 a.u. some of them begin to overlap and present a problem of multichannel autoionizing Rydberg series, although there is only one common series limit in the present case. This work exemplifies the usefulness of the R-matrix method for studying molecular doubly excited Rydberg states.

• Received 23 October 1989

DOI:https://doi.org/10.1103/PhysRevA.41.3545