The scattering of electrons by ${\mathrm{He}}^{+}$ ions has been studied below the N=2 threshold of the ion. A pseudostate close-coupling method has been used to examine the scattering in the nonresonant and resonant regions. The calculations are performed using an algebraic variational method. Extensive pseudostate basis sets of differing characters are employed. In the nonresonant region, short-range electron-electron correlations are emphasized. In the vicinity of the resonances, the dominant projectile-target electron correlations are comparatively long range. S-, P-, and D-wave phase shifts of high accuracy are obtained for both the singlet and the triplet spin states. The present phase shifts agree very well with those obtained by Shimamura by a variational procedure for the S wave and with those of McGreevy and Stewart by a many-body perturbation method for the singlet P wave. The present phase shifts are in disagreement with the polarized orbital results of Khan et al. Resonance parameters are calculated for 15 S-wave resonances, 16 P-wave resonances, and 19 D-wave resonances with the outer electron extending up to n≃8. Estimates of quantum defects and the reduced widths are obtained for various Rydberg series of the doubly excited states. A number of the high-lying resonances are predicted for the first time. The agreement of the present energy values and the auotionization widths with the available experimental values is excellent.

• Received 17 June 1985

DOI:https://doi.org/10.1103/PhysRevA.33.824