The hybrid theory of electron-hydrogen elastic scattering [Phys. Rev. A 75, 032713 (2007)] is applied to the $S$-wave scattering of electrons from ${\text{He}}^{+}$ and ${\text{Li}}^{2+}$. In this method, both short-range and long-range correlations are included in the Schrödinger equation at the same time. Phase shifts obtained in this calculation have rigorous lower bounds to the exact phase shifts and they are compared with those obtained using the Feshbach projection operator formalism [Phys. Rev. A 66, 064702 (2002)], the close-coupling approach [J. Phys. B 2, 44 (1969)], and the Harris-Nesbet method [J. Phys. B 35, 4475 (2002); J. Phys. B 36, 2291 (2003)]. The agreement among all the calculations is very good. These systems have doubly excited or Feshbach resonances embedded in the continuum. The resonance parameters for the lowest ${}^{1}S$ resonances in He and ${\text{Li}}^{+}$ are calculated and they are compared with the results obtained using the Feshbach projection operator formalism [Phys. Rev. A 11, 2018 (1975); Phys. Rev. A 15, 131 (1977)]. It is concluded that accurate resonance parameters can be obtained by the present method, which has the advantage of including corrections due to neighboring resonances and the continuum in which these resonances are embedded.

• Received 15 January 2008

DOI:https://doi.org/10.1103/PhysRevA.77.052707