Resonant Electron Scattering by Atoms

The Kapur-Peierls resonance formalism adapted for electron scattering by atomic systems is modified to allow for the exclusion principle, and a variational principle is derived for calculating the complex resonance energies. The theory is applied to calculate the first four resonance levels in the 1S state of the electron/atomic hydrogen system by using a trial wave function made up from singleparticle functions which are modified (1s), (2s) and (2p) hydrogen wave functions. We find two levels (at approximately — 13 and — 10 eV) whose widths are of the order of a few volts. There are also two levels (at about — 3 and 0 eV) which have very narrow widths, less than 10-2 eV, if they occur below the inelastic threshold, shooting up to widths of several volts at threshold. Such a narrow level occurs if the resonant state is energetically unable to decay to a state of the residual atom of which it contains a substantial component.