Theory of Electron Impact Excitation and Ionization of Atoms and Ions

Abstract

A theory of inelastic processes of electron-hydrogen and electron-ion collisions is formulated along the Gell-Mann-Goldberger approach describing all electrons by the eigenstates of the same Hamiltonian and satisfying the Pauli principle. It is found that this approach is satisfactory conceptually in that orthogonality between the initial and the final states is preserved, the boundary condition is met, the completeness relation for the unperturbed wave functions exists, and the unitarity of the scattering matrix is preserved. The conventional formalisms are also discussed with respect to these matters. Two consequences of the formulation— a finite-threshold law for excitations and the linear-threshold law, in energy, for ionization—are derived. It is shown that also obtaining are an Ochkur-like relation for excitation and the Peterkop relation for ionization. Furthermore, the theory is extended to cases of many-electron atoms and ions for which the same threshold laws are obtained. Finally, a theorem which is an essential assumption in the impulse approximation is proved, and the validity of the present formalism is noted.