Analytical calculation of logarithmic mean excitation energies for hydrogen and helium

The four logarithmic mean excitation energies I(ν), for ν = -1, 0, 1, and 2, have been calculated analytically for hydrogen and helium. They appear in the expressions of total cross section, stopping power, and straggling effect for fast charged particles, and in the expression of the Lamb shift of atomic energy levels. The method is based on a generalization of a method by Dalgarno and Lewis [Proc. R. Soc. London, Ser. A 233, 70 (1956)]. The only input is the wave function of the initial state of the atom (in the present paper only the ground state is considered). For hydrogen the method is rigorous. For helium, Hartree-Fock-type wave functions were used, which is the only approximation of the present method. The accuracy of the method is essentially independent of the value of ν