Mean Excitation Energy for Stopping Power of Molecular Hydrogen

The variational procedure of Chan and Dalgarno for the calculation of the mean excitation energy I occurring in the stopping-power formula is extended and modified in two ways. Using either method, we can obtain I without integration over a frequency parameter ω. The value of I can be obtained by matrix diagonalization and by expressing it in terms of a matrix power series. These methods, as well as the direct calculation involving integration over ω, are applied to the case of molecular hydrogen with the result $I=18.2$ eV, in agreement with experimental data. Employing the same trial functions, the dynamic polarizabilities are also calculated as a function of ω. The average polarizabilities α(ω) are in excellent agreement with the measured data, but the polarizability anisotropy does not agree so well.