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 $\omega$. 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 $\omega$, are applied to the case of molecular hydrogen with the result $I=18.2\mathrm{}$ eV, in agreement with experimental data. Employing the same trial functions, the dynamic polarizabilities are also calculated as a function of $\omega$. The average polarizabilities $\alpha \left(\omega \right)$ are in excellent agreement with the measured data, but the polarizability anisotropy does not agree so well.