Polarization Potential in Low-Energy Electron-H2Scattering

Abstract

An adiabatic polarization potential appropriate to low-energy electron-${\mathrm{H}}_2$ scattering has been calculated by a variational approach. The total energy of the static electron-${\mathrm{H}}_2$ system is minimized with respect to the parameters $C_{\alpha \beta }$ in a trial function of the form ${\psi }_0\mathrm{}(1,2)\mathrm{}\Sigma \stackrel{}{\alpha ,\beta }{C}_{\alpha \beta }{(x_1+x_2)}^{\alpha }{(z_1+z_2)}^{\beta },$ where ${\psi }_0\mathrm{}(1,2)\mathrm{}$ is Joy and Parr's one-center ground-state function. The subscripts 1 and 2 refer to the molecular electrons. The polarization potential is found to be well represented by ${v_p}^0\mathrm{}\left(r\right)+{v_p}^2\mathrm{}\left(r\right)\mathrm{}{P}_2\left(cos\theta \right)$, where $\theta$ specifies the position vector of the static electron with respect to the internuclear axis. The radial functions ${v_p}^0\mathrm{}\left(r\right)\mathrm{}$ and ${v_p}^2\mathrm{}\left(r\right)\mathrm{}$ have been determined over a wide range in $r$. The polarization potentials are used in a calculation of rotational-excitation cross sections. Comparisons are made with results of other investigations.