Electron Scattering by Noble Gases in the Limit of Zero Energy

Abstract

The elastic scattering at zero energy by argon depends strongly on the polarization tail, since the contribution to the scattering length by forces inside the atom cancel. Assuming this is true for all noble gases, one can approximate their zero-energy elastic cross section by $3.52\times {10}^{-16\mathrm{}}{\left(\frac{p}{r_0}\right)}^2$ ${\mathrm{cm}}^2$, where both $p$, the polarizability, and $r_0$, the size of the atom, are in atomic units. Using published values of the polarizability and scaling $r_0$ as the cube root of the atomic number from $r_0=8\mathrm{}$ for argon, we find that this expression is consistent with existing experimental data. It is conjectured that the success of this approximation is a result of the Pauli exclusion principle.