14.6: Ramsauer-Townsend effect
( \newcommand{\kernel}{\mathrm{null}\,}\)
This is the name given to the fact that electrons with energy about 1 eV can pass almost freely through Xe, Kr, and Ar:- there is a sharp minimum in electron scattering cross-section for these noble gases.
Due to polarization of these atoms by the incoming electron the potential appears to increase as K increases (more localized electrons are better able to polarise the atom). Thus δ0(k→0)=nπ, in accordance with Levinson’s theorem, and δ0 initially increases as k increases, before eventually decreasing. Thus at a certain value of k, the phase shift is again δ0(k)=nπ, and the total scattering cross section σT has an abrupt minimum. Although there are subsequent s-wave minima at e.g. δ0(k)=(n−1)π, these occur at sufficiently large values of k that s-wave scattering is no longer dominant.
Figure 14.6.1: Minimum in scattering cross section in Ar due to δ0=3π; No such effect in Ne due to weaker polarization.
By contrast, neon and helium have lower polarisability, due to fewer bound electrons. Thus the phase shift δ0 decreases monotonically with k from nπ at k=0 at there is no low-energy minimum.
Higher l phase shifts may increase with k because higher k implies smaller impact parameter (classically, more chance of hitting the atom). The cross section increases more slowly due to the additional K−2 dependence. The maximum in the Ar cross section at about 13 eV is mainly due to the d-wave δ2=π/2.