14.6: Ramsauer-Townsend effect

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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 \(\delta_0(k \rightarrow 0) = n\pi\), in accordance with Levinson’s theorem, and \(\delta_0\) initially increases as \(k\) increases, before eventually decreasing. Thus at a certain value of \(k\), the phase shift is again \(\delta_0(k) = n\pi\), and the total scattering cross section \(\sigma_T\) has an abrupt minimum. Although there are subsequent \(s\)-wave minima at e.g. \(\delta_0(k) = (n − 1)\pi\), these occur at sufficiently large values of \(k\) that \(s\)-wave scattering is no longer dominant.

By contrast, neon and helium have lower polarisability, due to fewer bound electrons. Thus the phase shift \(\delta_0\) decreases monotonically with \(k\) from \(n\pi\) 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 \(\delta_2 = \pi /2\).

14.3.PNG — Figure \(\PageIndex{2}\): More-localized electrons polarise atoms and thus increase the attractive potential