# 14.6: Ramsauer-Townsend effect


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 $$\delta_2 = \pi /2$$.

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