The Free-Free Transitions of an Electron in the Field of a Hydrogen Atom at Infra-red Frequencies

For the limiting case $$\Delta k^2 \rightarrow 0$$, an exact formula for the absorption coefficient is derived in terms of the phase shifts for the elastic scattering of electrons by hydrogen atoms. We give a simple empirical formula for the absorption cross section as a function of θ and Δk² which gives the exchange approximation results to an accuracy of 10%. A table of the free–free absorption coefficient taking into account exchange and polarization effects is given; this shows only small changes from the exchange approximation, but should be more reliable for applications in astrophysics especially for small values of Δk².