The thermally averaged cross-section can be expanded as = a + bv^2+... where the first term corresponds to s-wave, second term corresponds to p-wave and so on. Why these terms are such named and what is the reason for this expansion?
If m is the mass of a heavy particle ( such as the RH neutrino) undergoing a decay, and you define x=m/T, where T is temperature then, thermally averaged cross section can be expanded (in non relativistic limit) as = b0 + 3/2 b1 x-1 + ...
The first rem is called the S-wave term and second term is called a p-wave term.
A (differential) scattering cross section depends on θ,φ coordinates, i.e. it is a function of variables θ,φ. Then one can expand such a function in terms of a complete basis Ylm(θ,φ). In case there is an azimuthal symmetry one can expand a cross section in terms of Pl(cos θ) and then name coefficients accordingly. Coefficient of l=0 will be s-wave cross section, coefficient of l=1 will be p wave cross section and so on. Perhaps you should see some old nuclear physics books which discusses partial wave analysis of low energy scattering theory.
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