In the low energy limit, the s-wave scattering amplitude is parameterized by the scattering length a0:
f0≈−a0
and the total cross section is σ≈4πa02.
(a) Find the scattering length for a hard sphere of radius R.
(b) Show that the scattering length can be negative (attractive potential that is not quite strong enough to bind a state).
(c) What happens to the scattering length at a zero-energy resonance?