The T Approximation

All our Green’s function approximations so far have been based on the idea that the potential is small. Even the shielded potential approximation depends on there being a dimensionless parameter, proportional to the strength of the interaction, which is small. For zero-temperature fermions, this parameter is r_s = (1/a₀)(3/4πn)^l/3, and in the classical limit it is (1/r_D)(3/4πm)^l/3. However, in many situations of practical interest, the potential is not small, but nonetheless the effects of the potential are small because the potential is very short-ranged. For example, a gas composed of hard spheres with radius r₀ has the potential (13-1) v ( r ) = 0 for r > r 0 = ∞ for r > r 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429493218/2723bf93-af84-4d1d-955c-798a77ad6aa2/content/eq966.tif"/>