Sommerfeld enhancement: general results from field theory diagrams

Assuming that two incoming annihilating particles interact by exchanging a generally massive attractive vector ( or scalar) boson, we find, by taking the non-relativistic limit of the field theory ladder diagrams, that the complete annihilation amplitude A is equal to: the convolution of a solution of the Schroedinger equation ( including the attractive potential) with the Fourier transform of the bare (i.e. ignoring the attraction) annihilation amplitude A(0). The main novelty is that A(0) can be completely arbitrary. For a Coulomb potential we find analytically the enhancement for the l-partial-wave cross-section, e. g. the P wave enhancement 2 pi(alpha/v)(3) (v relative velocity), for a Yukawa potential we describe a simple algorithm and give numerical results showing an important P wave enhancement with a resonant pattern.