Separable approximation to two-body matrix elements

Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the transformation to center of mass and relative coordinate ( in the spirit of Talmi's method) and therefore it is only useful ( finite number of expansion terms) for harmonic oscillator single particle states. The converge of the expansion with the number of terms retained is studied for a Gaussian two body interaction. The limit of a contact ( delta) force is also considered. Ways to handle the general case are also discussed.