Hi there,

It's of importance for what specific problem you ask this question.

For contact interactions, we usually directly evaluate the W_sl integrals analytically and work with this.

There's thus no difference with the analytical delta distribution. In more than one spatial dimension, however, issues do arise with contact potentials.

Then, in >1D, one needs either renormalization or just to consider a short-ranged interaction with the same scattering properties (see for instance: Phys. Rev. A 87, 033631 (2013) ).

Regards,

Axel