Solvable separable nonlocal potential models

We introduce a generalized Yamaguchi rank-one separable potential with three parameters which has the separable Yukawa or central Yamaguchi potentials as limiting cases. The three parameters can be obtained, when possible, from the set of experimental data (binding energy, scattering length and effective range) by solving a simple cubic equation. We also discuss a rank-two separable potential with one of the strengths infinite. For both potentials the solutions can be expressed analytically.