Collision integrals for attractive potentials

Motivated by previous discussions of particle interactions under the Manev potential U(r)= alpha/r - epsilon/r(2), we construct the collision integrals for attractive potentials U(r) satisfying the condition U(r) r(2) --> -epsilon as r --> 0 with epsilon greater than or equal to 0. For epsilon = 0, we obtain a Boltzmann-type integral with a collision law allowing "spiral" interactions and nonunique correspondence between impact parameter and scattering angle. For epsilon>0, an additional Smoluchowski-type coagulation integral arises. All these integrals are derived and possible applications are discussed.