  We discuss the regularization of attractive singular potentials $-\alpha
_{s}/r^{s}$, $s\geq 2$ by infinitesimal imaginary addition to interaction
constant $\alpha_{s}=\alpha_{s}\pm i0$. Such a procedure enables unique
definition of scattering observables and is equal to an absorption (creation)
of particles in the origin. It is shown, that suggested regularization is an
analytical continuation of the scattering amplitudes of repulsive singular
potential in interaction constant $\alpha_{s}$. The nearthreshold properties of
regularized in a mentioned way singular potential are examined. We obtain
expressions for the scattering lengths, which turn to be complex even for
infinitesimal imaginary part of interaction constant. The problem of
perturbation of nearthreshold states of regular potential by a singular one is
treated, the expressions for level shifts and widths are obtained. We show,
that the physical sense of suggested regularization is that the scattering
observables are insensitive to any details of the short range modification of
singular potential, if there exists sufficiently strong inelastic short range
interaction. In this case the scattering observables are determined by
solutions of Schrodinger equation with regularized potential $-(\alpha_{s}\pm
i0)/r^{s}$. We point out that the developed formalism can be applied for the
description of systems with short range annihilation, in particular low energy
nucleon-antinucleon scattering.
