Description of the pair potentials for which the scattering in the quantum system of three one-dimensional particles is free of diffractional effects

The coordinate asymptotics of a solution of the scatterinq problem in the quantum system of three one-dimensional particles contains besides plane and spherical waves the diffraction waves, which also occur in the two-dimensional problem of diffraction of the plane wave on the semi-infinite screen. The class of potentials is found for which there are no diffraction waves in the asymptotics of the solution. This class is somewhat wider then well-known Bargmann class.