On additional reduction of the Faddeev equations in case of finite-range forces

The familiar approach to the two-body problem in nuclear physics based on using a parameter characterizing a finite size of the interaction region is extended to the three-body problem. It is shoin that the problem of three particles interacting by means of arbitrary finite-range pair potentials, in general, without using any approximation, is reduced to solution of a set of one-dimensional integral equations for a function dependending on the spectator-particle variable. The kernels of the obtained equations are determined by the two-particle scattering wave function off the energy shell in the pair interaction region and satisfy an auxiliary set of equations. A new approach to solution of the three-body problem based upon the performed reduction is proposed. The problem of a three-particle bound state in the case of the square-well local interaction potential is considered as an example of the present approach