Additional reduction of the Faddeev equations for the case of finite-range forces

A well known approach to the two-body problem in nuclear physics, based on the use of the parameter that characterizes the finite size of the region of interaction, is generalized to the three-body case. It is shown that in the general case, without any approximations, the problem of three particles interacting through arbitrary finite-range pair potentials reduces to the solution of a system of one-dimensional integral equations for a function depending on the variable of the spectator particle. The kernels of the equations obtained are determined by the off-energy-shell two-particle wave function inside the interaction region of the pair and satisfy an auxiliary system of equations. On the basis of this reduction a new approach to the three-body problem is proposed. The case of the bound state of three particles with local square-well interactions is considered as an illustration