Three-dimensional integral Faddeev equations without a certain symmetry

TL;DR

This paper presents a method for directly integrating three-dimensional Faddeev equations for three particles of different masses without assuming symmetry, highlighting changes in the singularity structure of the integral kernels.

Contribution

It introduces a formulation of Faddeev equations without symmetry assumptions and an algorithm for finding non-relativistic three-body wave functions with different masses.

Findings

Explicit equations without symmetry constraints

Algorithm for wave function search

Altered singularity domain based on particle masses

Abstract

The approach of direct integration of the three-dimensional Faddeev equations with respect to the breakup T-matrix in momentum space for three bodies of different masses is presented. The Faddeev equations are written out explicitly without the requirement for symmetry or antisymmetry of two-body t matrices, taking into account the difference in the masses of three interacting particles. An algorithm for the algebraic search for non-relativistic wave functions of a system of three bodies of different masses is described. A significant change in the domain of logarithmic singularities of the integral kernels of the Faddeev equations from the choice of masses of interacting particles is demonstrated.