A new method of description of three-particle Coulombic systems

TL;DR

This paper introduces a universal method for analyzing three-particle Coulombic systems, applicable to both bound and continuum states, using a finite rank approximation to simplify the three-body Hamiltonian.

Contribution

The paper presents a novel, universal approach employing finite rank approximation for three-particle Coulomb systems, enabling treatment of both bound and continuum states.

Findings

Preliminary numerical results for atomic and molecular systems like H−, He, and pμ.

Method simplifies three-body Coulomb problems into coupled integral equations.

Applicable to a wide range of three-particle Coulombic systems.

Abstract

We present a method for treatment of three charged particles. The proposed method has universal character and is applicable both for bound and continuum states. A finite rank approximation is used for Coulomb potential in three-body system Hamiltonian, that results in a system of one-dimensional coupled integral equations. Preliminary numerical results for three-body atomic and molecular systems like $H^{-}$, He, $pp\mu$ and other are presented.