Two-body problems with confining potentials

TL;DR

This paper introduces a formalism for accurately solving two-body problems with confining potentials, applicable in atomic, nuclear, and particle physics, by expanding short-range terms in a Coulomb-Sturmian basis.

Contribution

It provides an asymptotically exact method for non-relativistic and semi-relativistic two-body problems with linear and quadratic confinement potentials.

Findings

Applicable to atomic, nuclear, and particle physics models.

Handles both linear and quadratic confining potentials.

Uses Coulomb-Sturmian basis for expansion of short-range terms.

Abstract

A formalism is presented that allows an asymptotically exact solution of non-relativistic and semi-relativistic two-body problems with infinitely rising confining potentials. We consider both linear and quadratic confinement. The additional short-range terms are expanded in a Coulomb-Sturmian basis. Such kinds of Hamiltonians are frequently used in atomic, nuclear, and particle physics.