New integrals in few-body problems

TL;DR

This paper introduces methods to reduce complex multi-dimensional integrals in few-body physics to simpler forms, enabling explicit analytic evaluation using hypergeometric functions, and presents some integrals for the first time.

Contribution

It provides new reduction techniques for multi-dimensional integrals in few-body problems and derives explicit analytic forms for these integrals using hypergeometric functions.

Findings

Reduction of 2D and 3D integrals to 1D form

Explicit analytic expressions for integrals in terms of hypergeometric functions

Presentation of some integrals for the first time

Abstract

This work is concerned with multi-dimensional integrals, which are making their appearance in few-body atomic and nuclear physics. It is shown that the relevant two- and three-dimensional integrals can be reduced to one-dimensional form. This implies that the internal one- and two-dimensional integrals can be evaluated in explicit analytic form in term of the familiar generalized hypergeometric functions. Some of the integrals are presented here for the first time.