Adiabatic expansion approximation solutions for the three-body problem

TL;DR

This paper applies the adiabatic expansion method to analyze the three-body problem involving a muon in a two-center Coulomb field, calculating bound states and energy levels with results consistent with prior methods.

Contribution

It introduces the use of the adiabatic expansion approach for short-range interactions in the muonic three-body system, providing new calculations of bound states and energy levels.

Findings

Results agree well with previous calculations

Bound states and energy levels are accurately determined

Method proves effective for short-range three-body interactions

Abstract

The motion of a muon in two centers coulomb field is one of the interesting problems of quantum mechanics. The adiabatic expansion method is powerful approach to study the muonic three-body system. In this investigation the three-body problem is studied for short-range interactions. Bound states and energy levels of this system were calculated and compared with their Born-Oppenheimer method counterparts. The obtained results are in good agreement with the previous calculations.