Numerical approach to the lowest bound state of muonic three-body systems

TL;DR

This paper presents a numerical method using hyperspherical harmonics to calculate the lowest bound state energies of Coulomb three-body systems involving electrons, muons, and nuclei, providing precise energy estimates.

Contribution

The paper introduces a hyperspherical harmonic expansion approach to accurately compute energies of muonic three-body systems, advancing computational techniques in quantum few-body problems.

Findings

Calculated energies for various Z nuclei

Demonstrated convergence of the hyperspherical harmonic method

Provided a framework for future three-body system studies

Abstract

In this paper, calculated energies of the lowest bound state of Coulomb three-body systems containing an electron ($e^-$), a negatively charged muon ($\mu^-$) and a nucleus ($N^{Z+}$) of charge number Z are reported. The 3-body relative wave function in the resulting Schr\"odinger equation is expanded in the complete set of hyperspherical harmonics (HH). Use of the orthonormality of HH leads to an infinite set of coupled differential equations (CDE) which are solved numerically to get the energy E.