# Few-body model approach to the lowest bound S-state of non-symmetric exotic few-body systems

## TL;DR

This paper investigates the lowest bound S-state energies of Coulomb three-body systems with a nucleus, muon, and electron using hyperspherical harmonics expansion and a Yukawa potential with screening.

## Contribution

It introduces a few-body model approach employing hyperspherical harmonics and a Yukawa potential to analyze non-symmetric exotic three-body systems.

## Key findings

- Calculated bound state energies for specific Coulomb three-body systems.
- Demonstrated the effectiveness of hyperspherical harmonics in solving three-body Schrödinger equations.
- Provided insights into the effects of screening parameters on system energies.

## Abstract

Lowest bound S-state energy of Coulomb three-body systems ($N^{Z+}\mu^-e^-$) having a positively charged nucleus of charge number Z ($N^{Z+}$), a negatively charged muon ($\mu^-$) and an electron ($e^-$), is investigated in the framework of hyperspherical harmonics expansion method. A Yukawa type Coulomb potential with an adjustable screening parameter ($\lambda$) is chosen for the 2-body subsystems. In the resulting Schr\"odinger equation (SE), the three-body relative wave function is expanded in the complete set of hyperspherical harmonics (HH). Thereafter use of orthonormality of HH in the SE, led to a set of coupled differential equations which are solved numerically to get the energy (E) of the systems investigated.