Application of hyperspherical harmonics expansion method to the low-lying bound S-states of exotic two-muon three-body systems

TL;DR

This paper applies the hyperspherical harmonics expansion method to calculate the energies of low-lying bound S-states in exotic three-body systems with a nuclear core and two muons, analyzing convergence and comparing results with existing literature.

Contribution

It introduces the use of hyperspherical harmonics expansion method for calculating energies of exotic three-body systems with varying nuclear charge, including an extrapolation scheme for higher partial waves.

Findings

Convergence pattern of energies checked up to Λ_max=28 partial waves.

Calculated energies show dependence on nuclear charge Z.

Results compared with existing literature for validation.

Abstract

Energies of the low-lying bound S-states (L=0) of exotic three-body systems, consisting a nuclear core of charge +Ze (Z being atomic number of the core) and two negatively charged valence muons, have been calculated by hyperspherical harmonics expansion method (HHEM). The three-body Schr\H{o}dinger equation is solved assuming purely Coulomb interaction among the binary pairs of the three-body systems X$^{Z+}\mu^-\mu^-$ for Z=1 to 54. Convergence pattern of the energies have been checked with respect to the increasing number of partial waves $\Lambda_{max}$. For available computer facilities, calculations are feasible up to $\Lambda_{max}=28$ partial waves, however, calculation for still higher partial waves have been achieved through an appropriate extrapolation scheme. The dependence of bound state energies has been checked against increasing nuclear charge Z and finally, the calculated energies have been compared with the ones of the literature.