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

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.