Few-body model approach to the lowest bound S-state of non-symmetric exotic atoms and ions

Abstract

Lowest bound S-state energy of Coulombic three-body systems (N Z+ μ − e −) consisting of a positively charged nucleus of charge number Z (N Z+), a negatively charged muon (μ −) and an electron (e −), is investigated in the framework of few-body (i.e., two- and three-body) cluster model approach. For the three-body cluster model, we adopted the hyperspherical harmonics expansion (HHE) method. An approximated two-body model calculation is also performed for all the three-body systems considered here. A Yukawa-type screened Coulomb potential with an arbitrary screening parameter (λ) is chosen for the two-body subsystems of the three-body system. In the resulting Schrödinger equation (SE), the three-body relative wave function is expanded in the complete set of hyperspherical harmonics (HH). The use of the orthonormality of HH in the SE leads to a set of coupled differential equations (CDEs) which are solved numerically for a manageable basis size to get the energy (E). The pattern of convergence in energy relative to increasing basis size is also investigated. Results are compared with some of those found in the literature.