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

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 Schrődinger 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.

20 pages including 5 figures Updates: #1. Tiltle slightly modified for relevance to the content but results unchanged #2. Some text modified in the introduction section without any change in the results #3. Figure captions are corrected and figure-1 modified slightly

References in corpus (5)

• Lamb shift in muonic deuterium atom
• Ground State Hyperfine Structure of Muonic Helium Atom
• Bound state spectra of three-body muonic molecular ions
• The effective interaction hyperspherical harmonics method for non-local potentials
• Muonic atoms with extreme nuclear charge

Cited by in corpus (1)

• Hyperspherical three-body model calculation for the bound ${}^{1,3}$S-states of Coulombic systems