Muonic three-body Coulomb systems in the hyperspherical approach.

Abstract

Muonic three-body bound states and resonances are treated within a hyperspherical adiabatic expansion scheme. A new method for determining the basis functions of this expansion is developed: decomposing these functions into Faddeev-type components, an equivalent treatment of all two-body contributions, and thus the correct asymptotics, are guaranteed. This approach is characterized by its high symmetry and a considerable reduction of the numerical effort. Using partial wave and B-spline expansions for the components, wave functions and energies of the dt\ensuremath{\mu} and ${\mathit{d}}^{3}$He\ensuremath{\mu} molecules are calculated in extreme and uncoupled adiabatic approximation. For dt\ensuremath{\mu} good agreement with alternative calculations, which are based on a much higher number of expansion functions, is found, and the results for the ${\mathit{d}}^{3}$He\ensuremath{\mu} system are rather close to variational calculations. \textcopyright{} 1996 The American Physical Society.