Muonic three-body Coulomb systems in the hyperspherical approach

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 mu and d(3)He mu molecules are calculated in extreme and uncoupled adiabatic approximation. For dt mu good agreement with alternative calculations, which are based on a much higher number of expansion functions, is found, and the results for the d(3)He mu system are rather close to variational calculations.