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 dtμ and d3Heμ molecules are calculated in extreme and uncoupled adiabatic approximation. For dtμ good agreement with alternative calculations, which are based on a much higher number of expansion functions, is found, and the results for the d3Heμ system are rather close to variational calculations. copyright 1996 The American Physical Society