Adiabatic hyperspherical approach to the coulomb three-body problem: Theory and numerical method

The adiabatic hyperspherical (AH) approach to the three-body Coulomb bound-state problem is considered. The variational method of computation of the AH harmonics potential curves and coupling matrix elements is developed. The method takes into account the asymptotic behaviour of the AH harmonics at large and small values of the hyperradius ρ. The developed method allows to perform calculations with high accuracy and stability for any hyperradius ρ ε (0,∞) with only a few AH harmonics. The efficiency of the method and its convergence is illustrated by calculations of energy levels of the mesic molecules ddμ and dtμ. (Authors)