Adiabatic representation in the Coulomb three-body problem in the united-atom limit: Nuclear widths of the energy levels of the muonic molecule $tt\mu$

We study the asymptotic behavior of the wave function of the system of three Coulomb particles in the united-atom limit in the adiabatic representation of the three-body problem. This result is used to calculate the nuclear widths of muonic-molecule energy levels. We discuss features of the approach with regard to excited states of the muonic molecule $tt\mu$ with a nonzero orbital angular momentum.