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Total energies and other bound state properties of the weakly-bound (1,1)-states and rotationally excited (2,0)-states in the three-body muonic molecularandions are determined to high numerical accuracy and investigated. Our current numerical accuracy achieved for the total and binding energies of the weakly-bound (1,1)-states in the bothandions significantly exceeds similar accuracy obtained in earlier computations of these weakly-bound states in these two ions. The bound state properties of the weakly-bound (1,1)-states and (2,0)-states in theandmuonic ions have never been determined to high accuracy in earlier studies. We also briefly discuss the current status of muon-catalysed nuclear fusion and develop the new universal variational expansion which can be used for extremely accurate bound state calculations of arbitrary three-body systems, including the truly adiabaticHion and close systems.

Properties of the weakly-bound (1,1)-states and rotationally excited (2,0)-states in the muonic molecular and ions