Series of resonance states of muonic molecules

Two infinite series of resonance states of muonic molecular ions (ppμ${)}^{+}$ and their isotopes converging to the dissociation limit n=2 are theoretically studied within nonrelativistic quantum mechanics. These resonance states are supported by the attractive long-range dipole potential originating from the linear Stark effect and behaving as $R^{\mathrm{-}2}$. The positions ${\epsilon }_v$ (v=0,1,2,. . .) of the resonances relative to the dissociation threshold satisfy a simple power law ${\epsilon }_v$=A${\alpha }^v$ for high v, the constant α being easily calculable in terms only of the total angular momentum and the masses of the nuclei and the muon. The size of a muonic molecule in a state ${\epsilon }_v$ is ∼${10}^{\mathrm{-}8}$ cm/[4 √‖${\epsilon }_v$ (eV)‖ ], which is comparable to (or even larger than) the size of ground-state electronic molecules if the resonance lies within a fraction of an electron volt from the dissociation threshold. The theory is useful in the classification of resonances in muonic molecules. The systems (dtμ${)}^{+}$ and (ddμ${)}^{+}$ are analyzed as examples.