Bound and Resonant States of Muonic Few-Body Coulomb Systems: Extended Stochastic Variational Approach

Abstract

We compute the bound and resonant states of hydrogen-like muonic ions ($\mu\mu p$, $\mu\mu d$, $\mu\mu t$) and three-body muonic molecular ions ($pp\mu$, $pd\mu$, $pt\mu$, $dd\mu$, $dt\mu$, $tt\mu$), and the four-body double-muonic hydrogen molecule ($\mu\mu pp$) using an extended stochastic variational method combined with complex scaling. The approach provides a unified treatment of bound and quasibound states and achieves an energy accuracy better than $0.1~\mathrm{eV}$ across all systems studied. Complete spectra below the corresponding $n=2$ atomic thresholds are obtained, including several previously unresolved shallow resonances in both three- and four-body sectors.