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

TL;DR

This paper presents a unified stochastic variational method with complex scaling to accurately compute bound and resonant states of various muonic few-body Coulomb systems, revealing new shallow resonances.

Contribution

The study introduces an extended stochastic variational approach combined with complex scaling for precise energy calculations of muonic systems, including bound and quasibound states.

Findings

Achieved energy accuracy better than 0.1 eV across all systems.

Computed complete spectra below n=2 thresholds, including unresolved shallow resonances.

Unified treatment of bound and quasibound states in muonic few-body systems.

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.