Stability of the three-body muonic atoms with screened Coulomb potentials

Abstract The stability limits of three-body muonic atoms in environments that screen the Coulomb interaction, such as plasmas, are poorly characterized, especially across isotopic chains and for heavier nuclei. To address this, we performed high-precision variational calculations of the ground-state energies for 14 such systems, from light-helium isotopes to neon, interacting via Yukawa-screened Coulomb potentials. A correlated exponential wave function basis within the Rayleigh-Ritz framework is used to compute the binding energies over a wide range of screening parameters λ, allowing us to pinpoint the critical value for the disappearance of the bound state in each case. This work provides a systematic mapping of the stability thresholds, revealing the dependence on both nuclear mass and charge. A comprehensive tabulation of energies and critical parameters is presented, establishing reliable benchmarks for future theoretical and experimental studies in areas including muon-catalyzed fusion and the physics of exotic atoms in dense or plasma environments.