We present the ab initio calculation of leading-order relativistic corrections to the pure vibrational energies of the muonium-muonium molecule (${\mathrm{Mu}}_2$), an exotic four-lepton system composed of two positive muons ${\mu }^{+}$ and two electrons. These corrections are evaluated perturbatively using variational wave functions constructed from an explicitly correlated Gaussian basis, within a fully non-Born-Oppenheimer framework. We accurately determine the rotationless vibrational spectrum, dissociation energy, and key spectroscopic constants, including the harmonic constant ${\omega }_e=13322.11{\text{cm}}^{-1}$ and the anharmonicity constant ${\omega }_e{x}_e=1097.37{\text{cm}}^{-1}$. Furthermore, we present a range of expectation values for various structural quantities that provide insight into the intrinsic properties of this system. Our results represent a meaningful step toward a more accurate theoretical description of ${\mathrm{Mu}}_2$.

Close

PrevNext

View figure in article

• Fine & hyperfine structure
• Vibrational states