Many-Body Quantum Muon Effects and Quadrupolar Coupling in Solid Nitrogen

Quantum zero-point motion (ZPM) of light particles in materials has only recently begun to be explored from an ab initio perspective, through several competing approximations. Here we develop a unified description of muon (or light nucleus) ZPM and establish the regimes of anharmonicity and positional quantum entanglement where different approximation schemes apply. Via density functional theory and path-integral molecular dynamics simulations we demonstrate that in solid nitrogen, $\alpha$--N$_2$, muon ZPM is both strongly anharmonic and many-body in character, with the muon forming an extended electric-dipole polaron around a central, quantum-entangled [N$_2$--$\mu$--N$_2$]$^+$ complex. By combining this quantitative description of quantum muon ZPM with precision muon quadrupolar level-crossing resonance experiments, we independently determine the static $^{14}$N nuclear quadrupolar coupling constant of pristine $\alpha$--N$_2$ to be $-5.36(2)$ MHz, a significant improvement in accuracy over the previously-accepted value of $-5.39(5)$ MHz.