Quantum effects of nuclear motion in three-particle diatomic ions

Abstract

A high-accuracy, nonrelativistic wave function is used to study nuclear motion in the ground state of three-particle ${{a}_{1}^{+}{a}_{2}^{+}{a}_{3}^{\ensuremath{-}}}$ electronic and muonic molecular systems without assuming the Born-Oppenheimer approximation. Intracule densities and center-of-mass particle densities show that as the mass ratio ${m}_{{a}_{i}}/{m}_{{a}_{3}}, i=1,2$, becomes smaller, the localization of the like-charged particles (nuclei) ${a}_{1}$ and ${a}_{2}$ decreases. A coordinate system is presented to calculate center-of-mass particle densities for systems where ${a}_{1}\ensuremath{\ne}{a}_{2}$. It is shown that the nuclear motion is strongly correlated and depends on the relative masses of the nuclei ${a}_{1}$ and ${a}_{2}$ rather than just their absolute mass. The heavier particle is always more localized and the lighter the partner mass, the greater the localization. It is shown, for systems with ${m}_{{a}_{1}}<{m}_{{a}_{2}}$, that the ratio of (i) the density maximum and (ii) the FWHM of the radial distribution of each nucleus from the center of mass is directly proportional to the mass ratio of the nuclei: ${m}_{{a}_{1}}/{m}_{{a}_{2}}$ for the former and ${m}_{{a}_{2}}/{m}_{{a}_{1}}$ for the latter, thus quantifying a quantum effect of nuclear correlation.