Non-Born–Oppenheimer study of the muonic molecule ion ⁴He μ⁺*

Abstract

Accurate non-Born–Oppenheimer variational calculations of all bound states of the positive muon molecular ion 4Heμ+ have been performed using explicitly correlated Gaussian functions in conjunction with the global vectors. All the energies obtained are accurate in the order of 10−6 Hartree (1 Hartree = 27.2114 eV). Compared with the binding energies obtained from calculations based on the Born–Oppenheimer potential with the mass-weighted adiabatic corrections (Chem. Phys. Lett. 110 487 (1984)), the largest relative deviation is up to 15%. By analyzing the average interparticle distances and possibility distributions of interparticle distances of this system, it is confirmed that the Born–Oppenheimer approximation is reasonable for this system and that 4He μ+ can be regarded as a system of positive muon bound to a slightly distorted helium atom.

F-μ bond length and μSR depolarization spectrum calculation for fluoride using two-component density functional theory

“…[24] for muonic molecules is not valid for fluorides. [8] As the electron-muon correlation functionals have only been addressed currently, fluoride can provide a precise platform to compare their correctness in ionic crystals.…”

“…[3,4] Density-functional theory (DFT) has been used to account for the perturbation of the implanted muon to local crystallographic and electronic structures. [5][6][7][8] Considering the proton-like muon, a proton can be placed in candidate interstitial sites and the structure is relaxed to estimate the µ + -sample interaction, while all atoms and the proton are allowed to move until convergence to find the lowest energy site for µ. This method is often referred to as "DFT+µ".…”