Stability of four-unit-charge systems: A quantum Monte Carlo study

Abstract

The family of four-particle systems (${\mathrm{M}}^{+}$${\mathrm{m}}^{+}$${\mathrm{M}}^{\mathrm{\ensuremath{-}}}$${\mathrm{m}}^{\mathrm{\ensuremath{-}}}$) has been studied by means of Monte Carlo techniques. Nonadiabatic explicitly correlated wave functions for different values of the mass ratio M/m have been obtained using a variational Monte Carlo optimization method. These wave functions have been used in diffusion Monte Carlo simulations of (${\mathrm{M}}^{+}$${\mathrm{m}}^{+}$${\mathrm{M}}^{\mathrm{\ensuremath{-}}}$${\mathrm{m}}^{\mathrm{\ensuremath{-}}}$) to compute exact ground-state energies. Our results enlarge the stability range of the mass ratio for these and for similar less symmetric systems and address the problem of the stability of the hydrogen-antihydrogen system. For the special case of the dipositronium molecule (M=m) we report the ground-state energy, consistent with previous accurate calculations, and average values of various observables.