Quasibound states of an antiproton and a hydrogen atom

Abstract

Accurate three-body quantal calculations of the system composed of a proton, an antiproton, and an electron are performed in perimetric coordinates with the Lagrange-mesh method, an approximate variational calculation with the simplicity of a calculation on a grid. Quasibound states with respect to the p + H(n = 2) threshold are obtained for L = 60 to 71 for various vibrational excitations. Their energies have accuracies up to about 10 −14 atomic units while less precise energies are determined for L = 56 − 59 broader resonances. Their structure is analyzed with the help of mean distances between the particles. These mean distances indicate that the proton-electron subsystem is in excited states, mostly n = 2, as predicted by Sakimoto (Phys. Rev. A 98, 042503, 2018) with the Born-Oppenheimer approximation. A comparison performed with this approximation provides the accuracies of its energies and of its proton-antiproton mean distances.