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Quasibound states of an antiproton and a hydrogen atom

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 $\bar{p}$ + 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.