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arXiv:1911.10931 · Physical Review A

Quasibound states of an antiproton and a hydrogen atom

D. Baye, Jérémy Dohet-Eraly

Published Feb 28, 2020• 5 citations
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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 approximately variational calculation with the simplicity of a calculation on a grid. Quasibound states with respect to the $\overline{p} + \mathrm{H}(n=2$) threshold are obtained for $L=60\ensuremath{-}73$ for various vibrational excitations. Their energies have accuracies up to about ${10}^{\ensuremath{-}14}$ 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.

DOI
10.1103/physreva.101.022507

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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 approximately variational calculation with the simplicity of a calculation on a grid. Quasibound states with respect to the p‾+H(n=2\overline{p} + \mathrm{H}(n=2p​+H(n=2) threshold are obtained for L=60\ensuremath−73L=60\ensuremath{-}73L=60\ensuremath−73 for various vibrational excitations. Their energies have accuracies up to about 10\ensuremath−14{10}^{\ensuremath{-}14}10\ensuremath−14 atomic units, while less precise energies are determined for L=56−−59L=56--59L=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=2n=2n=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.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.
Accurate quantum-mechanical calculations on the system hydrogen-antihydrogen (HH‾\mathrm{H}\overline{\mathrm{H}}HH) are presented. The energy is calculated using the Ritz variational principle, and is obtained as a function of the proton-antiproton distance in the Born-Oppenheimer approximation. It is everywhere lower and therefore more accurate than that recently calculated by Junker and Bardsley. In particular, the maximum in the interatomic interaction reported by these authors is not seen in this calculation. The cross section for rearrangement annihilation is calculated and found to be uniformly larger than that reported by Junker and Bardsley.
A description of the excited lepton states of the hydrogen-antihydrogen quasimolecule is presented. Potential energy curves and the leptonic part of the wave functions corresponding to a variety of such states are calculated within the Born-Oppenheimer approximation employing the Ritz variational principle. Nonadiabatic corrections to the leptonic potentials are also obtained. Basis functions are constructed as products of explicitly correlated Gaussians and spherical harmonics which describe correctly the motion of leptons with arbitrary orbital angular momentum projection onto the molecular (internuclear) axis. The hadronic part of the wave function for each leptonic level of the hydrogen-antihydrogen system is calculated by solving the Schr\"odinger equation with the obtained leptonic potentials. Corresponding solutions are generated utilizing precise B-spline representations. Employing leptonic and hadronic parts of the wave function the electron-positron and proton-antiproton annihilation rates are computed for a number of quasimolecular states. The decay rates of the hydrogen-antihydrogen system into separate positronium and protonium atoms are also estimated for the quasimolecular levels under consideration.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.
The stability of antiproton-hydrogen compound states (p‾H)(\overline{p}\mathrm{H})(p​H) is investigated theoretically. The p‾H\overline{p}\mathrm{H}p​H compound state has decay channels of atomic electron detachment $(\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+\overline{p}p)$ and hadronic pair $(\overline{p}\text{\ensuremath{-}}p)$ annihilation, and hence it cannot be permanently stable even if the dissociation channel $(\ensuremath{\rightarrow}\overline{p}+\mathrm{H})$ is energetically closed. In this paper, information on the metastable p‾H\overline{p}\mathrm{H}p​H states at energies below the dissociation limit is obtained by analyzing low-energy resonances in ${e}^{\ensuremath{-}}+\overline{p}p$ scattering. The scattering calculation is carried out by using an R-matrix method, which also allows for the annihilation channel simultaneously. The metastable states are found to be identified as vibrational levels supported by a Born-Oppenheimer (BO) potential. The energy-level widths attributed to the electron detachment and the annihilation are also calculated using a model based on the BO picture.
A new vibrational level of the H 2 + molecular ion with binding energy of 1.09 × 10 −9 a.u. ≈ 30 neV below the first dissociation limit is predicted, using highly accurate numerical non-relativistic quantum calculations, which go beyond the Born-Oppenheimer approximation. It is the first-excited vibrational level v = 1 of the 2 p σ u electronic state, antisymmetric with respect to the exchange of the two protons, with orbital angular momentum L = 0. It manifests itself as a huge p-H scattering length of a = 750 ± 5 Bohr radii.