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Physical Review A

Hydrogen-antihydrogen interactions

W Kołos, David L. Morgan, David M. Schrader, L. Wolniewicz

Published Jun 1, 1975• 73 citations
Publisher

Abstract

Accurate quantum-mechanical calculations on the system hydrogen-antihydrogen ($\mathrm{H}\overline{\mathrm{H}}$) 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.

DOI
10.1103/physreva.11.1792

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arXiv:0704.2197•Physical Review Letters•Mar 5, 2007•1 citation
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.
The stability of antimatter in contact with matter has been investigated. The interaction between hydrogen and antihydrogen is considered as the prototype reaction. We have focused interest on the rates for proton-antiproton and/or electron-positron annihilation during hydrogen-antihydrogen collisions at low energies. In particular, we have concentrated on the calculation of the rates for the rearrangement reaction leading to formation of protonium and positronium, ending inevitably in particle-antiparticle annihilation. The cross section for the rearrangement collision has been calculated in a fully quantum-mechanical treatment. Additionally, we have calculated cross sections for direct annihilation during the collision process, which was found to be comparable to the rearrangement cross section. The elastic cross section and its low-energy limit, given by the scattering length, have been calculated, allowing, by comparison to the inelastic processes, a prediction for the efficiency of cooling antihydrogen via collisions with ultracold hydrogen atoms.
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.
Calculations of leptonic and hadronic annihilation rates in the hydrogen-antihydrogen molecule are presented. Both the leptonic potential and leptonic wave function are evaluated within the Born-Oppenheimer approximation employing the Ritz variational principle. Nonadiabatic corrections to the leptonic potential are also obtained. Explicitly correlated Gaussians are employed as basis functions, which describe accurately the hydrogen-antihydrogen interaction. Given the leptonic potential the hadronic part of the wave function for each molecular level of the hydrogen-antihydrogen quasimolecule is calculated by solving the corresponding Schr\"odinger equation by means of precise BBB-spline representations. The decay rates of the quasimolecule into separate positronium and protonium systems are estimated for a number of molecular levels. Utilizing the leptonic and hadronic wave functions the leptonic- and hadronic-annihilation rates for different molecular levels are computed.
Ever since antiparticles were discovered their nature has been something of a mystery. They were postulated to be identical to regular particles except for having opposite charge, but this would imply that an equal amount of antiparticles and particles should have been created at the beginning of time. However, everywhere we look the Universe seems to be constituted of regular particles, giving rise to the question whether there is something else that differentiates antiparticles from regular particles, or if there is something amiss in the Standard Model of particle physics. This thesis focuses on a central system of study in this field, the hydrogen-antihydrogen system and the theory surrounding it, as well as an expansion into systems with an antiproton interacting with small molecules, bridging the fields of quantum physics and quantum chemistry. Methods expanding on the Born-Oppenheimer approximation for the interaction between the two atoms are presented. The resulting 2-body interaction potential is then used for creating a part of the basis in a non-adiabatic 4-body method in order to look for resonance states whose existence could impact cross-sections of hydrogen-antihydrogen scattering. The eigenfunctions obtained from the non-adiabatic method are used by extracting the 2-body hadronic density function and comparing it to the adiabatic wave function, for measuring the adiabaticity of the hydrogen-antihydrogen system. The antiproton-matter interaction is first investigated by a quantum dynamical approach of an antiproton scattering on molecular hydrogen, common products in high-energy collision experiments, continued by a study of the potential energy surfaces of an antiproton interacting with a range of functional groups present in the human body.
The interaction potential between hydrogen and antihydrogen is obtained by a variational calculation. A potential maximum is found, but its peak is below the dissociation limit. A classical calculation shows that the cross section for total annihilation decreases monotonically from 31a0231{{a}_{0}}^{2}31a0​2 at 0.01 eV to 4a024{{a}_{0}}^{2}4a0​2 at 20 eV.
Potential energy curves for excited leptonic states of the helium-antihydrogen system are calculated within the Ritz variational approach. An explicitly correlated ansatz for the leptonic wave function is employed describing accurately the motion of the leptons (two electrons and positron) in the field of the helium nucleus and of the antiproton with an arbitrary orbital angular momentum projection Lambda onto the internuclear axis. Results for Lambda=0, 1, and 30 are presented. For quasibound states with large values of Lambda and rotational quantum numbers J>Lambda no annihilation and rearrangement decay channels occur; i.e., they are metastable.