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MATTER-ANTIMATTER INTERACTIONS : The hydrogen-antihydrogen system and antiproton-matter interactions

Henrik Stegeby

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

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.

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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 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.
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.
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.
Recent productions of large numbers of cold antiprotons as well as the formation of antihydrogens at CERN and Fermilab have raised basic questions about possible coexistence of matter and antimatter in nature. In the present work, previous mathematical considerations are revisited which support the possible coexistence of Antihydrogen with Hydrogen, Deuterium and Tritium atoms. In particular, the main objective of the present work is to present computational treatments which confirm the possible formation of these quasi molecules in laboratory. These treatments are based on a nonadiabatic picture of the system in which generalized basis functions are adjusted within the framework of Rayleigh-Ritz' variational method. Thus, it is ruled out in the present work the Born-Oppenheimer adiabatic picture of the system, which demands the existence of bound states composed of fixed quasi heavy atoms (containing at least two baryons, e.g. protonium (Pn), with mean lifetime 1.0x10^^-6 s) and quasi light atoms (composed of two leptons, e.g. positronium (Ps), with mean lifetime 125x10^^-12 s for para-Ps and 142.05x10^^-9 s for ortho-Ps). Our calculations of the binding energies and internal structure of Antihydrogen-Hydrogen, Antihydrogen-Deuterium and Antihydrogen-Tritium show that these quasi molecules are bound and could be formed in nature. On the other hand, having in mind the adiabatic picture of the systems, our results suggest the possible formation of these molecules as resonant states in Antihydrogen-Atom interaction. Nevertheless, several arguments are accumulated in the conclusion as consequences of the proposed bound states.
Antihydrogen atoms, H― , are now routinely created and can be stored for long enough to allow comparison with ordinary matter. A major goal of these efforts is to test potential physics beyond the Standard Model. This will require further developments in the experiments including the accumulation of more antihydrogen atoms and their storage over longer times. The latter is limited by the unavoidable presence of normal hydrogen molecules. Interactions of H― with H2 lead to the destruction of the hard-won antimatter. Little is known about these interactions but quantitative information will be crucial in guiding experimental developments. Physically realistic modelling of rearrangement scattering of “heavy” antimatter particles (antiprotons, p― , and antihydrogen atoms) by normal matter molecules, such as H2 + H―→ Pn + Ps + H (where Pn represents protonium and Ps positronium), requires the development of new theoretical and computational methodologies. R-matrix theory offers a strong prospect for tackling such problems having proved itself in atomic, molecular and optical physics. It divides the problem into a computationally demanding but energy-independent inner region and simpler energy-dependent outer regions. We propose to adapt the new RmatReact ultracold chemistry approach for the more complex molecular matter-antimatter problems. Here, developments required for the inner region, the boundary and outer regions are outlined. We also report some preliminary bound-state calculations on the {p,p, p― } system and a study of the required mixed coordinate systems for the general effective 3-body case and their transformations at the R-matrix boundary surfaces.
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.