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arXiv:0711.2283

Possible Coexistence of Antihydrogen with Hydrogen, Deuterium and Tritium Atoms

Mohamed Assad Abdel-Raouf

Published Nov 14, 2007• 2 citations

Abstract

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.

DOI: 10.48550/arxiv.0711.2283

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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.

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

B

-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.