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Physical Review A

Decay channels and decay rates for the hydrogen-antihydrogen quasimolecule

Leonti N Labzowsky, V. Sharipov, A. Prozorov, G. Plunien, G. Soff

Published Aug 30, 2005• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.72.022513

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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.
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.
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.
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.
Adopting explicitly correlated Kolos-Wolniewicz-type basis functions, the Born-Oppenheimer potential curves of a number of excited ΣΣΣ states of the hydrogen-antihydrogen system (Hˉ\bar{\rm H}Hˉ) were calculated for both, even and odd, Q symmetries, including also free positronium states. It is demonstrated that the excited leptonic states support ro-vibrational states with energies close to the ground-state dissociation threshold. As a consequence, the excited leptonic states need to be considered in theoretical treatments of ground-state H-Hˉ\bar{\mathrm{H}}Hˉ collisions.
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.