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Fortschritte der Physik/Progress of Physics

Positronium Molecules: Their Existence, Formation and Annihilation

M. A. Abdel-Raouf

Published Jan 1, 1988• 12 citations
Publisher

Abstract

The theoretical bases for establishing the existence of four-body molecules are discussed. A review of the theory of positronium molecules (Ps2) is presented. Special attention is given to the role of Ps2 in understanding the structure of similar quantum mechanical systems created in molecular crystals and semiconductors.
DOI
10.1002/prop.2190360703

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Abstract We present the actual state of affairs and future perspectives in the study of a quantum system of a collection of positronium (Ps) atoms. The interaction of a Ps atom with other atoms and molecules and specially with another Ps atom is described in some detail as Ps‐Ps interaction should play a crucial role in the dynamics of an assembly of Ps atoms. Using a simple model‐exchange potential, we could describe the available experimental results of Ps scattering reasonably well. The present scenario of the observation of Ps2 molecule, Ps Bose‐Einstein condensate (BEC) and the annihilation laser from a Ps BEC is presented. Possibilities of a Ps BEC formation via laser cooling of Ps atoms and via Ps formation in cavities are considered and difficulties with each procedure discussed (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The positronium molecule (Ps2)({\mathrm{Ps}}_{2})(Ps2​) has not been experimentally observed yet because its tiny (4.5 eV) binding energy cannot be detected when the molecule annihilates by emitting two photons with energy of 0.51 MeV each. It is shown in this paper that the electric dipole transition between the recently found L=1L=1L=1 excited state and the L=0L=0L=0 ground state with its characteristic photon energy of 4.94 eV is a clear signature of the existence of the positronium molecule and the possibility of its experimental observation is realistic. The probability of this transition is about 17% of the total decay rate. Another Coulomb four-body system containing positron HPs (the positronium hydride or hydrogen positride), is also included for comparison.
The (${\mathit{e}}^{\mathrm{\ensuremath{-}}}$,e+{\mathit{e}}^{+}e+)-pair annihilation in the bound 1^{1}1S0{\mathit{S}}_{0}S0​ state of the Ps2{\mathrm{Ps}}_{2}Ps2​ molecule (${\mathit{e}}^{\mathrm{\ensuremath{-}}}$e+{\mathit{e}}^{+}e+${\mathit{e}}^{\mathrm{\ensuremath{-}}}$e+{\mathit{e}}^{+}e+) is studied. It is shown that the expectation values of the two-, three-, and four-body Dirac \ensuremath{\delta} functions 〈${\mathrm{\ensuremath{\delta}}}_{+\mathrm{\ensuremath{-}}}$〉, 〈${\mathrm{\ensuremath{\delta}}}_{++\mathrm{\ensuremath{-}}}$〉 (\ensuremath{\equiv}〈${\mathrm{\ensuremath{\delta}}}_{+\mathrm{\ensuremath{-}}\mathrm{\ensuremath{-}}}$〉), and 〈${\mathrm{\ensuremath{\delta}}}_{++\mathrm{\ensuremath{-}}\mathrm{\ensuremath{-}}}$〉 determine the photonless, one- and many-photon annihilation rates, i.e., the values of ${\mathrm{\ensuremath{\Gamma}}}_{0\ensuremath{\gamma}}$, ${\mathrm{\ensuremath{\Gamma}}}_{1\ensuremath{\gamma}}$, and ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{n}\ensuremath{\gamma}}$, where n\ensuremath{\ge}2. The appropriate analytical expressions are presented together with numerical estimates. As expected, the two-photon annihilation process dominates.
Abstract Our recent experiment on Ps‐Ps spin exchange quenching represents the first time that two Ps atoms have been observed interacting with each other. The implication is that experimentation on various systems containing more than one Ps atom is now possible, including the Ps2 molecule, the Ps Bose‐Einstein condensate, the Ps atom laser and the annihilation gamma ray laser. Here we describe various aspects of such research, including the development of new techniques, work currently underway and some possible future experiments. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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