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Physical Review A

Necessary condition for an atom-positron bound state

Rajeev K. Pathak

Published Jun 1, 1994• 5 citations
Publisher

Abstract

Following closely a technique due to Lieb [Phys. Rev. Lett. 52, 315 (1984)], a rigorous condition for an atom-positron bound state is derived in terms of the electrostatic Coulomb attractive potential between the positron and the atomic electrons. Further, it is demonstrated that for a joint electron-positron pair density distribution that is spherically symmetric around the nucleus in the positron and/or the electron coordinate, a bound state between a neutral atom and a positron is not possible.

DOI
10.1103/physreva.49.5100

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Following closely a technique due to Lieb [Phys. Rev. Lett. 52, 315 (1984)], a rigorous condition for an atom-positron bound state is derived in terms of the electrostatic Coulomb attractive potential between the positron and the atomic electrons. Further, it is demonstrated that for a joint electron-positron pair density distribution that is spherically symmetric around the nucleus in the positron and/or the electron coordinate, a bound state between a neutral atom and a positron is not possible.
The effect of an electric quadrupole moment QQQ is studied for positron-atom bound systems. It is demonstrated that for Q>50Q>50Q>50 a.u. the electric quadrupole potential is sufficiently strong to bind a positron (or an electron) even in the absence of the dipole polarization potential. Such large values of QQQ are not known for atomic ground states; however, they exist in molecules and excited atoms. In the 2s2p3P2o2s2{p}^{3}{P}_{2}^{o}2s2p3P2o​ state of beryllium, the quadrupole contribution makes the difference between a stable bound state and an unstable state, which decays to a Be+\mathrm{Be}{}^{+}Be+ ion and positronium. In the majority of atoms the quadrupole contribution is small and can be neglected.
Predicted 20 years ago, positron binding to neutral atoms has not yet been observed experimentally. A scheme is proposed to detect positron-atom bound states by colliding Rydberg positronium (Ps) with neutral atoms. Estimates of the charge-transfer reaction cross section are obtained using the first Born approximation for a selection of neutral atom targets and a wide range of incident Ps energies and principal quantum numbers. We also estimate the corresponding Ps ionization cross section. The accuracy of the calculations is tested by comparison with earlier predictions for charge transfer in Ps collisions with hydrogen and antihydrogen. We describe an existing Rydberg Ps beam suitable for producing positron-atom bound states and estimate signal rates based on the calculated cross sections and realistic experimental parameters. We conclude that the proposed methodology is capable of producing such states and of testing theoretical predictions of their binding energies.
The hydrogen atom is the Rosetta stone of the early twentieth century atomic physics. The attempt to decipher its structure and properties led to the development of quantum mechanics and the unraveling of many of the mysteries of atomic, molecular, and solid state physics, and a good deal of chemistry and modern biology. Unlike the various one-dimensional model problems that we have been studying in the previous chapters, the hydrogen atom is a real physical system in three dimensions. It consists of an electron moving in a spherically symmetric potential well due to the Coulomb attraction of the positively charged nucleus. In three dimensions, the electron is not constrained to move linearly. It can execute orbital motions and, thus, has angular momentum. Not only is the total energy of the electron in the atom quantized, its angular momentum also has interesting and unexpected quantized properties that cannot possibly be understood on the basis of classical mechanics and electrodynamics. They are, however, the natural and necessary consequences of the basic postulates of quantum mechanics, as will be shown in this chapter. According to classical mechanics and electrodynamics, it is not possible to have a stable structure consisting of a small positively charged nucleus at the center of an electrically neutral atom with an electron sitting in its vicinity. For the electron not to be attracted into the positive charge, it must be orbiting around the nucleus so that the centrifugal force will counter the Coulomb attraction of the nucleus and maintain a constant electron orbit.