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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Model-potential theory of positron-alkali-atom bound states

P. Cavaliere, G. Ferrante

Published Mar 1, 1973• 6 citations
Publisher
DOI
10.1007/bf02738644

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We report a theoretical calculation of the relativistic corrections to the binding energy of positronic alkali-metal atoms. The ground state for the positronic alkali-metal atom is a loosely bound state with the structure of an alkali-metal ion surrounded by a positronium cloud. The correlation between the valence electron and positron in the field of a residual core ion is taken into account using a three-body model. Relativistic corrections to the binding energy for positronic alkali-metal atoms are evaluated based on the Breit-Pauli perturbation theory up to the second order of the fine structure constant. The relativistic corrections caused by the interaction between the valence electron and core ion was evaluated from the decomposed expectation values of the perturbation Hamiltonian. We found that the importance of relativistic corrections to the binding energy, namely the ratio of the net relativistic correction in the total binding energy, is remarkably enhanced in the loosely bound states of positronic alkali-metal atoms, where the charge of the valence electron is screened by the positron as positronium in the outermost region, while the electron is released from the positron near the nucleus. The results imply that positronic atoms with a dominant positronium can serve as an apt testing ground for relativistic quantum mechanics.

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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.

Physical Review A•Jun 1, 1994•5 citations
In order to investigate the binding mechanism of weakly bound states of positronic alkali atoms, we calculate the energies and wavefunctions using the Gaussian expansion method (GEM) where a positronium (Ps)–alkali ion channel and a positron–alkali atom channel are explicitly introduced. The energies of the bound states are updated using a model potential that reproduces well the observed energy levels of alkali atoms. The binding mechanism of the positronic alkali atom is analyzed by the wavefunctions obtained. The structure of the positronic alkali atom has been regarded as a Ps cluster orbiting the alkali ion, which is described by the Ps–alkali ion channel. We point out that the fraction having the positron–alkali atom configuration is small but plays an indispensable role for the weakly bound system.
We report a theoretical calculation of the relativistic corrections to the binding energy of positronic alkali-metal atoms. The ground state for the positronic alkali-metal atom is a loosely bound state with the structure of an alkali-metal ion surrounded by a positronium cloud. The correlation between the valence electron and positron in the field of a residual core ion is taken into account using a three-body model. Relativistic corrections to the binding energy for positronic alkali-metal atoms are evaluated based on the Breit-Pauli perturbation theory up to the second order of the fine structure constant. The relativistic corrections caused by the interaction between the valence electron and core ion was evaluated from the decomposed expectation values of the perturbation Hamiltonian. We found that the importance of relativistic corrections to the binding energy, namely the ratio of the net relativistic correction in the total binding energy, is remarkably enhanced in the loosely bound states of positronic alkali-metal atoms, where the charge of the valence electron is screened by the positron as positronium in the outermost region, while the electron is released from the positron near the nucleus. The results imply that positronic atoms with a dominant positronium can serve as an apt testing ground for relativistic quantum mechanics.
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.