Bound state properties, positron annihilation and hyperfine structure splittings in the four-body positron-helium He()] and He()] ions

Alexei M. Frolov

doi:10.1140/epjd/s10053-025-00990-3

2023 Impact factor 1.5

Atomic, Molecular, Optical and Plasma Physics

Eur. Phys. J. D (2025) 79: 38
https://doi.org/10.1140/epjd/s10053-025-00990-3

Regular Article - Atomic Physics

Bound state properties, positron annihilation and hyperfine structure splittings in the four-body positron-helium $e^{+} [^{3}$ $e^{+} [^{3}$ He( $2^{3} S_{e}$ $2^{3}S_e$ )] and $e^{+} [^{4}$ $e^{+} [^{4}$ He( $2^{3} S_{e}$ $2^{3}S_e$ )] ions

Alexei M. Frolov^a

Department of Applied Mathematics, University of Western Ontario, N6H 5B7, London, ON, Canada

^a alex1975frol@gmail.com

Received: 22 November 2024
Accepted: 25 March 2025
Published online: 24 April 2025

Abstract

Bound states properties of the four-body, positively charged positron-helium $e^{+} [^{M}$ $e^{+} [^{M}$ He( $2^{3} S_{e}$ $2^{3}S_e$ )] ions, where M = 3, 4 and $\infty$ $\infty$ , are determined to high accuracy and investigated. In each of these four-body ions, the positron $e^{+}$ $e^{+}$ forms a weakly bound state with the two-electron helium atom He in which the two electrons are located in the lowest triplet $2^{3} S$ $2^{3}S$ -state. Our highly accurate expectation values of the electron-positron delta-function(s), which have been determined for each of the positron-helium $e^{+} [^{3}$ $e^{+} [^{3}$ He( $2^{3} S_{e}$ $2^{3}S_e$ )] and $e^{+} [^{4}$ $e^{+} [^{4}$ He( $2^{3} S_{e}$ $2^{3}S_e$ )] ions, are used to evaluate (to very good accuracy) the corresponding rates of two-, three-, four- and five-photon annihilation. The hyperfine structures of both $e^{+} [^{3}$ $e^{+} [^{3}$ He( $2^{3} S_{e}$ $2^{3}S_e$ )] and $e^{+} [^{4}$ $e^{+} [^{4}$ He( $2^{3} S_{e}$ $2^{3}S_e$ )] ions are described in detail. The corresponding hyperfine structure splittings are also evaluated to high accuracy which is sufficient for all current and future experimental and theoretical needs.

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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.