Properties of the Positronium Negative Ion Embedded in Non-ideal Classical Plasmas
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Biswajit Das · Arijit Ghoshal
Properties of the Positronium Negative Ion Embedded in Non-ideal Classical Plasmas
Received: 13 March 2020 / Accepted: 20 June 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract Properties of the positronium negative ion embedded in non-ideal classical plasmas have been studied theoretically. A pseudopotential, derived from a solution of Bogolyubov’s hierarchy equations, is used to describe the interaction potentials of the charged particles in the ion. A large basis set is employed in Rayleigh–Ritz variational method to compute accurately various quantities, such as binding energy, cusp values, annihilation rate, associated with the ground state of the ion. A detailed study is made on the effects of non-ideality of plasma on those quantities. In particular, special emphasis is given to determine the ranges of plasma screening parameters within which the ion remains stable.
1 Introduction An electron (e− ) and its anti-particle (positron, e+ ), interacting with Coulomb potential (CP) can form bound states. The resulting bound state is called positronium atom (Ps). This atom resembles hydrogen atom, except the reduced mass is half of the hydrogen atom, which leads to the doubling of first Bohr radius and halving the energy levels of Ps than of the hydrogen atom. Another e− can be attached weakly to the ground state of Ps to form what is known as positronium negative ion (Ps− ). This ion exists only in the ground state (1 S) which is stable against disassociation into an e− and Ps, but unstable against e+ + e− annihilation. As the ion consists of three leptons (e− , e− , e+ ) of equal mass, it provides an ideal platform for testing quantum threebody problems. The stability of Ps− was first discussed by Wheeler [1] by proposing its formation through the interaction of a photon with atomic electrons. Subsequently Mills [2] observed this ion by using a beam foil method of production. Since its observation, the ion has been drawing the attention of both theorists and experimentalists due to its applicability in various branches of physics, such as solid state physics, astrophysics, plasma physics including modern communication devices [3]. So far, a number of theoretical investigations have been performed to study various aspects of Ps− . Particular mention may be made of the works attempting to calculate accurately the ground state energy [4–14], annihilation rate [11–16], resonance states [17–23], photodetachment cross section [24–28], polarizability [29–31] etc. At the same time, several experiments were also performed to study the properties of Ps− [32–40]. These have been well documented in the articles of Nagashima [41,42]. It is well known that an atom or an ion behaves differently, when it is embedded in finite density plasma at a given temperature. The plasma screening alters the interaction potentials of the constituent charged particles of the embedded atom. As a result, stability and other structural properties, such as energy levels, line shapes, ioni
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