Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z

Sabyasachi Kar,Yang Wang,Yew Kam Ho,Yu-Shu Wang

doi:10.3390/atoms7020053

Abstract

The question of stability of a given quantum system made up of charged particles is of fundamental interest in atomic, molecular, and nuclear physics. In this work, the stability for the negatively charged positronium (Ps)-like ions or the three-body system ( Z e + , e − , e − ) with Yukawa potentials is studied using correlated exponential wavefunctions based on the Ritz variational method. We obtained the critical screening parameter μ C as a function of the continuously varied nuclear charge Z , the critical nuclear charge Z C as a function of the screening parameter μ , and the ionization energies in terms of the screening parameter μ and Z . The critical nuclear charge for the bare Coulomb system ( Z e + , e − , e − ) obtained using 700-term correlated exponential wavefunctions is in accord with the reported results. The ionization energy, μ C , and Z C for the Yukawa system ( Z e + , e − , e − ) exhibit interesting behaviors. The present study describes the possible nonexistence of Borromean binding as well as Efimov states. The possible existence of quasi-bound resonances states for the negatively charged screened Ps-like ions is briefly discussed.

Highlights

This paper deals with an investigation on the stability of three-body Coulomb systems, made up of two electrons and a particle of charge Z having the mass of a positron, with continuously varying Z and interacting with Yukawa potentials [16] or the Debye potentials [17]
We present the critical nuclear charge as a function of Z, the critical nuclear charge as a function of screening parameter, the ionization energy in terms of screening parameter, and Z for the Yukawa system (Ze+, e−, e− ) with varying Z using the correlated exponential wavefunctions based on Ritz variational principle
Z = 1, that is, for the positronium negative ion is taken from our earlier work [36]

Summary

Introduction

Despite the fact that the stability of few-body Coulomb systems is an old topic of research [1,2,3,4,5,6]. This paper deals with an investigation on the stability of three-body Coulomb systems, made up of two electrons and a particle of charge Z having the mass of a positron, with continuously varying Z and interacting with Yukawa potentials [16] or the Debye potentials [17]. We define such three-body system as (Ze+ , e− , e− ). The stability of few-body systems with Yukawa potentials or Debye potentials are of great interest due to its extreme importance in determining several features in atomic, nuclear, and molecular physics, such as the Borromean states, Efimov effects, quasi-bound states, critical screening parameter, critical nuclear charge, etc.

Calculations

Results and Discussion

Conclusions