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Atoms

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

Sabyasachi Kar, Yu-Shu Wang, Yang Wang, Y. K. Ho

Published Jun 3, 2019• 8 citations
Publisher

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.

DOI
10.3390/atoms7020053

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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.
The stability of the ground state of three-unit charge ${q}_{i}=\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}1\ensuremath{\mp}1$, interacting through a statically screened Coulomb potential, has been studied as a function of the values of the constituent masses for different values of the screening parameter. General conditions are given and accurate variational calculations have been performed to determine the region where the three-body ground state is Borromean. The possible existence of Efimov states when the screening parameter is equal to the two-body critical screening parameter is discussed. The critical exponent for the energy in different regions of the stability diagram has been also calculated.
Abstract We investigate the bound states, Borromean states and resonant states for the 3Po (J = 1) states of ppμpp\muppμ, ddμdd\muddμ andttμtt\muttμ molecular ions interacting with exponential-cosine-screened Coulomb potential. The bound 3Po state energies are calculated using the Rayleigh-Ritz variational method and the resonance parameters are calculated using the stabilization method. Highly correlated exponential wave functions are used. The bound 3Po state energies, the 3Po resonance parameters (energy and width), along with 1S and 2S threshold energies of the pμp\mupμ, dμd\mudμ andtμt\mutμ atoms are also reported for different shielding parameters. The critical values of the screening parameters for the 3Po states are also reported for which the three-body exotic molecular systems are stable while all the possible fragments are unbound, that is shows windows for Borromean binding.
In an effort to unravel the dependence of the dynamics of three-bound-particle systems on the relative masses of the particles, an adiabatic treatment in hyperspherical coordinates is used to study the ground state and some doubly excited states of Ps('-) (positronium negative ion) and other three-particle systems, including H('-) and M('-) (muonium negative ion). Two different methods for the solution of the adiabatic eigenvalue equation are presented; one uses a "prediagonalized" basis of hyperspherical harmonics, and the other uses an asymptotic basis which consists of hydrogenic functions for the positronium. Potential curves for Ps('-) and M('-) in the ('1)S('e), ('1)P('o), ('3)P('e), ('3)P('o) and ('1)D('e) states and for H('-) in the ('1)P('o) states are presented. A method for calculating the probability density as a function of the hyperspherical coordinates (R,(alpha),(theta)(,12)) is introduced and used for the P states of Ps('-). This helps to understand the different symmetries and to distinguish among them. A remarkable linear dependence of the binding energy of the ground state and of the doubly excited states on the reduced mass of the atom, discovered in this study, is presented and discussed.
We study the ground state energy and the critical screening parameter of the Yukawa potential in nonrelativistic quantum mechanics. After a short review of the existing literature on these quantities, we apply fifth-order perturbation theory to the calculation of the ground state energy, using the exact solutions of the Coulomb potential together with a cutoff on the principal number summations. We also perform a variational calculation of the ground state energy using a Coulomb-like radial wave function and the exact solution of the corresponding minimization condition. For not too large values of the screening parameter, close agreement is found between the perturbative and variational results. For the critical screening parameter, we devise a novel method that permits us to determine it to 10 digits. This is the most precise calculation of this quantity to date, and allows us to resolve some discrepancies between previous results.
The positronium ion Ps−−{\mathrm{Ps}}^{--}Ps−− is often qualitative described as a positronium Ps with a loosely bound second electron, since the value of the annihilation rate for Ps−−{\mathrm{Ps}}^{--}Ps−− is nearly equal to that of the spin-averaged neutral positronium. This similarity however has never been fully explained. To study its internal structure, we decompose the electron-positron distribution function of Ps−−{\mathrm{Ps}}^{--}Ps−− into the sum of two terms: one for the electron closest to the positron and the other for the farthest. We show that the inner electron behaves almost as if the outer electron were not present, forming a Ps substructure inside Ps−−{\mathrm{Ps}}^{--}Ps−− and that the effect of electron correlation is such that the outer electron tries to stay as close as possible to the positron but without interfering too much with the distribution of the inner electron. We show that this phenomenon is closely related to the problem of the critical stability of the system (Z+,e−−,e−−)({Z}^{+},\phantom{\rule{0.28em}{0ex}}{e}^{--},\phantom{\rule{0.28em}{0ex}}{e}^{--})(Z+,e−−,e−−) with varying ZZZ charge.
In this review we discuss quantum phase transitions and the mapping between symmetry breaking of electronic structure configurations at the large-dimension limit and mean-field theory of phase transitions. We show that the finite size scaling method can be used for the calculations of the critical parameters of the few-body Schrodinger equation. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given Hamiltonian. The critical parameters such as the critical nuclear charges will be used to explain and predict the stability of atomic and molecular negative ions. For N-electron atoms with 2 N 86, results show that, at most, only one electron can be added to a free atom in the gas phase. However, doubly charged atomic negative ions might exist in a strong magnetic field.