The positronium ion
Ps−− is often qualitative described as a positronium Ps with a loosely bound second electron, since the value of the annihilation rate for
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−− 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−− 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−−) with varying
Z charge.
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.
Non-relativistic quantum chemical calculations of the particle mass, m±2, corresponding to the dissociation threshold in a range of Coulomb three-particle systems of the form m±1m±2m±3, are performed variationally using a series solution method with a Laguerre-based wavefunction. These masses are used to calculate an accurate stability boundary, i.e., the line that separates the stability domain from the instability domains, in a reciprocal mass fraction ternary diagram. This result is compared to a lower bound to the stability domain derived from symmetric systems and reveals the importance of the asymmetric (mass-symmetry breaking) terms in the Hamiltonian at dissociation. A functional fit to the stability boundary data provides a simple analytical expression for calculating the minimum mass of a third particle required for stable binding to a two-particle system, i.e., for predicting the bound state stability of any unit-charge three-particle system.
The stability and structure of the $({m}^{Z+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system is studied as a function of the mass of the
mZ+ particle and for
Z=1, 2, 3, and 10. The
Z=1 system can be regarded as an analog of the
APs system (where
A is a group I or IB atom of the periodic table) and was found to be stable for all values of
m+. This is supportive of the idea that all the group I and IB atoms can bind Ps. The $({m}^{2+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system is stable for all ${m}^{2+}∕{m}_{e}\ensuremath{\leqslant}0.68$ and evolves into a configuration best described as $({m}^{2+},{\mathrm{Ps}}^{\ensuremath{-}})$ when ${m}^{2+}∕{m}_{e}\ensuremath{\rightarrow}0$. The $({m}^{3+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system was stable for a mass range given by ${m}^{3+}∕{m}_{e}\ensuremath{\leqslant}0.066\phantom{\rule{0.2em}{0ex}}32$, which suggests that positrons could form Feshbach resonances in collisions with positive ions which are isolectronic with the group II and IIB columns of the periodic table. The $({m}^{3+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system has the unusual property that it has a mass range where it becomes more compact while its binding energy simultaneously decreases. The $({m}^{10+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system is also stable at
m10+∕me=0.00254, which implies stability for all mass ratios less than 0.002 54. In total, the calculations suggest that the $({m}^{Z+},{e}^{\ensuremath{-}},{e}^{\ensuremath{-}},{e}^{+})$ system is stable whenever the ${m}^{Z+}+{\mathrm{Ps}}^{\ensuremath{-}}$ or $({m}^{Z+},{e}^{\ensuremath{-}})+\mathrm{Ps}$ breakups represent the lowest energy dissociation channel. As part of the analysis some improved estimates of the properties of the KPs ground state are reported.
The stability of the ${(m}^{2+}{,e}^{\ensuremath{-}}{,e}^{\ensuremath{-}}{,e}^{+})$ system is studied as a function of the mass of the
m2+ particle. The system is found to be stable for all values of
m2+<0.68me. At the smallest values of
m2+ the system evolves into a ${m}^{2+}+{\mathrm{Ps}}^{\ensuremath{-}}$ configuration, which is absolutely stable since both fragments are electrically charged. This suggests that a positron can be expected to bind to all the group II and IIB atoms with the possible exception of mercury.