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Physical Review A

Binding energy and structure of e+Li and e−Li using a parametric model potential

Janine Shertzer, Sandra J. Ward

Published Feb 7, 2006• 18 citations
Publisher

Abstract

The parametric model potential developed by Peach for describing the electron interaction with the alkali-metal ion core yields energy levels that are in excellent agreement with the measurements of the spectra. Because of its relative simplicity, the $l$-independent model potential is an attractive choice for studying positron--alkali-metal collisions. In order to test how well the model potential can be used to describe an effective three-body system, we use the Peach model potential to calculate the energy and geometry of the weakly bound ${e}^{+}\mathrm{Li}$ and ${e}^{\ensuremath{-}}\mathrm{Li}$ systems. The binding energy is in good agreement with calculations using the exact Hamiltonian.

DOI
10.1103/physreva.73.022504

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The parametric model potential developed by Peach for describing the electron interaction with the alkali-metal ion core yields energy levels that are in excellent agreement with the measurements of the spectra. Because of its relative simplicity, the lll-independent model potential is an attractive choice for studying positron--alkali-metal collisions. In order to test how well the model potential can be used to describe an effective three-body system, we use the Peach model potential to calculate the energy and geometry of the weakly bound e+Li{e}^{+}\mathrm{Li}e+Li and e\ensuremath−Li{e}^{\ensuremath{-}}\mathrm{Li}e\ensuremath−Li systems. The binding energy is in good agreement with calculations using the exact Hamiltonian.
We calculate the nonadiabatic binding energy and geometry of the weakly bound state of e+{e}^{+}e+Na. We use the Peach model potential, which includes both the dipole and an effective quadrupole term in the polarization, to describe the interaction of the electron and positron with the ion core. The effective three-body Schr\"odinger equation is solved with the finite element method. Because the model potential gives rise to three spurious states, the true ground state of e+{e}^{+}e+Na is embedded in a dense spectrum of spurious states. We develop a method for extracting the correct ground state for e+{e}^{+}e+Na, even when the energy is nearly degenerate with a spurious level. The calculated value for the binding energy is consistent with other calculations.
In order to investigate the binding mechanism of weakly bound states of positronic alkali atoms, we calculate the energies and wavefunctions using the Gaussian expansion method (GEM) where a positronium (Ps)–alkali ion channel and a positron–alkali atom channel are explicitly introduced. The energies of the bound states are updated using a model potential that reproduces well the observed energy levels of alkali atoms. The binding mechanism of the positronic alkali atom is analyzed by the wavefunctions obtained. The structure of the positronic alkali atom has been regarded as a Ps cluster orbiting the alkali ion, which is described by the Ps–alkali ion channel. We point out that the fraction having the positron–alkali atom configuration is small but plays an indispensable role for the weakly bound system.
We report a theoretical calculation of the relativistic corrections to the binding energy of positronic alkali-metal atoms. The ground state for the positronic alkali-metal atom is a loosely bound state with the structure of an alkali-metal ion surrounded by a positronium cloud. The correlation between the valence electron and positron in the field of a residual core ion is taken into account using a three-body model. Relativistic corrections to the binding energy for positronic alkali-metal atoms are evaluated based on the Breit-Pauli perturbation theory up to the second order of the fine structure constant. The relativistic corrections caused by the interaction between the valence electron and core ion was evaluated from the decomposed expectation values of the perturbation Hamiltonian. We found that the importance of relativistic corrections to the binding energy, namely the ratio of the net relativistic correction in the total binding energy, is remarkably enhanced in the loosely bound states of positronic alkali-metal atoms, where the charge of the valence electron is screened by the positron as positronium in the outermost region, while the electron is released from the positron near the nucleus. The results imply that positronic atoms with a dominant positronium can serve as an apt testing ground for relativistic quantum mechanics.
Abstract We study theoretically interaction potentials and low-energy collisions between different alkali atoms and alkali ions. Specifically, we consider systems such as X + Y + , where X( Y + ) is either Li(Cs + ) or Cs(Li + ), Na(Cs + ) or Cs(Na + ) and Li(Rb + ) or Rb(Li + ). We calculate the molecular potentials of the ground and first two excited states of these three systems using a pseudopotential method and compare our results with those obtained by others. We derive ground-state scattering wave functions and analyze the cold collisional properties of these systems for a wide range of energies. We find that, in order to get convergent results for the total scattering cross sections for energies of the order 1 K, one needs to take into account at least 60 partial waves. The low-energy scattering properties calculated in this paper may serve as a precursor for experimental exploration of quantum collisions between an alkali atom and an alkali ion of a different nucleus.
The fixed-core stochastic variational method has been used to demonstrate the existence of an electronically stable ground state for the Li + Ps 2 and Na + Ps 2 systems. The stability of Li + Ps 2 has been indicated previously in an ab initio calculation by Varga, but the present estimate of the binding energy is much closer to convergence. The Li + Ps 2 system has a binding energy of 0.013 149 Hartree and a 2 annihilation rate of 3.86 × 10 9 s -1 . The Na + Ps 2 system has a binding energy of 0.005 736 Hartree and an annihilation rate of 4.02 × 10 9 s -1 . Examination of the interparticle expectation values, correlation functions and the annihilation rates suggests that both of these systems can be best described as a Ps 2 molecule weakly bound to an alkali atom cation.
We calculate the binding energy and geometry of the weakly bound e(+)Li and e(+)Na systems within the framework of hyperspherical coordinates. The Schrodinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B-splines and the resulting coupled hyper-radial equation is solved using the slow variable discretization method developed by Tolstikhin et al. [J. Phys. B 29, L389 (1996)]. Great efforts are made in optimizing the distribution of B-splines to overcome the slow convergence of the binding energy and geometrical quantities. This approach allows us to obtain the results with improved convergence that are in good agreement with the best values reported to date. In addition, an analysis of the structure of the two systems is also made and the e(+)Na system is seen to exhibit quantum halo features.