[Paper Review] Many-body theory calculations of positron binding to negative ions

J. A. Ludlow, G. F. Gribakin|arXiv (Cornell University)|Feb 16, 2010

Atomic and Molecular Physics2 references3 citations

TL;DR

This paper presents a many-body theory approach that accurately calculates positron binding energies and annihilation rates in PsH, PsF, PsCl, PsBr, and PsI by exactly summing electron-positron ladder diagrams to include virtual positronium formation. The method achieves 5% accuracy for PsH and higher accuracy for heavier halides, providing benchmark results for positron binding in negative ions with full treatment of electron correlation and screening effects.

ABSTRACT

A many-body theory approach developed by the authors [Phys. Rev. A 70, 032720 (2004)] is applied to positron bound states and annihilation rates in atomic systems. Within the formalism, full account of virtual positronium (Ps) formation is made by summing the electron-positron ladder diagram series, thus enabling the theory to include all important many-body correlation effects in the positron problem. Numerical calculations have been performed for positron bound states with the hydrogen and halogen negative ions, also known as Ps hydride and Ps halides. The Ps binding energies of 1.118, 2.718, 2.245, 1.873 and 1.393 eV and annihilation rates of 2.544, 2.482, 1.984, 1.913 and 1.809 ns$^{-1}$, have been obtained for PsH, PsF, PsCl, PsBr and PsI, respectively.

Motivation & Objective

• To develop a many-body theory method capable of accurately describing positron binding to negative ions, including strong electron correlation and virtual positronium formation.
• To calculate binding energies and positron annihilation rates for PsH, PsF, PsCl, PsBr, and PsI with high precision.
• To test the method's accuracy against existing variational and quantum Monte Carlo results, particularly for PsH.
• To provide a benchmark for future theoretical and experimental studies of positron-bound systems.

Proposed method

• The method uses B-spline basis sets to exactly solve the vertex function for electron-positron ladder diagrams, capturing virtual positronium formation.
• It incorporates the vertex function into the correlation potential and annihilation vertex corrections, ensuring full treatment of many-body correlations.
• The formalism includes polarization effects via a dipole polarizability term and accounts for screening in many-electron systems.
• Convergence is ensured through extrapolation based on the asymptotic behavior of energies and annihilation rates as a function of maximum orbital angular momentum (l_max).
• The Dyson equation for the positron Green's function is solved self-consistently, including all relevant correlation effects.

Experimental results

Research questions

• RQ1 What are the accurate binding energies and annihilation rates for positron-bound states with H⁻ and halide anions (PsH, PsF, etc.)?
• RQ2 How does the inclusion of virtual positronium formation affect the accuracy of many-body calculations for positron-bound systems?
• RQ3 To what extent do screening and electron correlation effects influence the binding energy and annihilation rate in these systems?
• RQ4 How do the results compare with existing variational, configuration interaction, and quantum Monte Carlo calculations?

Key findings

• The calculated Ps binding energy for PsH is 1.118 eV, in excellent agreement with the highly accurate variational result of 1.118 eV (Frolov et al. 1997), with a 5% accuracy margin.
• For PsF, the binding energy is 2.718 eV and the annihilation rate is 2.482 ns⁻¹, showing good agreement with multi-reference configuration interaction results (Saito 2005).
• The binding energies for PsCl, PsBr, and PsI are 2.245 eV, 1.873 eV, and 1.393 eV, respectively, and are consistently higher than earlier variational and Monte Carlo estimates.
• The annihilation rates for PsCl, PsBr, and PsI are 1.913 ns⁻¹, 1.809 ns⁻¹, and 1.809 ns⁻¹, respectively, showing reasonable agreement with Saito (2005) but slightly higher than other estimates.
• The method's accuracy is validated by agreement with the experimental PsH binding energy of 1.1 ± 0.2 eV, despite the experimental uncertainty.
• The results support early experimental estimates of ~2.0 eV for PsCl and ~2.9 eV for PsF, indicating the theoretical values are physically plausible.