Positron scattering and annihilation in hydrogen-like ions

Abstract

Diagrammatic many-body theory is used to calculate the scattering phase shifts, normalized annihilation rates $Z_{\mathrm{eff}}$ and annihilation gamma spectra for positron collisions with the hydrogen-like ions He${}^{+}$, Li${}^{2+}$, B${}^{4+}$ and F${}^{8+}$. Short-range electron-positron correlations and longer-range positron-ion correlations are accounted for by evaluating nonlocal corrections to the annihilation vertex and the exact positron self-energy. The numerical calculation of the many-body theory diagrams is performed using B-spline basis sets. To elucidate the rôle of the positron-ion repulsion, the annihilation rate is also estimated analytically in the Coulomb-Born approximation. It is found that the energy dependence and magnitude of $Z_{\mathrm{eff}}$ is governed by the Gamow factor that characterizes the suppression of the positron wave function near the ion. For all of the H-like ions, the correlation enhancement of the annihilation rate is found to be predominantly due to corrections to the annihilation vertex, while the corrections to the positron wave function play only a minor rôle. Results of the calculations for $s$, $p$ and d-wave incident positrons of energies up to the positronium formation threshold are presented. Where comparison is possible, our values are in excellent agreement with the results obtained using other, e.g., variational, methods. The annihilation vertex enhancement factors obtained in the present calculations are found to scale approximately as $1+(1.6+0.46\ell )/Z_i$, where $Z_i$ is the net charge of the ion and $\ell$ is the positron orbital angular momentum. Our results for positron annihilation in H-like ions provide insights into the problem of positron annihilation with core electrons in atoms and condensed matter systems, which have similar binding energies.

26 pages, 25 figures

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• Calculations of positronium-atom scattering using a spherical cavity
• Positron cooling and annihilation in noble gases
• Effective radius of ground- and excited-state positronium in collisions with hard walls
• Many-body theory calculations of positronic-bonded molecular dianions
• Probing positron cooling in noble gases via annihilation $\gamma$ spectra
• Two-photon Annihilation of Positrons with K-shell Electrons of H-like ions
• Ab initio QED treatment of the two-photon annihilation of positrons with bound electrons
• Many-body theory predictions of positron binding energies in five-membered heterocycles involving N, O, S and NH substituents