Positron scattering and annihilation in hydrogenlike ions

Abstract

Diagrammatic many-body theory is used to calculate the scattering phase shifts, normalized annihilation rates Z eff , and annihilation γ spectra for positron collisions with the hydrogenlike 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 role 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 eff are 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 role. 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)/Z i , where Z i is the net charge of the ion and 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.

Positron scattering and annihilation on noble-gas atoms

“…4 ) leads to terms quadratic in k in the lowenergy expansions (27) and (28). As a result, the s-wave phase shift reaches a maximum and then fall off with increasing k, passing through zero (Ramsaur-Townsend effect) to negative phase shifts at higher k. The higherorder contributions to the correlation potential (Σ In Fig.…”

“…The diagrams in Fig. 4 provide a complete description of Z eff for one-electron systems, such as hydrogen and hydrogenlike ions [28]. Algebraic expressions for these diagrams can be found in [17].…”

“…The corresponding eigenvectors are used to construct the positron and electron wave functions. This provides effectively complete sets of positron and electron basis states covering both bound states and the positive-energy continuum [17,28]. These states are then used to calculate the Coulomb and δ-function matrix elements (A1) and (A3), and to evaluate the many-body diagrams by summing over intermediate electron and positron states.…”

“…The complete evaluation of the ladder-diagram series was implemented in the positron-hydrogen study [17] which used B-spline basis sets to discretize the positron and electron continua. This approach has since been applied to positron binding to the halogen negative ions [27], to positron scattering and annihilation on hydrogen-like ions [28], to the calculation of gamma-ray spectra for positron annihilation on the core and valence electrons in atoms [9,29] and in molecules [30]. Another many-body theory technique that allows one to sum the dominant series of diagrams to all orders is the linearized coupled-cluster method which was used to calculate positron-atom bound states for a large number of atoms [31,32].…”

Transport theory for low-energy positron thermalization and annihilation in helium

“…This means that the errors in using an energy-independent enhancement factor should not be too large [31,32]. There have been a number of investigations that have shown that a single multiplicative factor (for each L) can adequately represent the magnitude and energy dependence over the energy range below the first excitation threshold [15,[33][34][35][36].…”