Convergence and Momentum Dependence of the Correlation Correction to the Amplitude of Positron Annihilation on Atoms

Positron annihilation rates in solids and in gases are strongly affected by electron-positron correlations. Observed rates exceed those evaluated in the independent-particle approximation many times. In solids this effect is usually taken into account through an enhancement factor (EF), which depends on the electron density [1]. Correlations also affect the momentum distribution of the annihilating electron-positron pairs, which determines the shape of the annihilation gamma spectrum. This effect is beyond the EF approximation and is often neglected [1]. Using a many-body theory framework [2] we analyse the convergence of the 1st-order correction to the annihilation amplitude with the orbital angular momentum $l$ of the intermediate electron and positron states. We find that these contributions converge as $(l+1/2)^{-2}$, and have a distinctly different momentum dependence compared with the 0th-order amplitude, narrowing the annihilation spectra. \begin{enumerate}\setlength{\itemsep}{-3pt}\setlength{\itemindent}{-12pt} \item M. Alatalo et al., Phys. Rev. B {\bf 54}, 2397 (1996). \item G. F. Gribakin and J. Ludlow, J. Phys. B {\bf 35}, 339 (2002); L. Dunlop and G. F. Gribakin, {\em ibid.} {\bf 39}, 1647 (2006). \end{enumerate}