γ-Ray Spectra and Enhancement Factors for Positron Annihilation with Core Electrons

Many-body theory is developed to calculate the $\gamma$ spectra for positron annihilation in noble-gas atoms. Inclusion of electron-positron correlation effects and core annihilation gives spectra in excellent agreement with experiment [K. Iwata et al., Phys. Rev. Lett. 79, 39 (1997)]. The calculated correlation enhancement factors ${\gamma }_{nl}$ for individual electron orbitals $nl$ are found to scale with the ionization energy $I_{nl}$ (in eV), as ${\gamma }_{nl}=1+\sqrt{A/I_{nl}}+(B/I_{nl}{)}^{\beta }$, where $A\approx 40\mathrm{eV}$, $B\approx 24\mathrm{eV}$, and $\beta \approx 2.3$.