Positron annihilation spectra and core-electron enhancement factors

$\gamma$-spectra for positron annihilation with core and valence electrons in the noble gases are calculated using many-body theory (MBT). We show that proper inclusion of core annihilation is crucial to accurately describe the measured spectra [Phys. Rev. Lett. 79, 39 (1997)]. We use the MBT to calculate `exact' enhancement factors $\bar{\gamma}_{n\ell}$ for annihilation on individual $n\ell$ subshells. They parameterize the important effects of (non-local) short-range electron-positron correlations, including the non-perturbative process of virtual positronium formation. We show that they follow a simple and physically motivated scaling with the subshell ionization energy $I_{n\ell}$: $\bar{\gamma}_{n\ell}=1+\sqrt{A/I_{n\ell}}+(B/I_{n\ell})^{\beta}$, where $A$, $B$ and $\beta$ are positive constants. We suggest that this formula can be used with relatively simple independent-particle-approximation calculations to determine accurate core-annihilation spectra for atoms across the periodic table and in condensed matter.