Many-body theory is developed to calculate the γ 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 γnl for individual electron orbitals nl are found to scale with the ionization energy Inl (in eV), as γnl=1+ √A/Inl+(B/Inl)β, where A≈40 eV, B≈24 eV, and β≈2.3.