  We present a novel method for the analysis of the Doppler broadened spectrum
of gamma photons emitted following the annihilation of surface trapped
positrons with the electrons of bilayer graphene supported on polycrystalline
Cu substrate. The method relies on the measurement of the energy of the Doppler
shifted annihilation gamma photons in coincidence with the Auger electrons
emitted following the decay of the contemporaneously produced annihilation
induced hole. Through the selection of annihilation gamma corresponding to O
KVV (adsorbed O), C KVV (graphene), and Cu MVV (substrate) Auger transitions,
we have decomposed the annihilation gamma spectrum into spectral components
representing annihilation of the positron with 1s electrons of C and O and 3p
electrons of Cu. These experimentally derived Doppler broadened gamma line
shapes agrees well with the theoretically derived model line shapes
demonstrating the ability of our method to resolve a complex Doppler line
shapes into its veiled electronic level constituents which has, heretofore,
only been achieved through theoretical analysis. We have also demonstrated the
reversibility of the analysis method by decomposing the Auger spectra into
regions which corresponds to the annihilation gamma photons with a large
Doppler shift or to Auger spectra correlated with annihilation gamma photons
with a small doppler shift. The reverse analysis provides additional proof that
Auger transitions following deep valence annihilations result in the emission
of low energy electrons.
