Core-level spectra from bilayer graphene

We derive core-level spectra for doped free-standing bilayer graphene. Numerical results are presented for all nine combinations of the doping concentrations ${10}^{12}{\mathrm{c}\mathrm{m}}^{-2}$, ${10}^{13}{\mathrm{c}\mathrm{m}}^{-2}$, and ${10}^{14}{\mathrm{c}\mathrm{m}}^{-2}$ in the two graphene sheets and we compare the results to the reference spectra for monolayer graphene. We furthermore discuss the spectrum of single-particle inter-band and intra-band excitations in the $\omega q$-plane, and show how the dispersion curves of the collective modes are modified in the bilayer system.