Vibrational broadening of x-ray emission spectra: A first-principles study on diamond

We present a general theoretical scheme that allows an accurate account of the vibrational broadening of core-level line shapes in crystals, using state-of-the-art electronic-structure techniques within the Franck-Condon approximation. Electronic and vibrational degrees of freedom are consistently treated using ab initio density-functional theory. Neglecting the core-hole lifetime, anharmonic effects are treated within a self-consistent phonon approach. Finite core-hole lifetime effects are simulated by an independent-boson model, which, however, we have been able to apply only when lattice distortions are treated in the harmonic approximation. We apply the theory to the diamond Is core-level emission spectrum. In the limit of infinite core-hole lifetime, we find that (i) the Stokes shift is about 3 eV, (ii) the harmonic approximation overestimates the Stokes shift by similar to 1.4 eV, and (iii) phonon broadening is about 2 eV. A comparison with experiment reveals that the phonon bandwidth is comparable to the core-hole lifetime, which we estimate Gamma approximate to 110 meV.