Phonon relaxation in soft-x-ray emission of insulators

Phonon-relaxation effects on the ${\mathit{L}}_{2,3}$ soft-x-ray emission of MgO, ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$, and ${\mathrm{SiO}}_2$ are measured by comparing soft-x-ray emission spectra to photoelectron spectra. The observed shifts of the soft-x-ray emission spectra relative to the photoelectron spectra are identified as Stokes shifts and are described in terms of partial phonon relaxation. The observed Stokes shifts are 0.5, 0.9, and 1.2 eV for MgO, ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$, and ${\mathrm{SiO}}_2$, respectively. Similar measurements on Mg, Al, and Si show no detectable Stokes shift within the experimental uncertainty of 0.2 eV. The larger Stokes shifts observed in the oxides are due to the longer core-hole lifetime, the faster phonon relaxation, and larger phonon relaxation energy in the oxides.