X-ray absorption and resonant x-ray emission spectra by electric quadrupole excitation in light rare-earth systems

Abstract

We have made precise theoretical calculations for both ${2p}_{3/2}\ensuremath{\rightarrow}4f$ x-ray absorption spectra and $3\stackrel{\ensuremath{\rightarrow}}{d}{2p}_{3/2}$ resonant x-ray emission spectra involving electric quadrupole excitations at the ${L}_{3}$ edge of light rare-earth elements from La to Eu. It is shown that the energy separation of a double-peak structure observed by x-ray absorption spectroscopy (XAS) does not agree with that determined from resonant x-ray emission spectroscopy (RXES), in contrast to recent experimental results by Bartolom\'e et al. The reason for this difference is that the energy separation in XAS is determined by the $4f\ensuremath{-}4f$ interaction only, while that in RXES is determined by both $4f$-$4f$ and $3d\ensuremath{-}4f$ interactions.