a
an X-ray photon with energy ω (wave vector k2 ) and polarization λ2 (polarization vector ek2 λ2 ) is emitted due to the electron-photon interaction in the material. The RIXS spectrum is represented by the coherent second order optical formula in the following form [4]:
λ λ j|T2 2 |i i|T1 1 |g Eg + Ei + iΓi 2
F (, ω) =
j i
×
Γj /π , (Ej + ω Eg )2 + Γj2
(1)
where |g , |i , and |j are initial, intermediate, and nal states of the material system, Eg , Ei , and Ej are their energies, Γi and Γj are the core hole lifetime broadenings λ in the intermediate and nal states, respectively, and T1 1 λ2 and T2 represent optical transition operators. In the soft X-ray region, Tiλi (i = 1, 2) is given by the electric dipole (ED) transition (2) Tiλi ∝ eki λi r, but in the hard X-ray region, the electric quadrupole (EQ) transition (3) Tiλi ∝ i(eki λi r)(ki r) plays sometimes an important role, in addition to the ED transition. RIXS is divided into two categories depending on the electronic levels participating the transition of X-ray emission. In the rst category, the transition occurs from the valence state to the core state, and we have no core hole left in the nal state of RIXS. Typical examples are the 3d
e-mail: kotani@spring8.or.jp
4
The European Physical Journal B

上一页下一页