X-RAY RESONANT SCATTERING INVOLVING DISSOCIATIVE STATES

Time-independent and time-dependent theory of radiative and nonradiati ve resonant x-ray scattering (RXS) involving dissociative molecular st ates is presented. A strong space correlation between excitation and d ecay is found. This space correlation has a characteristic length equa l to the path propagated during the lifetime of the core-excited state . It is shown that for internuclear distances beyond this characterist ic length the RXS signal grows exponentially small. Additional untrivi al properties of the RXS cross section for continuum-bound or bound-co ntinuum decay transitions are predicted. Selection rules operate for c ontinuum-bound transitions if the slope of the continuum potential is small; only transitions to vibrational states with odd quantum numbers are allowed in the harmonic approximation. We show that the main cont ribution to the RXS cross section is obtained at the dissociative limi t if the lifetime of the core-excited state is sufficiently long. Emis sion transitions in the molecular region form the wing of the dissocia tive resonances. The spectral shape of this wing is in general oscilla tory. The cross sections for both type of transitions are proportional to the square of the wave function of the vibrational state involved in the RXS process. The spectral shape copies the space distribution o f the square of this wave function, and so, indirectly, maps the shape of the corresponding molecular potential. The zeros of the RXS cross section caused by the nodes of the vibrational wave function can be us ed to assign vibrational states. The spectral width of the RXS resonan ces involving dissociative molecular states strongly depends on the fe atures of the interatomic potentials. In the general case the spectral shapes consist of a narrow part and a broad background, and will be d etermined by different limiting factors, such as the spectral photon s hape, the Franck-Condon vibrational distribution, and the lifetime wid th for the core-excited states. The role of these limiting factors dep ends on the different combinations of dissociative and bound potential s for the ground state, the core-excited state, and the optically exci ted state.