X-ray resonant scattering involving dissociative states

Time-independent and time-dependent theory of radiative and nonradiative resonant x-ray scattering (RXS) involving dissociative molecular states is presented. A strong space correlation between excitation and decay is found. This space correlation has a characteristic length equal to the path propagated during the lifetime of the core-excited state. It is shown that for internuclear distances beyond this characteristic length the RXS signal grows exponentially small. Additional untrivial properties of the RXS cross section for continuum-bound or bound-continuum decay transitions are predicted. Selection rules operate for continuum-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 contribution to the RXS cross section is obtained at the dissociative limit if the lifetime of the core-excited state is sufficiently long. Emission transitions in the molecular region form the wing of the dissociative resonances. The spectral shape of this wing is in general oscillatory. 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 of 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 used to assign vibrational states. The spectral width of the RXS resonances involving dissociative molecular states strongly depends on the features of the interatomic potentials. In the general case the spectral shapes consist of a narrow part and a broad background, and will be determined by different limiting factors, such as the spectral photon shape, the Franck-Condon vibrational distribution, and the lifetime width for the core-excited states. The role of these limiting factors depends on the different combinations of dissociative and bound potentials for the ground state, the core-excited state, and the optically excited state.