Extreme narrowing, or collapse, of electron-vibrational bands is predi
cted as a new phenomenon in resonant radiative and nonradiative x-ray
scattering (RXS) spectra. It is shown that in the inelastic scattering
case, that is, when the potential surfaces of ground and final slates
are different, a considerable narrowing of the vibronic RXS band resu
lts from detuning the excitation Photon frequency omega away from the
absorption resonance. By fine tuning the frequency, this may under spe
cial circumstances also occur in the region of strong photoabsorption.
In the case of elastic Rayleigh scattering, that is, when the potenti
al surfaces of ground and final states are identical, the narrowing re
sults in a total collapse to a single resonance by detuning the freque
ncy. The theory predicts how the differencies in vibrational structure
of resonant and nonresonant photoemission spectra depends on the exci
tation frequency. The effect of frequency detuning on complex spectral
multilevel structures due to multiplet: and spin-orbit splittings is
discussed qualitatively. It is shown that the notion of: duration time
for the x-ray scattering process plays a crucial role in the understa
nding of RXS spectra.