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Core excitation of gaseous HCl to the dissociative σ* state leads to a deexcitation spectrum with two qualitatively different contributions—a broad molecular background and narrow atomic lines. The experiment demonstrates that the ratio of integrated intensities from these two contributions depends crucially on the excitation frequency; the molecular background is enhanced with increased detuning of the photon frequency. This is discussed in a time-dependent model, using the concept of an effective duration time for the resonant x-ray scattering process.