Dynamic structure function of two interacting atoms in 1D

We consider two atoms trapped in a one-dimensional harmonic-oscillator potential interacting through a contact interaction. We study the response of the system against a monopolar perturbation during the transition from the non-interacting to the strongly interacting Tonks-Girardeau regime, as the interaction is varied from zero to infinitely large repulsive values. The response of the system is then characterized by the moments of the dynamic structure function which are explicitly calculated from the dynamic structure function and by means of sum rules.