Finite range effects in trapped bosons systems

Abstract

We consider a system of two bosons trapped in a one-dimensional harmonic oscillator potential interacting by a finite-range gaussian potential. We study the dependence of its energy spectrum as a function of the strength and range of the interaction. The dynamic structure function associated with the monopolar excitation is computed and analysed by explicitly employing the eigenstates of the system. We also characterise the dynamic structure function with the energy sum rules. Finally, a comparison with the results provided by a contact interaction is also presented