Localization of particles in harmonic confinement: Effect of the interparticle interaction

We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation and vibrational modes of localized particles. We show that for a small number of particles the localization is similar for bosons and fermions. Moreover, independent of the range of the interaction the quantum mechanical spectrum at large angular momenta can be understood by vibrational modes of localized particles.