What is a roton?

Many models of a roton in superfluid He-4 have been proposed over the years but no general consensus has been reached yet on the nature of such excitation. We present a number of new results relating to this question. We have developed an accurate representation of the wave function of such excitation which is based on a shadow function. This allows to treat the short range backflow effects in a non perturbative way. The theory gives results in quantitative agreement with experiment. Starting from such eigenstates of momentum we build wave-packets and study local quantities like density, momentum and vorticity. No model agrees with our results for the excitations in the roton minimum region because we End that the excitations have in a varying degree characters of single particle, of non quantized smoke ring and of collective excitation. We have also considered He-4 in two dimensions and we find similar results. In 2D we have studied also maxon and high frequency phonon wave-packets.