Cluster model of roton excitations in liquid 4He

We have proposed a model of roton cluster excitations in liquid 4He based on a Schroedinger-type equation with a self-consistent confining potential. We have derived an equation for the number of atoms in the roton cluster, which can be treated as quantum 3D solitons depending on vibrational quantum numbers. It is shown that the smallest roton cluster is in the symmetric vibrational quantum state and consists of 13 helium atoms. We have also used a modified Born approximation to calculate the s-scattering length for helium atoms. This allows us to calculate all parameters of Landau's roton excitation spectrum, in agreement to high accuracy with experimental measurements from neutron scattering. It is also shown that the model leads to the saturation of the elementary excitation energy curve at twice the roton gap