Self-Consistent Model of Roton Cluster Excitations in Liquid Helium II

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We have proposed a model of roton cluster excitations in liquid helium II based on a Schrödinger-type equation with a self-consistent confining potential. We have derived an equation for the number of atoms in roton excitations, which can be treated as quantum 3 D 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.