  We have proposed a model of roton cluster excitations in liquid helium~II
based on a Schr\"odinger-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 $3{\rm D}$ 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.
