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

TL;DR

This paper presents a self-consistent quantum model of roton cluster excitations in liquid helium II, accurately predicting their properties and spectrum in agreement with experimental data.

Contribution

It introduces a novel Schrödinger-type model with a self-consistent potential to describe roton clusters as quantum solitons, identifying the smallest cluster size and calculating excitation parameters.

Findings

Smallest roton cluster has 13 helium atoms.

Model accurately reproduces experimental roton spectrum.

Uses modified Born approximation for scattering length calculation.

Abstract

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.