Velocity dependent interactions and a new sum rule in bcc He

TL;DR

This paper explains a new optic-like mode in bcc helium through a model of correlated atomic zero-point motion, showing that velocity-dependent interactions modify the sum rule for phonons, aligning theory with recent experiments.

Contribution

It introduces a velocity-dependent interaction model for correlated dipoles in bcc helium, providing a theoretical explanation for observed phonon anomalies and new optic-like modes.

Findings

Velocity-dependent interactions modify the phonon sum rule.

The model aligns well with recent neutron scattering data.

New optic-like modes are explained by dipolar correlations.

Abstract

Recent neutron scattering experiments [PRL,{\bf 88},p.195301 (2002)] on solid $^4$He, discovered a new optic-like mode in the bcc phase. This excitation was predicted by a recently proposed model that describes the correlated atomic zero-point motion in bcc Helium in terms of dynamic electric dipole moments. Modulations of the relative phase of these dipoles between different atoms describes the anomalously soft T$_1$(110) phonon and two new optic-like modes, one of which was recently found in the neutron scattering experiments. In this work we show that the correlated dipolar interactions can be written as a velocity dependent interaction. This then results in a modified f-sum rule for the T$_1$(110) phonon, in good agreement with the recent experimental data.