Theory of a Narrow roton Absorption Line in the Spectrum of a Disk-Shaped SHF Resonator

TL;DR

This paper presents a theoretical analysis of the narrow roton absorption line in superfluid helium, linking it to the creation of circular rotons at specific frequencies where the group velocity is zero, and matches experimental linewidths.

Contribution

It introduces a new theoretical framework connecting c-roton creation probabilities to the observed absorption spectrum in helium, explaining the narrow line width and Stark effect.

Findings

Probability peaks at roton and maxon frequencies

Calculated line width agrees with experiments

Proposed interpretation of Stark effect

Abstract

We calculate the probability of the birth of a circular phonon (c-phonon) in He II by a c-photon of the resonator. It is shown that this probability has sharp maxima at frequencies, where the effective group velocity of the c-phonon is equal to zero; the density of states of c-phonons strongly grows at such frequencies. For He II, these frequencies correspond to a roton and a maxon. From the probability of the c-roton birth, we calculate the roto line width which is found to approximately agree with the experimental one. We conclude that the roton line observed in the super-high-frequency (SHF) absorption spectrum of helium is related to the birth of c-rotons. A possible interpretation of the Stark effect observed for the roton line is also proposed.