Roton Linewidth Research Articles

On the Nature of a Narrow Roton Absorption Line in the Spectrum of a Disk-shaped SHF Resonator

We calculate the probability of the creation 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 theprobability of the c-roton creation, we calculate the roton 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 creation of c-rotons. A possible interpretation of the Stark effect observed for the roton line is also proposed.

Theory of a supernarrow roton absorption line in the spectrum of a disk-shaped microwave resonator

We calculate the probability of the creation 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. For He II, these frequencies correspond to a roton and a maxon. From the probability of the c-roton birth, we calculate the roton linewidth which is found to approximately agree with the experimental one.

Static Structure Factor and Static Response Function of Superfluid Helium 4: a Comparative Analysis

Extensive neutron scattering data on liquid helium 4 are available, and have been analyzed to give a number of physical quantities, e.g. static structure factor S(q), excitation energy, and roton linewidth. X-rays also give access to S(q) .H ow- ever, a comprehensive comparison between experimental data and theoretical results, including their dependence on pressure, is still lacking. The static response function χ(q) has been particularly overlooked, despite its fundamental role in theories of inhomogeneous helium. We present here a critical review about the strength of the main peaks of S(q) and χ(q). We include in the comparison the analysis of unpub- lished neutron data and new Monte-Carlo calculations of χ(q). We find a significant discrepancy between experiments, and suggest corrections which account for some of the differences. We give recommendations for the best values to use for S(q) and χ(q).

Implementation of a zero-field spin-echo option at the three-axis spectrometer IN3 (ILL, Grenoble) and first application for measurements of phonon line widths in superfluid 4He

We report on a new zero-field spin-echo spectrometer (ZETA), installed at the thermal three-axis spectrometer IN3 at ILL, Grenoble. In this technique the two long precession solenoids from neutron spin echo are replaced by two pairs of magnetic resonance coils in a zero-field region. This allows easy adaptation of tilted field geometries, necessary for measurements of phonon line widths with μeV energy resolution. First test measurements of the roton line width and energy shift as well as line width of the low- Q phonon and in the “region beyond the roton” in superfluid 4He are described. The results are in agreement with the literature and show the good operation of ZETA. The implementation of ZETA at the high-flux three-axis spectrometer IN20, foreseen in the near future, will increase the count rate by typically one order of magnitude.

Surface excitations in thin helium films on silica aerogel

First measurements are reported on pure surface excitations in thin superfluid 4He films on silica aerogel. The ripplon dispersion curve is found to be the same for helium on graphite and silica aerogel substrates. However, the layered roton line width in helium films on aerogel shows a pronounced broadening with respect to that found in helium films on graphite.

High-resolution neutron-scattering study of the roton in confined superfluid4He

We report high-resolution neutron inelastic-scattering measurements of the roton energy and linewidth of superfluid ${}^{4}\mathrm{He}$ confined in 95% porosity aerogel glass for temperatures $0.08<T<1.2\mathrm{K}.$ The confined roton line shape can be described well by a damped harmonic oscillator (DHO) function, as in the bulk. The energy of the confined roton is essentially temperature independent over this temperature range. The roton linewidth does not exhibit a finite width of greater than 0.1 \ensuremath{\mu}eV at low temperature. This result is in contrast to previous measurements carried out at lower resolution.

High-Resolution Measurements of Rotons in 4He.

We have measured the temperature dependence of the roton line shape (energy and width) using neutron backscattering. An energy resolution of less than 1 μeV was obtained, allowing a determination of the roton linewidth down toT=0.8 K. These results constitute a significant improvement on the previous best determination and extend the measured range of roton linewidth and energy shift by an order of magnitude. The temperature dependence of the measured linewidths is found to be in excellent agreement with calculations based on the 4-phonon decay process. The roton energy, however, is found to vary significantly more slowly with temperature than expected from the same theory. The origin of this discrepancy is not yet understood.

High-resolution measurements of rotons in4He

We have measured the temperature dependence of the roton line shape (energy and width) using neutron backscattering. An energy resolution of less than 1 μeV was obtained, allowing a determination of the roton linewidth down toT=0.8 K. These results constitute a significant improvement on the previous best determination and extend the measured range of roton linewidth and energy shift by an order of magnitude. The temperature dependence of the measured linewidths is found to be in excellent agreement with calculations based on the 4-phonon decay process. The roton energy, however, is found to vary significantly more slowly with temperature than expected from the same theory. The origin of this discrepancy is not yet understood.

Study of rotons in superfluid4He by Raman scattering

There is a long standing disagreement between neutron and Raman scattering from rotons in superfluid4He near Tλ. In neutron scattering the linewidth becomes very large and the roton signal seems to disappear at Tλ. A substantially smaller linewidth is observed with Raman scattering and the roton signal is present even at Tλ. We have interpreted this difference (J. Low Temp. Phys. 93, 879 (1993)) as due to a modulation of the roton energy by a fluctuating local superfluid velocity due to proliferation of vorticity as Tλ is approached. This gives rise to an extra contribution to the roton linewidth in neutron scattering but not in Raman scattering in which two rotons with almost opposite momenta are excited. We propose a test of this explanation with evanescent field Raman scattering. It has been suggested (A. Kuklov, A. Bulatov and J.L. Birman, Phys. Rev. Lett. 72, 3855 (1994)) that in such a measurement the scattering by a single roton should be measurable. In this case the presence of a fluctuating local superfluid velocity should show up as in neutron scattering and corroborate our proposal.

Relaxation times of k=0 rotons in pure parahydrogen crystals and roton scattering by orthohydrogen impurities.

A high-resolution Raman investigation is presented of the linewidth of the $J=2$ rotons in solid $p\ensuremath{-}{\mathrm{H}}_{2}$ measured by means of a tandem interferometer-monochromator. The magnitude of the linewidths (\ensuremath{\cong} 0.08 ${\mathrm{cm}}^{\ensuremath{-}1}$) at extremely low $o\ensuremath{-}{\mathrm{H}}_{2}$ concentration is in good agreement with a recent microscopic calculation, but a variation of the experimental widths by a factor of 2 was observed for different $|{M}_{J}|$. The dependence of the roton linewidth on the concentration of $o\ensuremath{-}{\mathrm{H}}_{2}$ impurities is found to be linear, indicating that the $o\ensuremath{-}{\mathrm{H}}_{2}$ act as noninteracting random scattering centers.

Theory of excitations inHe3-He4mixtures

The elementary excitation spectrum of liquid $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixture is calculated from first principles. The boson quasiparticles are treated by a density-variable formalism, and their interaction with the $^{3}\mathrm{He}$ excitations is explicitly derived. Using the liquid-structure factor for pure $^{4}\mathrm{He}$, we calculate the $^{3}\mathrm{He}$ excitation dispersion over a wide momentum range; renormalization of the phonon-roton (boson) spectrum due to the presence of $^{3}\mathrm{He}$; lifetime of the roton excitations as a function of momentum and $^{3}\mathrm{He}$ concentration; and we estimate the possibility of resonances formed by rotons and $^{3}\mathrm{He}$ quasiparticles. The results are in contrast to previous speculations regarding the existence of a $^{3}\mathrm{He}$ roton excitation. However, our calculations provide good agreement with available experimental data. The sensitivity of the roton linewidth to the $^{3}\mathrm{He}$ quasiparticle interactions indicates that future light and neutron scattering experiments may provide insight into the microscopic nature of the interatomic helium potential.

Scattering of Quasiparticles inHe3-He4Mixtures

Considering the elementary excitation spectrum of ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures to be of the form proposed by Landau and Pomeranchuk, we calculate the scattering cross section for roton and ${\mathrm{He}}^{3}$ quasiparticle collisions, taking final-state interactions into account. Our theory demonstrates the importance of final-state interactions in renormalizing the roton energy and lifetime. Previous theories based on the Born approximation are shown to give unreliable results for the change of the energy and lifetime for rotons in dilute ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures owing to roton-${\mathrm{He}}^{3}$ scattering. We obtain upper bounds on the changes in the energy and lifetime of a roton as a function of the roton-${\mathrm{He}}^{3}$ coupling strength, using a simplified model for the coupling. These bounds give an insignificant change of the roton energy with the ${\mathrm{He}}^{3}$ concentration and thus explain recent neutron-scattering and Raman data on the mixtures. Effects of level repulsion between rotons and the ${\mathrm{He}}^{3}$ quasiparticle-hole continuum are calculated, and estimated to be small on the basis of recent Raman data. However, decay of a roton into a ${\mathrm{He}}^{3}$ quasiparticle-hole pair may give rise to an interesting concentration dependence of the roton linewidth. Further experimental studies of the mixtures are suggested, which may check the detailed predictions of the theory and provide insight into the momentum dependence of the coupling parameters. The present analysis represents an essential link between microscopic theories of the quasiparticle coupling and related experiments on dilute ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures.

Emission and absorption of phonons by rotons in superfluid helium

The roton spectrum of superfluid helium apparently has a threshold for phonon emission and absorption processes. We calculate the roton spectral function near the threshold for phonon emission in order to determine the effect of the phonon emission process on the roton line width. The spectral function develops a line shape anomaly due to a strong energy dependence of the roton self-energy. The line width is generally smaller than the sum of the phonon emission rate and the roton-roton collision rate. We also derive the ultrasonic attenuation due to the absorption of phonons by thermal rotons above the threshold.

Theory of the Roton Lifetime in Superfluid Helium

We have extended the theory of the roton lifetime to include two-roton resonances in the final-state interaction. When resonances are taken into account, the final density of states ${\ensuremath{\rho}}_{2}$ exhibits a complicated energy dependence and bears little resemblance to the noninteracting roton density ${\ensuremath{\rho}}_{2}^{(0)}$ used in the Landau-Khalatnikov theory. Using a point-interaction model for the roton coupling and including only direct roton-roton scattering, we obtain a single-roton linewidth which is consistent with the upper bound given by other authors; we then obtain a linewidth for the two-roton resonance which is smaller than the experimental value. In contrast to previous work, we have proceeded to include roton hydridization in the lifetime theory. The effect of hybridization is twofold: (a) The final density of states ${\ensuremath{\rho}}_{2}$ is markedly altered, and (b) the hybridization opens new scattering channels involving a single quasiparticle in the final state. Although the net effect of mechanism (a) on the roton lifetime seems to be small, the additional scattering (b) gives a non-negligible contribution. Furthermore, we discuss the importance of self-consistency and roton scattering in nonzero angular momentum channels. Our theory predicts an unusual pressure dependence for the roton linewidth which may be checked experimentally. We conclude that further experiments, such as light and neutron scattering, are needed to resolve the strength of the various contributions to the linewidth and thereby provide a truly quantitative analysis of the roton lifetime.