Influence of neutron scattering in the walls of a 3He spectrometer

It is demonstrated that neutron scattering in the stainless steel housing of a ³He spectrometer gives rise to spurious peaks in the spectra. Calculations show that the observed peak structure in the β-delayed neutron spectrum of ⁹Li is explained by this effect.Distortion of the response function for monoenergetic neutrons is discussed with regard to scattering by iron.     

Deep inelastic neutron scattering from liquid4He in aerogel glass

We report highQ inelastic neutron scattering studies of liquid⁴He confined inside porous aerogel glass in both the normal and superfluid phases. The scattering consists of a broad component, which we interpret as due to atoms localized on the surface of the glass, and a narrow component, which we interpret as due to the confined liquid inside the pores. The broad component is quite small, and no quantitative analysis is attempted. However, the narrow component due to the confined liquid is sufficiently large that information on the kinetic energy and condensate fraction may be obtained. The measurements are at large enoughQ (23 Å^–1) that the incoherent approximation may be used to directly extract the kinetic energy. Furthermore, the observed scattering is consistent with the impulse approximation, allowing information on both the momentum distribution and the condensate fraction to be extracted. The kinetic energy of the confined liquid is close to previous measurements of the kinetic energy in the bulk liquid. The condensate fraction of the confined liquid, which is estimated using a modification of a method due to Sears, is close to previous estimates of the condensate fraction in the bulk liquid.     

Comment on anomalous dispersion and scattering rates for multiphonon spontaneous decay in He II

We report on new measurements of the spontaneous decay threshold energyE _c for high-frequency phonon propagation in He II at saturated vapor pressure atT=0.1 K. Superconducting tin tunnel generators and aluminum tunnel detectors were used in this study. The measurements show that the mean free path becomes much larger than the propagation length of 1.1 mm for a value ofE _c =9.8±0.15 K. This agrees with the value originally reported (E _c =9.5±0.4 K) by Dynes and Narayanamurti using aluminum tunnel generators, but is shown to correspond to the point where the phase velocity equals the sound velocity, when the phonons become stable, as first proposed by Pitayevski and Levinson. Evidence forn-phonon decay at energies lower thanE _c is presented forn2 with a short mean free path (<0.3 mm) at the two-phonon decay energy. The measured values of the dispersion parameters are shown to agree closely with the spline fit to neutron data due to Donnelly, Donnelly, and Hills.     

Dynamics in He at 4 and 8 K from inelastic neutron scattering

From inelastic neutron scattering we determine the dynamic structure factor S(q, ) of fluid He at 4K (1 bar; 19.51 nm^–3) and 8K (18.7 bar; 19.46 nm^–3) as a function of frequency cofor wavenumbers 1 <q < 30 nm^–1. Forq 4 nm^–1, S(q, ) is given by the Rayleigh-Brillouin triplet of hydrodynamics. For q > 4 nm^–1 the central Rayleigh line vanishes and S(q, ) is given by the phonon Damped Harmonic Oscillator model similar as in superfluid helium. The phonons are overdamped for a small region nearq = 20 nm^–1. At 8K, helium starts to behave in a visco-elastic manner, similar as seen in classical fluids. We discuss a unifying model that connects the properties of superfluid helium to those of classical fluids.     

Energy spectrum,normal-fluid density,and specific heat of3He quasiparticles in dilute3He-He II mixtures

Several recently proposed forms of the³He quasiparticle energy spectrum in³He-He II mixtures are examined. Contributions of the quasiparticles to the normal-fluid density _n3 and the specific heatC ₃ are calculated by using various impurity spectra and compared. Influence of deviations from the Landau-Pomeranchuk quadratic dispersion relation on the momentum distribution of _n3 andC ₃ is discussed. The two examined theoretical results for the³He excitation spectrum overestimate the magnitude of deviations in the small-momentum region.     

Theory of heat transfer between phonons and quasiparticles in dilute solutions of3He in4He

A calculation of the heat transfer rate between phonons and quasiparticles in solutions of³He in⁴He is described. The phonon-quasiparticle interaction of Baym and Ebner is used, and two processes contributing to the heat transfer are considered. One process is phonon absorption and emission with the excess momentum distributed among the quasiparticles by quasiparticle-quasiparticle interactions. The other is quasielastic scattering of the phonons by quasiparticles. Numerical results are presented for 0.1% and 0.5% solutions. The calculated heat transfer rate for the 0.1% solution is in agreement with the one reported experiment atT40 mK, but is too small at higher temperatures (50T60 mK).     

4He films on graphite studied by neutron scattering

The properties of ⁴He films adsorbed on graphite have been studied by neutron scattering. In particular excitations of the commensurate phase of the monolayer are discussed. The first two adsorbed layers are solid and the next ones stay liquid. At the boundaries of the superfluid film excitations could be studied. Also the phonons, maxon and rotons of the film are investigated. An explanation of the lower density of the very thin films compared to bulk ⁴He is given.Presented by H. J. Lauter.     

Sum rules for a binary solution and effective interactions between3He quasiparticles in superfluid4He

Sum rules are derived for dynamic structure factors for a binary solution and applied to the Woo-Tan-Massey theory of ³ He- ⁴ He solutions. We demonstrate that in the long-wavelength region the effective ³ He quasiparticle interactionV _k contains no lineark dependence. In other words, $$V_k \to A + Bk^2 {\text{ }}as k \to 0$$ This result is exact, and requires no empirical information. It is consistent with expressions ofV _k assumed by Eckstein, Eckstein, Kuper, and Ron, and by Ebner, based on fitting experimental data such as osmotic pressure measurements.     

Theory of neutron scattering from the two-roton,two-maxon and maxon-roton states in superfluid4He

In 1970, Ruvalds and Zawadowski (RZ) outlined a microscopic theory of the two-roton pair excitation spectrum in superfluid⁴He. They pointed out that because of a Base condensate-induced coupling into the density fluctuation spectrum, these pair excitations show up in inelastic neutron data for S(Q, ) as high energy multiparticle scattering above the maxon-roton quasiparticle peak. Stimulated by recent high-resolution neutron data from ILL, we have carried out an extensive study of the single-particle ₁(Q, ) and the two-particle ₂(Q, ) spectral densities within the RZ scenario, over a wide range of wavevectors (1 Q 3 Å^–1), frequencies and temperatures. We extend the original RZ analysis (which concentrated on the two-roton spectrum) to include the multiparticle structure associated with the maxonroton and maxon-maxon spectra and present numerical results for both attractive and repulsive quasiparticle interactions. We also point out that the microscopic theory of S(Q, ) in a Bose-condensed fluid shows that it involves a weighted sum of both ₁(Q, )and ₂(Q, ). As a result, multiparticle structure exhibited by S(Q, ) is not easily related to theoretical results for ₁(Q, ) and ₂(Q, ). Previous attempts in the literature to fit neutron data for S(Q, ) to either ₁(Q, ) or ₂(Q, ) would not appear to have much quantitative basis, especially in the two-roton frequency region 2_R.     

Experimental studies of the excitation spectrum of3He-4He mixtures using neutron inelastic scattering

Neutron inelastic scattering techniques have been used to study the excitation spectrum of mixtures containing 6%, 12%, and 25% of³He in⁴He at 0.75 K. The 6% mixture has also been investigated at temperatures of 0.6, 1.0, and 1.5 K. The measurements have been made in the wave-vector transfer rangeQ=0.8–2.3 Å^–1. The energy spectra observed contain two principal features, which are interpreted as scattering from (a) phonon-roton excitations arising from the⁴He, and (b) quasiparticle-quasihole excitations arising from the³He. In the dilute³He-⁴He mixture, our results indicate a³He particle-hole continuum which deviates from the quadratic form, proposed by Landau and Pomeranchuk, and which lies below the⁴He phonon-roton dispersion curve. However, we are unable to say whether or not the continuum exhibits a minimum as a function of energy, as has recently been proposed by several authors, because we were unable to resolve the scattering from the particle-hole continuum forQ1.7 Å^–1. In this region ofQ space the energy spectra are dominated by the roton excitations. We have also determined the shifts in energy and increases in linewidth of the phonon-roton excitations relative to those of pure⁴He and compared these measurements to several theoretical predictions.Work performed under a grant from the Science Research Council of Great Britain.     

Inelastic neutron scattering from vortex lattice in type-II superconductors. II. The London model

The inelastic neutron scattering from the vortex lattice in type-II superconductors is considered. Use is made of the London model to describe the vibration of the vortex lattice. We find that the differential cross section has sharp peaks besides the Bragg peaks when the transferred momentumq approaches the reciprocal lattice vectorG. These peaks are due to excitation of the vibrational modes and diverge as ¦q –G¦^–2. We also calculate the Debye-Waller factor, which is extremely small.     

Theoretical analysis of neutron scattering spectra of4He films on graphite

We compare microscopic calculations of the dynamic structure function of helium films adsorbed to a graphite substrate with neutron scattering data. Starting from a generalized Feynman theory of collective excitations, we include successively, three-phonon interactions, self-energy corrections, and experimental broadening and thereby improve the agreement between theoretical predictions and experiments. The inclusion of three-phonon vertices allows high-lying excited states to decay into lesser energetic ones and thus leads to a natural linewidth. It is shown that the theoretical linewidth of the excitations is typically smaller than the experimental resolution, and that much structure of the spectrum in the neutron scattering data is obscured under a broad plateau between the ripplon and the phonon excitations. This analysis leaves little doubt of the existence of layer-phonons and that the observed shoulder in the dynamic structure function, near the roton minimum, is actually a 2D roton propagating in the inner-most liquid layer.     

Raman scattering from He II near the two-roton threshold. II. Comparison with experiments

Based on the new formalism which is developed in the preceding paper and is free from the difficulty with which the conventional theories could not cope, we shall examine experimental Roman spectra of He II near the two-roton threshold. The intensity spectrum is determined by the generalized density of states of interacting rotons (GDOSIR). For the form factor of a roton-pair creation from the atomic density fluctuation which appears in GDOSIR, a power law in total energy is assumed. After investigating what types of characteristic structures and how they appear in GDOSIR as , the power of the form factor, and g, the coupling constant, change, we shall perform line shape analysis between theory and experiment by varying g and _R , the roton-minimum energy, by including the instrumental width. It is found that in the margin 0 1/2 well reproduces experiments at SVP, 5, 10, 15 and 20 kg/cm², the margin including that set by the direct roton-roton scattering experiment, namely 1/2. Further it also includes the conventional theories as a special case ( = 0), thereby solving the puzzle that the theories in error could have predicted the Roman feature so successfully. In addition the values of the coupling constant obtained by the Roman data here are in remarkable correspondence with those determined by the roton-roton scattering, thereby suggesting a possibility for the form of the interaction with 1/2 to lead to a unified understanding of roton dynamics. Further the results for _R are not only in close agreement with each other for in the Roman margin but also with the neutron results, from SVP to 20 kg/cm². Therefore the Roman data alone can afford reliable information on the fundamental parameter of elementary excitations in He II. The results will also be presented for the bound-state energy and the relative peak intensity as functions of pressure and suggestions for experiment are given both for Raman and direct roton-roton scattering which may help narrowing the margin for further.     

Neutron scattering from liquid3He at intermediate to large wavevectors

Neutron inelastic scattering experiments have been performed on liquid³He at saturated vapour pressure and T = 1.4 K covering a wide range of energy and momentum transfers (9 Q 20 Å^–1). Allowing for the very strong³He neutron absorption, the data is of excellent quality and it has been analysed to extract information on the scattering function widths, peak positions and single particle kinetic energies. It is found that there are no width oscillations with momentum transfer and that the average atomic kinetic energy is approximately 20% lower than theoretical predictions, in agreement with previous neutron scattering results. A new method of analysis aimed at extracting both the atomic momentum distribution and final state effects is also presented and the results discussed in the light of current theory.     

Neutron scattering from liquid 4He

In this lecture the study of excitations in quantum fluids and solids using neutrons is briefly introduced. The remainder focuses on liquid ⁴ He, giving a brief historical sketch of ideas on phonons and rotons, a survey of some recent neutron scattering data particularly on the temperature dependence of S(Q, ) and a new interpretation of phonons and rotons in superfluid ⁴He.Now at Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716.