Excitations in Two-Dimensional 4He

We present the study of the ground state and of the low-energy excited states of liquid⁴He in two dimensions (2D) within the Variational Monte Carlo method. As trial wave function a shadow wave function is used. The energies of the maxon and of the roton are close together at the equilibrium density ρ_eq due to the low value of ρ_eq in 2D but at higher densities a well developed roton minimum is present. The short range backflow effects are stronger in 2D than in 3D and close to freezing the roton energy is about 5 K. This value is close to the lowest branch of excitations found from inelastic neutron scattering from thin⁴He film on graphite and interpreted as due to layer rotons. Some strong similarities between the 2D and 3D case are present: the maxon energy close to freezing is about twice the roton energy, the relative strength of the single roton peak in the dynamical structure factor is essentially density independent and very close in value to the 3D case, there is a similar shift between the wave vectors of the roton and of the position of the main maximum of the static structure factor.     

Excitations of inhomogeneous liquid He4: A density functional study

Excitations of the free surface, films and bounded channels of liquid⁴He are investigated with a non-local density functional theory at zero temperature in the Feynman approximation. The nature of the various branches is discussed. At the free surface, for large momentum (k2 Å^–1), a hybridization occurs between ripplons and bulk rotons. For low momentum, the ripplon dispersion relation in thick films and the third sound mode in thin films are recovered, including the expected oscillations of the third sound velocity as a function of film thickness due to the layering of the film close to the substrate. Low energy 2-dimensional (2D) rotons confined at the liquid-wall interface are found on most substrates, except on the weakest binding surfaces such as Cs, for which we consider a channel geometry. In thin films, non trivial coverage dependence of the heat capacity may result from the interplay between the contribution of the low momentum part of the spectrum, characterized by the third sound velocity oscillations, and that of the large momentum part, dominated by the 2D rotons.Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS.     

Excitations of Liquid 4He in Disorder

We discuss the effect of disorder and confinement on the excitations in superfluid and normal liquid ⁴ He. Neutron scattering measurements of the excitations to date are limited to helium in aerogel. There the phonon-roton energy and width are slightly modified by disorder but there is no evidence for additional excitations at low energy nor of a gap in the phonon energy at long wavelengths. Experimental difficulties are discussed. In a recent path-integral Monte-Carlo study, in which a high density of point impurities are introduced at random positions, a significant broadening and energy shift are found together with additional low-energy excitations.     

Dielectric model of roton interactions in dilute solutions of 3He in 4He

The analogy between the theory of superfluidity and the theory of dielectrics can be extended to account for some of the properties of rotons in dilute solutions of ³He in superfluid ⁴He. These include the normal fluid density ratio and the shifts in energy of roton excitations relative to those of pure ⁴He.This research is supported in part by National Science Foundation grant DMR 76-21814 and by the Air Force Office of Scientific Research under grant AFOSR 76-2880A.     

Excitations Beyond the Roton of Liquid 4He in Aerogel

The dynamic structure factor, S(Q, ), for wavevectors, 2.0Q3.6 Å ^–1 of liquid ⁴ He in 95% porous aerogel has been measured by inelastic neutron scattering methods. The aerogel was grown with deuterated materials and the multiple scattering involving the aerogel was negligible. S(Q, ) in the superfluid phase consists of a single peak plus broad intensity at higher energy , as in bulk superfluid ⁴ He. The single peak is identified with the phonon-roton excitation at higher Q. The weight in the peak, Z_Q , and the excitation energy dispersion curve, _Q , has the same basic wavevector dependence as in the bulk. The energy _Q is 2–3% below the bulk value at the end point and the peak is unobservable beyond Q=3 Å ^–1 within the present statistical precision. No peak is observed at T=2.3 K in normal ⁴ He suggesting, as in bulk ⁴ He, that the characteristic excitation at higher Q is associated with the superfluid phase.     

Pressure Dependence of Excitations of Liquid 4He

No Heading Confinement of liquid ⁴He in porous glasses increases its solidification pressure and suppresses the superfluid transition temperature T. It has been reported that a sufficiently high degree of confinement suppresses T to zero at high pressure, signifying a quantum phase transition. We evaluate the behaviour of the excitation spectrum at wave vectors Q < 2.3 Å^–1 at pressures well above 25 bar by calculating the dynamic structure factor, S(Q, E), using the theory of hybridization of one- and two-particle excitations. The aim is to explore whether well-defined excitations exist at high pressures, and whether there is some critical pressure at which they disappear. We find that as the pressure increases, the one-particle excitation energy is well-defined if its energy lies below the two-roton energy, and ceases to exist as a well-defined excitation if its energy lies above the two-roton energy. We relate these findings to potential inelastic neutron scattering measurements.     

Pressure Dependence of the Multiphonon Excitations of Superfluid 4He

The pressure dependence of the multiphonon excitations in superfluid ⁴He has been studied, using neutron inelastic scattering. High-resolution measurements have been made at 0,5 K over a wavevector range 0.6<Q<2.2 Å^–1, at various pressures between 0 and 20 bars. The experimental data are presented and existing theoretical calculations are discussed.     

Excitations and Stability of 2D Liquid 4He

The excitation modes of two-dimensional liquid ⁴He are approached from two angles: Firstly, the phonon-roton spectrum is calculated and the related transition currents examined to gain insight into the detailed microscopic structure of the excitations and to look for possible evidence of the proposed spontaneous formation of vortex-antivortex pairs at low densities. The roton excitation is interpreted as a resonance effect in which the wavelength of the long-range density fluctuation matches favorably with the short-range oscillations caused by two-particle correlations. Contrary to the 3D case, no backflow rolls are observed in the two-body current at high momenta. The calculations reproduce reasonably the density dependence of the spectrum, and the saturation of the high-momentum part following from the decay processes of excitations is satisfactorily predicted. The stability of the liquid ground state is then studied by searching for soft modes. It is found that at densities near the expected liquid-solid phase transition the energy of the liquid can be lowered by changing the symmetry of the pair distribution function from spherical to non-spherical. This two-body structure indicates the point-group symmetry of the emerging solid phase to be hexagonal.     

Diffusion of Impurity Excitations in Superfluid and Solid 3He–4He Mixtures

Starting from the system of linearized kinetic equations, the exact expressions for the spin and mass diffusion coefficients and thermal diffusion ratio in quantum mixtures of helium isotopes with any degree of degeneration is obtained. From the general expression the various limiting expressions have been obtained, which are determined by various relations between collision rates of quasiparticles. The results of the calculations are compared with available experimental data. It is shown that in the low-temperature region, where an impuriton gas is one-component, the relaxation of concentration of ³ He in superfluid ³ He– ⁴ He mixtures is determined by the acoustic and dissipative collective modes with an effective diffusion coefficient. From the general relation, the expression for a spin diffusion coefficient in solid ³ He– ⁴ He quantum mixtures is derived. The comparison of the results obtained with the experimental data makes it possible to find a numerical value for the width of the impuriton energy zone.     

Excitations and Their Temperature Dependence in Superfluid 4He Beyond the Roton

The temperature dependence of the dynamic structure factor S(Q,) for superfluid ⁴ He has been measured by inelastic neutron scattering for wave vectors between 2.3 and 2.6 Å ^–l. S(Q,) has two peaks: one sharp peak at low energies whose dispersion flattens out and whose strength decreases with increasing Q, and one broader peak at higher energies with a stronger dispersion. The first peak disappears gradually with increasing temperature, while only part of the second peak vanishes at T . This indicates the existence of a third broad contribution, related to atoms above the Bose condensate. The two-peak structure can be interpreted in terms of a Bose-condensate induced coupling of the two-particle spectrum to the one-particle spectrum. The overall temperature dependence is consistent with the density-quasiparticle picture.     

Elementary Excitations in Solid and Liquid 4He at the Melting Pressure

Recent discovery of a nonclassical rotational inertia (NCRI) in solid ⁴He below 0.2 K by Kim and Chan has revived great interest in the problem of supersolidity and initiated intensive study on the properties of solid ⁴He. A direct proof that the onset of NCRI corresponds to the supersolid transition would be the observation of a corresponding drop of the entropy of solid ⁴He below the transition temperature. We have measured the melting pressure of ultrapure ⁴He in the temperature range from 0.01 to 0.45 K with several single crystals grown at different pressures and with the accuracy of 0.5 μbar. In addition, supplementary measurements of the pressure in liquid ⁴He at constant volume have been performed, which allowed us to eliminate the contribution of the temperature-dependent properties of the pressure gauge from the measured melting pressure data. With the correction to the temperature-dependent sensitivity of the pressure gauge, the variation of the melting pressure of ⁴He below 320 mK obeys the pure T ⁴ law due to phonons with the accuracy of 0.5 μbar, and no sign of the transition is seen (Todoshchenko et al. in JETP Lett. 85:454, 2007). This sets the upper limit of ∼5⋅10⁻⁸ R for a possible excess entropy in high-quality ⁴He crystals below 320 mK. At higher temperatures the contribution from rotons in the superfluid ⁴He has been observed. The thermal expansion coefficient of the superfluid ⁴He has been measured in the range from 0.01 to 0.7 K with the accuracy of ∼10⁻⁷ 1/K, or by two orders of magnitude better than in previous measurements. The roton contributions to the melting pressure and to the pressure in liquid at a constant volume are consistent and yield the value of 6.8 K for the roton gap, which is very close to the values obtained with other methods. As no contribution due to weakly interacting vacancies to the melting pressure of ⁴He has been observed, the lower limit of about 5.5 K for their activation energy can be set.      

Scattering of Elementary Excitations at the Surface of Superfluid 4He

We study the scattering of atoms, rotons and phonons at the free surface of superfluid ⁴ He. We calculate the evaporation, condensation and reflection probabilities in the framework of linearized time dependent density functional theory accounting for elastic one-to-one processes. We explore the angular dependence of the scattering probabilities showing that most results are independent of the incidence angle and can be expressed in terms of a single energy dependent parameter.     

Layer- and Bulk Roton Excitations of 4He in Porous Media

Layer-roton excitations of ⁴He in porous media, such as aerogel, Gegtech or Vycor, depend on the number of atoms in the active liquid layer, which, in turn, depends on the substrate potential. Hence, by measuring or calculating the energetics of the layer modes, one can get first-hand information about the substrate potential. Layer rotons can have energies as high as 8 K, while calculated two-dimensional rotons never seem to reach 6 K. Further indication that layer modes are actually an intermediate case between two and three dimensions is given by the way layer modes show up in neutron scattering data of helium in porous materials. We argue that layer rotons should be regarded as a third, completely independent kind of excitation.     

Pressure dependence of the roton spectrum in liquid helium

We suggest consistency checks on neutron scattering data on liquid helium under pressure. The theoretically calculated static structure functionS(k|P) leads to pressure dependence of the roton gap, momentum, and curvature in general agreement with experiment.Work supported in part by the U.S. Atomic Energy Commission, and in part by the National Science Foundation under Grant No. GP-29130 and through the Materials Research Center of Northwestern University.Resident Student Associate at Argonne National Laboratory, Summer 1972 and 1973.Alfred P. Sloan Research Fellow.     

4He atom reflection from rough liquid4He surfaces

When an atom is evaporated from or added to a free liquid surface there is a density perturbation of the surface. We have detected this surface spoiling using a⁴He atomic beam at glancing angles to the surface. With a perfect free liquid surface some of the atoms reflect specularly and some condense. We find that the specular reflection coefficient decreases as the surface is spoiled by another beam of⁴He atoms. The degree of spoiling as measured by the decrease in reflectivity, is initially proportional to the spoiling beam flux, but at higher fluxes the spoiling saturates. A phenomenological model is developed to describe this behaviour.     

Finite-amplitude acoustic waves in liquid3He and4He

Finite-amplitude acoustic waves have been propagated in liquid³He and⁴He. The acoustic cell has been operated at 83, 250, and 420 MHz and down to 17 mK. Our measurements of the anharmonic effects are in agreement with theoretical predictions and with previous experimental work that investigated a restricted temperature range.     

Hydrogen isotope and3He impurities in liquid4He

Recently Reynolds, Hayden and Hardy(J. Low Temp. Phys. 84,87 (1991)) analyzed atomic deuterium lifetimes in a cell with walls covered by a saturated⁴He film. They were able to determine the deuterium chemical potential in⁴He and also discussed the possibility of estimating its effective mass. These measurements inspired our attempt to understand the properties of hydrogen isotope impurities in liquid⁴He using the extended Jastrow-Feenberg theory based on the correlated wave function. We present results for hydrogen isotope chemical potentials in the bulk⁴He as a function of density. The accuracy of the method is tested by calculating the chemical potential of the³He impurity. We find a good agreement with existing measurements. We also calculate the effective masses of the hydrogen impurities. For deuterium we predict a value,m _eff=4m _D .     

Elastic reflection of4He atoms from the surface of liquid4He

The reflection of incident⁴He atoms from the surface of liquid⁴He can yield information on the microscopic features of the liquid at the surface. Edwards et al. have measured this reflectivity and have developed a theoretical model which successfully described the measurements. However, the density profile of the liquid⁴He surface has recently been determined experimentally, and this can now be used to model the reflectivity without any freely adjustable parameters. We use this density profile and the experimentally-determined interatomic pair potential to derive an effective potential for the incoming atom, and then solve the single-particle Schroedinger equation to find the reflectivity as a function of wavevector perpendicular to the surface. Within the uncertainty in the density profile and interatomic potential, we have chosen values that give good agreement between the measured and calculated reflectivities.     

The interatomic potential in liquid4He

In this paper we examine the validity of and consider alternatives to the traditional Lennard-Jones (6, 12) potential as applied to liquid⁴He. We find the Lennard-Jones potential to be subject to a number of serious defects, the worst among them that it does not satisfy the virial theorem. In its place we propose to use the Morse-V _DD potential function, which has none of the flaws in the Lennard-Jones potential and has the convenient feature of possessing a Fourier transform. The parameters appropriate to liquid⁴He are computed for the new potential as are a number of quantities derivable from it which are of current theoretical interest. A comparison is made between the values of these quantities as they are obtained using both potential functions.