Quasi-diffusion between phonon and roton gases in two- and three-dimensional liquid helium

Temperature variations of the quasi-diffusion constant and thermal diffusion ratio between phonon and roton gases in two- and three-dimensional liquid helium are evaluated explicitly through the scattering of phonons by rotons. The diffusion constants in both dimensions decrease exponentially over the whole temperature range, while the thermal diffusion ratios increase and then decrease as temperature increases in the range from 0.6 to 1.1 K.     

Temperature dependence of the neutral current in liquid helium

We compute the energies of the bound state of an excited helium atom on the surface of liquid helium in a simple model. The consequent temperature dependence of the neutral current is in qualitative agreement with experiment.     

Power series expansion of phonon spectrum in liquid helium

With the aid of accurate microscopic calculations and rigorous sum rule arguments, available data on the phonon spectrum in liquid helium are analyzed. In particular we present a Tamm-Dancoff calculation of the correction to Feynman's spectrum and show that low-order perturbation calculations are valid. Without making any undue statement about the dispersion formula in the hydrodynamic region, we conclude that at least for 0.3<q<0.7 Å^?1 experimental data from inelastic neutron scattering and elastic x-ray scattering are on the whole consistent.     

Theory of the temperature dependence of the roton energy

The temperature dependence of the roton energy is examined considering its collision with another thermally excited roton and the interaction between one excitation and two rotons. The strong final state interaction strongly modifies the two-roton density of states, and therefore the Hartree-Fock approximation is not valid for the roton-roton scattering. Using the point interaction model for the roton-roton coupling and examining only the self-energy processes for the one-particle Green function linear in the number of rotons, it is shown that the amplitude of this temperature dependence changes sign as the roton-roton coupling strength is increased and an upper bound is obtained for the temperature dependence of the roton energy. As this upper bound is only one-seventh of the experimental result, they can be interpreted only by assuming more than seven independent channels with different angular dependence.This work is based on part of the author's Ph.D. thesis (Roland Eötvös University, Budapest). The support of the Central Research Institute for Physics is acknowledged.     

Excitations in liquid4He beyond the roton

The dynamic structure factor S(Q,E) for liquid⁴He at saturated vapor pressure has been measured by inelastic neutron scattering for wave vectors Q between 1.9 and 2.8 Å^–1. The temperature dependence is studied for Q=2.3 Å^–1. The sharp phonon-roton peak gradually disappears with increasing temperature, while the scattering at higher energies is nearly temperature independent. The experimental results are compared with the density-quasiparticle interpretation introduced by Glyde and Griffin, and with a model describing the hybridization with the multiparticle excitations.     

On the temperature dependence of the velocity of sound in liquid helium

The velocity of the first sound in helium II for the low-temperature region in which the lawT ⁴ ln(const/T) holds is calculated. The constant in the logarithm is shown to be very small, and therefore the known results of the logarithmic approximation are not sufficient.     

Density and temperature dependence of the momentum distribution in liquid helium 4

Deep inelastic neutron scattering measurements on liquid⁴He have been carried out for temperatures from 0.35 K to 4.2 K and densities from 0.125 to 0.200g/cm³ at a momentum transfer of 23 Å^–1. These measurements are at large enough momentum transfer that deviations from the Impulse Approximation are accurately described by current theories and information on the single particle momentum distribution may be extracted from the measured scattering. The scattering exhibits non-Gausian behavior in both the normal liquid and superfluid phases. A distinct change in the scattering, marked by a reduction in the width and increased deviations from the classical Gaussian shape, occurs at the suerfluid transition. We present a comparison of our experimental results with recent calculations at a variety of temperatures and densities and show that theory and experiment are in excellent agreement. We also present model scattering functions, obtained by correcting for instrumental resolution and final state effects, that represent the scattering in the IA limit. Finally, we present values for the average kinetic energy and the Bose condensate fraction over a broad range densities and temperatures.     

Calculation of theJ=3 roton spectrum of solid hydrogen and deuterium

A model for collective rotational excitations (rotons) with angular momentumJ=3 in solid ortho-hydrogen and para-deuterium at low temperatures is proposed. The theory is an extension of previous Bloch-type models of librons in orthohydrogen and rotons in para-hydrogen. The present model gives fairly good agreement with the positions and relative intensities of the observed Raman lines. As is the case for the libron spectrum, a discrepancy between theory and experiment is found. Improvements of the theory, which may give better agreement with the observed Raman spectra, are discussed.Supported by NSF Grant GP-9042.     

Impurity ions in liquid helium

A technique for introducing a wide variety of positive ions into liquid helium is described and used to investigate positive atomic ions of K, Rb, Cs, Ca, Sr, and Ba. The zero-field mobilities of the impurity ions were measured in He II in the temperature range 1.2 < T < 1.4 K. The dependence of mobility on ion mass alone was found directly for Ca⁺ ions by investigating two isotopes. Measurements were made of the ion drift velocities in high electric fields, where nucleation of quantized vortex rings occurs. All the data and its analysis are consistent with the assumptions that all the impurity ions are singly charged, that the size of the cluster surrounding the ion is significantly different for the different ions, and that the ion-roton cross section is approximately geometric. A possible alternative model for the structure of the ion complex is discussed and a mechanism is suggested which may account for the observed variations in ionic radii.     

Light scattering in liquid helium

A quantum-mechanical formulation of light scattering in a dielectric fluid is applied to liquid helium. To lowest order in the (small) dielectric susceptibilityn, the theory reproduces the usual expression for Brillouin scattering. Two-roton processes occur in both first and second order inn, and the relevant ground-state matrix elements are evaluated with Feynman wave functions in the convolution approximation. The resulting two-roton differential cross section is significantly smaller than Stephen's prediction, in good agreement with the experiments of Greytak and Yan. The depolarization is somewhat reduced from that of Stephen; present techniques should be able to detect this difference.Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, U.S. Air Force, under AFOSR Contract No. F44620-71-C-0044.Alfred P. Sloan Foundation Research Fellow.     

Dielectric tracking in liquid helium

Measurements of the breakdown field of typical magnet insulators of thickness < 0.7 mm, under conditions in which the breakdown is by surface tracking across the narrow dimension, yield values which are characteristic of helium gas at the saturated vapour pressure for temperatures above the lambda point. Below the λ point, the breakdown field rises again, but does not attain its 4.2 K value. Measurements also show that the tracking strength of a surface badly contaminated with metal particles is not appreciably less than that for a clean surface.     

Nucleation of bubbles in liquid helium

We give a brief survey of experiments that have been performed to study the nucleation of bubbles in liquid helium at negative pressures.     

Nonuniform states of liquid helium

We have generalized Nishiyama's theory of liquid helium to systems where the density is nonuniform. By a series of transformations the Hamiltonian can be diagonalized, the excitation energies being given by the eigenvalues of a pair of coupled differential equations. The theory is then used to discuss vortices, vapor-liquid surfaces, and impurities in nonuniform systems of helium.     

Magnetic Levitation of liquid helium

We report on the stable levitation of liquid helium drops of up to 2 cm diameter in a magnetic trap at temperatures down to 1.5 K in the earth's gravitational field. The production and properties of a magnetic trap for diamagnetic materials is discussed. The behavior of liquids in such a trap is analyzed, including the deformation of a liquid drop by the trap forces. We frequently observe two drops in the magnetic trap which are held in apparent contact for up to 3 minutes without coalescing. This non-coalescence effect was only seen above the superfluid transition temperature. We explain this effect in terms of the existence of a vapor layer between the drops caused by evaporation of the drops, much like the suspension of a liquid drop above a hot surface known as the Leidenfrost effect.     

Rotational spectrum of CO2 in helium clusters

We present a theoretical study, based on Reptation Quantum Monte Carlo simulations, of a single CO₂ molecule embedded in a Helium cluster (⁴He)_N, with 2 ≤ N ≤ 50. Upon studying density profiles and rotational dynamics, we find a nontrivial behaviour that corresponds to the formation of the first solvation shell. We determine the value of N for which the rotational constant begins to approach the nanodroplet limit. We also give an example of computational spectroscopy, illustrating the complementarity of simulations and experiments.PACS numbers: 61.46, +w, 02.70.Ss, 36.40.Mr     

Atomic order in liquid helium II

We study the gauge theory of superfluidity and find analytically the shape of the liquid structure factor for low values of the momentum transfer; in terms of our model we understand the diffraction data; new predictions are made.A preliminary version of this work was presented at the Sanibel Symposium of Quantum Fluids and Solids, held in Florida, January 1977.     

Temperature dependence of thermal conductivity of helium

Experimental data for the thermal conductivity of helium are generalized. A computational equation is proposed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 5, pp. 822–824, May, 1977.