Studies of single-particle momentum distributions in light atoms and molecules are reviewed with specific emphasis on experimental measurements using the deep inelastic neutron scattering technique at eV energies. The technique has undergone a remarkable development since the mid-1980s, when intense fluxes of epithermal neutrons were made available from pulsed neutron sources. These types of measurements provide a probe of the short-time dynamics of the recoiling atoms or molecules as well as information on the local structure of the materials. The paper introduces both the theoretical framework for the interpretation of deep inelastic neutron scattering experiments and thoroughly illustrates the physical principles underlying the impulse approximation from light atoms and molecules. The most relevant experimental studies performed on a variety of condensed matter systems in the last 20 years are reviewed. The experimental technique is critically presented in the context of a full list of published work. ...

Measurement of momentum distribution of lightatoms and molecules in condensed matter systems using inelastic neutron scattering

The fundamental problem is analyzed, the relation between Bose-Einstein condensation and spontaneous gauge symmetry breaking. This relation is largerly misunderstood in physics community. Numerous articles and books contain the statement that, though gauge symmetry breaking helps for describing Bose-Einstein condensation, but the latter, in principle, does not require any symmetry breaking. This, however, is not correct. The analysis is based on the known mathematical theorems. But in order not to overcomplicate the presentation and to make it accessible to all readers, technical details are often omitted here. The emphasis is made on the following basic general facts: Spontaneous breaking of gauge symmetry is the necessary and sufficient condition for Bose-Einstein condensation. Condensate fluctuations, in thermodynamic limit, are negligible. Their catastrophic behavior can arise only as a result of incorrect calculations, when a Bose-condensed system is described without gauge symmetry breaking. It is crucially important to employ the representative statistical ensembles equipped with all conditions that are necessary for a unique and mathematically correct description of the given statistical system. Only then one is able to develop a self-consistent theory, free of paradoxes.

https://iopscience.iop.org/article/10.1002/lapl.200710029/pdf

Bose-Einstein condensation and gauge symmetry breaking

The formation of a superfluid when 4He is cooled below the characteristic lambda transition temperature is accompanied by intricate quantum mechanical phenomena, including the emergence of a Bose condensate. A combination of path integral and semiclassical techniques is used to calculate the single-particle velocity autocorrelation function across the normal-to-superfluid transition. We find that the inclusion of particle exchange alters qualitatively the shape of the correlation function below the characteristic transition temperature but has no noticeable effect on the dynamics in the normal phase. The incoherent structure factor extracted from the velocity autocorrelation function is in very good agreement with neutron scattering data, reproducing the width, height, frequency shift, and asymmetry of the curves, as well as the observed increase in peak height characteristic of the superfluid phase. Our simulation demonstrates that the peak enhancement observed in the neutron scattering experiments below the transition temperature arises exclusively from particle exchange, illuminating the role of Bose-statistical effects on the dynamics of the quantum liquid.

https://www.pnas.org/content/pnas/102/12/4230.full.pdf

Simulation of dynamical properties of normal and superfluid helium.

The linearized approximation to the semiclassical initial value representation (LSC-IVR) is used to calculate time correlation functions relevant to the incoherent dynamic structure factor for inelastic neutron scattering from liquid para-hydrogen at 14 K. Various time correlations functions were used which, if evaluated exactly, would give identical results, but they do not because the LSC-IVR is approximate. Some of the correlation functions involve only linear operators, and others involve non-linear operators. The consistency of the results obtained with the various time correlation functions thus provides a useful test of the accuracy of the LSC-IVR approximation and its ability to treat correlation functions involving both linear and nonlinear operators in realistic anharmonic systems. The good agreement of the results obtained from different correlation functions, their excellent behavior in the spectral moment tests based on the exact moment constraints, and their semi-quantitative agreement with the inelastic neutron scattering experimental data all suggest that the LSC-IVR is indeed a good short-time approximation for quantum mechanical correlation functions.

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Test of the consistency of various linearized semiclassical initial value time correlation functions in application to inelastic neutron scattering from liquid para-hydrogen.

Progress made in measuring and interpreting the elementary excitations of superfluid and normal liquid [Formula: see text] in the past 25 years is reviewed. The goal is to bring up to date the data, calculations and our understanding of the excitations since the books and reviews of the early 1990s. Only bulk liquid [Formula: see text] is considered. Reference to liquid [Formula: see text], mixtures, reduced dimensions (films and confined helium) is made where useful to enhance interpretation. The focus is on the excitations as measured by inelastic neutron scattering methods. The review covers the dynamical response of liquid [Formula: see text] from the collective excitations at low energy and long wavelength (i.e. phonon-roton modes) to the single particle excitations at high energy from which the atomic momentum distribution and Bose-Einstein condensate fraction are determined. A goal is to show the interplay of these excitations with other spectacular properties such as superfluidity and the test of fundamental calculations of quantum liquids that is possible. The role of Bose-Einstein condensation in determining the nature of the [Formula: see text] mode and particularly it's temperature dependence is emphasized. The similarity of normal liquid [Formula: see text] with other quantum and classical liquids is discussed.

Excitations in the quantum liquid (4)He: A review.

We report high-resolution neutron scattering measurements at Q = 23 A−1 of 4He in the low-temperature superfluid and in the normal liquid phase at much higher momentum transfers than in previous measurements. When the impulse approximation prediction is broadened according to a recent theory for final-state effects, the data are in excellent agreement with ab initio Monte Carlo calculations of momentum distributions, which predict a Bose condensate fraction of 9.2% in the superfluid at T = 0 K.

W. M. Snow

Papers

Momentum Distributions in Liquid 4He