Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Momentum distributions in superfluid helium: bose condensate fraction

Paul E. Sokol, Ralph O. Simmons, D. L. Price, R.O. Hilleke

Published Aug 9, 1984• 0 citations
OpenAlex

Abstract

We have measured the momentum distributions in superfluid and normal Helium 4 at identical densities using inelastic neutron scattering as a function of temperature and density. At large enough momentum transfers Q the Impulse Approximation is valid and the single particle momentum distribution n(anti p) can be extracted from the inelastic scattering spectrum. Results are reported. (WHK)

Related papers

High-Energy Neutron Scattering from Liquid Helium in the Impulse Approximation

H. A. Gersch, Phil N. Smith

The impulse approximation is used to describe the inelastic cross section for high-energy neutron scattering from superfluid helium in terms of a ground-state momentum distribution of the helium atoms as given by existing variational calculations. The predicted shape of the cross section is compared with recent experimental data and with a previous theory which approximated the noncondensate contribution to the dynamic structure factor by a single-Gaussian function. In contrast to conclusions obtained using the single-Gaussian approximation, our predicted inelastic cross section omitting a condensate contribution provides an acceptable fit to the experimental data. This fit is worsened by introducing a contribution from a condensate fraction in the amount consistent with the variational calculations, namely 11%. If the condensate fraction is arbitrarily reduced from this value, it is found that a much smaller value, with an upper limit of about 3%, is consistent with the available experimental data. It appears that unique assignments of condensate-fraction contributions to inelastic neutron scattering, for the range of neutron energies presently available, will require an improved theory of final-state effects on the shape of the condensate contribution.

Physical Review A•Jul 1, 1971•15 citations

Search for Bose-Einstein Condensation in Superfluid He4

Herbert A. Mook, R. Scherm, M. K. Wilkinson

A search was made for Bose-Einstein condensation in superfluid $^{4}\mathrm{He}$ using neutron inelastic scattering. A two-component scattering distribution has been resolved for $^{4}\mathrm{He}$ at 1.2 \ifmmode^\circ\else\textdegree\fi{}K giving direct evidence for the existence of the zero-momentum state. Analysis of the measured data leads to a condensate fraction of (2.4 \ifmmode\pm\else\textpm\fi{} 1)%, a value much smaller than previously estimated.

Physical Review A•Dec 1, 1972•68 citations

Bose-Einstein Condensation in Solid He4

Souleymane Diallo, Jonathan V Pearce, R. T. Azuah +3 more

We present neutron scattering measurements of the atomic momentum distribution $n(\mathbf{k})$ in solid helium under a pressure $p=41\text{ }\mathrm{bar}$ (molar volume ${V}_{m}=20.01\ifmmode\pm\else\textpm\fi{}0.02\text{ }\text{ }{\mathrm{cm}}^{3}/\mathrm{mol}$) and at temperatures between 80 and 500 mK. The aim is to determine whether there is Bose-Einstein condensation (BEC) below the critical temperature, ${T}_{c}=200\text{ }\text{ }\mathrm{mK}$, where a superfluid density has been observed. Assuming BEC appears as a macroscopic occupation of the $k=0$ state below ${T}_{c}$, we find a condensate fraction of ${n}_{0}=(\ensuremath{-}0.10\ifmmode\pm\else\textpm\fi{}1.20)%$ at $T=80\text{ }\text{ }\mathrm{mK}$ and ${n}_{0}=(0.08\ifmmode\pm\else\textpm\fi{}0.78)%$ at $T=120\text{ }\text{ }\mathrm{mK}$, consistent with zero. The shape of $n(\mathbf{k})$ also does not change on crossing ${T}_{c}$ within measurement precision.

arXiv:cond-mat/0702347•Physical Review Letters•May 17, 2007•45 citations

Bose-Einstein Condensation in Liquid Helium

Paul E. Sokol

Liquid helium is the prototypical example of a superfluid – a liquid that flows without viscosity and transfers heat without a temperature gradient. These properties are intimately related to the Bose condensation that occurs in this strongly interacting liquid. Bose condensation is most directly observed in the single particle atomic momentum distribution, where the Bose condensate appears as a delta function singularity. In this article, we discuss the experimental techniques used to observe the condensate and the current status of measurments of the Bose condensate in liquid helium. Introduction Liquid helium ( 4 He) has fascinated physicists ever since Kammerlingh-Onnes liquified the last of the so called permanent gases in 1908. However, evidence of what is without doubt the most fascinating property of this unique liquid, superfluidity, was not reported until almost 25 years later [1]. The superfluid phase, where heat is transferred without a thermal gradient and mass flows without a driving pressure, is a macroscopic manifestation of microscopic quantum effects governing the behavior of atoms [2]. Bose–Einstein condensation was first proposed by London [3] as the microscopic explanation for these fascinating phenomena. Helium is unique among condensed atomic systems since the bulk properties of the liquid are dominated by quantum effects. The most important of these are the statistical effects that arise for identical particles. For bosons, such as 4 He atoms, there is no limitation on the number of particles that can occupy a single quantum state.

Cambridge University Press eBooks•Apr 6, 1995•69 citations

Scattering of neutrons on a Bose condensate

Dmitriy Baranov, Zh. A. Kozlov, L. Siurakshina +1 more

The spectrum of noncondensate excitations in neutron scattering on bosons is obtained in the framework of the Bogoliubov models both for liquid 4He and a dilute gas. The problem is solved using a path-integral representation of the partition function of the system. We describe the influence of scattering of neutrons on a Bose condensate in a stationary (time-independent) picture in the Gibbs equilibrium ensemble. This influence is a stationary boson response, and it depends on the initial neutron momentum k, transfer momentum p, and the neutron-boson interaction λ, which is related to the scattering length. The contribution of the neutrons to the initial Bogoliubov spectrum is found to be important for “quasi-elastic” scattering on the noncondensate, while the contribution of deep inelastic scattering is small; no contribution from elastic scattering on the Bose condensate is found. In the case of liquid Helium, the response is unlikely to be observable for all values p. On the other hand, for a gas one may expect a visible effect, in particular for a small momentum transfer p and a small density of the Bose condensate ϱ.

Annalen der Physik•Feb 1, 1999•3 citations

The momentum distribution of normal and superfluid liquid 4He

David M. Ceperley, E. L. Pollock

Path-integral methods can be employed to calculate properties of boson systems at any temperature. We have performed a number of simulations of liquid helium and have calculated the momentum distribution as a function of temperature. We find that liquid helium has a condensate below 2 K but not above. The momentum distribution is found to be non-Gaussian even in normal liquid helium. We have also calculated the difference in the momentum distribution between a boson system and a distinguishable particle system.

Canadian Journal of Physics•Nov 1, 1987•90 citations
We have measured the momentum distributions in superfluid and normal Helium 4 at identical densities using inelastic neutron scattering as a function of temperature and density. At large enough momentum transfers Q the Impulse Approximation is valid and the single particle momentum distribution n(anti p) can be extracted from the inelastic scattering spectrum. Results are reported. (WHK)
The impulse approximation is used to describe the inelastic cross section for high-energy neutron scattering from superfluid helium in terms of a ground-state momentum distribution of the helium atoms as given by existing variational calculations. The predicted shape of the cross section is compared with recent experimental data and with a previous theory which approximated the noncondensate contribution to the dynamic structure factor by a single-Gaussian function. In contrast to conclusions obtained using the single-Gaussian approximation, our predicted inelastic cross section omitting a condensate contribution provides an acceptable fit to the experimental data. This fit is worsened by introducing a contribution from a condensate fraction in the amount consistent with the variational calculations, namely 11%. If the condensate fraction is arbitrarily reduced from this value, it is found that a much smaller value, with an upper limit of about 3%, is consistent with the available experimental data. It appears that unique assignments of condensate-fraction contributions to inelastic neutron scattering, for the range of neutron energies presently available, will require an improved theory of final-state effects on the shape of the condensate contribution.
A search was made for Bose-Einstein condensation in superfluid 4He^{4}\mathrm{He}4He using neutron inelastic scattering. A two-component scattering distribution has been resolved for 4He^{4}\mathrm{He}4He at 1.2 \ifmmode^\circ\else\textdegree\fi{}K giving direct evidence for the existence of the zero-momentum state. Analysis of the measured data leads to a condensate fraction of (2.4 \ifmmode\pm\else\textpm\fi{} 1)%, a value much smaller than previously estimated.
We present neutron scattering measurements of the atomic momentum distribution n(k)n(\mathbf{k})n(k) in solid helium under a pressure p=41 barp=41\text{ }\mathrm{bar}p=41 bar (molar volume ${V}_{m}=20.01\ifmmode\pm\else\textpm\fi{}0.02\text{ }\text{ }{\mathrm{cm}}^{3}/\mathrm{mol}$) and at temperatures between 80 and 500 mK. The aim is to determine whether there is Bose-Einstein condensation (BEC) below the critical temperature, Tc=200  mK{T}_{c}=200\text{ }\text{ }\mathrm{mK}Tc​=200  mK, where a superfluid density has been observed. Assuming BEC appears as a macroscopic occupation of the k=0k=0k=0 state below Tc{T}_{c}Tc​, we find a condensate fraction of ${n}_{0}=(\ensuremath{-}0.10\ifmmode\pm\else\textpm\fi{}1.20)%$ at T=80  mKT=80\text{ }\text{ }\mathrm{mK}T=80  mK and ${n}_{0}=(0.08\ifmmode\pm\else\textpm\fi{}0.78)%$ at T=120  mKT=120\text{ }\text{ }\mathrm{mK}T=120  mK, consistent with zero. The shape of n(k)n(\mathbf{k})n(k) also does not change on crossing Tc{T}_{c}Tc​ within measurement precision.
Liquid helium is the prototypical example of a superfluid – a liquid that flows without viscosity and transfers heat without a temperature gradient. These properties are intimately related to the Bose condensation that occurs in this strongly interacting liquid. Bose condensation is most directly observed in the single particle atomic momentum distribution, where the Bose condensate appears as a delta function singularity. In this article, we discuss the experimental techniques used to observe the condensate and the current status of measurments of the Bose condensate in liquid helium. Introduction Liquid helium ( 4 He) has fascinated physicists ever since Kammerlingh-Onnes liquified the last of the so called permanent gases in 1908. However, evidence of what is without doubt the most fascinating property of this unique liquid, superfluidity, was not reported until almost 25 years later [1]. The superfluid phase, where heat is transferred without a thermal gradient and mass flows without a driving pressure, is a macroscopic manifestation of microscopic quantum effects governing the behavior of atoms [2]. Bose–Einstein condensation was first proposed by London [3] as the microscopic explanation for these fascinating phenomena. Helium is unique among condensed atomic systems since the bulk properties of the liquid are dominated by quantum effects. The most important of these are the statistical effects that arise for identical particles. For bosons, such as 4 He atoms, there is no limitation on the number of particles that can occupy a single quantum state.
The spectrum of noncondensate excitations in neutron scattering on bosons is obtained in the framework of the Bogoliubov models both for liquid 4He and a dilute gas. The problem is solved using a path-integral representation of the partition function of the system. We describe the influence of scattering of neutrons on a Bose condensate in a stationary (time-independent) picture in the Gibbs equilibrium ensemble. This influence is a stationary boson response, and it depends on the initial neutron momentum k, transfer momentum p, and the neutron-boson interaction λ, which is related to the scattering length. The contribution of the neutrons to the initial Bogoliubov spectrum is found to be important for “quasi-elastic” scattering on the noncondensate, while the contribution of deep inelastic scattering is small; no contribution from elastic scattering on the Bose condensate is found. In the case of liquid Helium, the response is unlikely to be observable for all values p. On the other hand, for a gas one may expect a visible effect, in particular for a small momentum transfer p and a small density of the Bose condensate ϱ.
Path-integral methods can be employed to calculate properties of boson systems at any temperature. We have performed a number of simulations of liquid helium and have calculated the momentum distribution as a function of temperature. We find that liquid helium has a condensate below 2 K but not above. The momentum distribution is found to be non-Gaussian even in normal liquid helium. We have also calculated the difference in the momentum distribution between a boson system and a distinguishable particle system.