Critical and surface phenomena of quantum fluids

Lead Research Organisation: Lancaster University
Department Name: Physics


Neutron scattering provides a powerful tool for investigation of excitations in condensed matter. As a technique, it offers special advantages in the case of quantum fluids (liquid He4, liquid He3, and liquid isotopic mixtures). It can be applied both to excitations in the bulk and to those on the free surface of the fluid.The current research plan consists of two main parts:1. investigation of critical phenomena in He3, He4, and He3-He4 mixtures; and2. exploration of the possibility of using neutron reflection for studying quantum excitations on the surfaces of quantum fluids in the ultra-low temperature limit. The use of neutrons to study phenomena such as critical opalescence has special advatantages, compared to the traditional optical technique. In particular, it does not require the already-complicated cryogenic equipment to have optical windows. For example proposed method allows studies of the critical behaviour of fluid 3He and 3He-4He mixtures. Measurements of neutron opalescence in the vicinity of the critical point promise a rigorous test of the exact predictions of Renormalization Group theory, including several different classes of critical phenomena. We also wish to establish how the critical phenomena change if we place the fluid inside a nanoporous material: how the size of the critical fluctuations will be affected by the dimension of the host nano-matrix. Neutrons provide unique probes for this kind of research, especially at low temperatures.We now propose the use of neutron reflection to study the liquid helium surface, enabling us to test the long-standing theory of Fomin that, in the high-frequency limit, the Fermi liquid should support, not only ordinary capillary waves, but Rayleigh-type waves as well. It seems likely that unpredicted, unforeseen, physical effects will be observed as well. Slow neutrons exhibit a range of phenomena closely analogous to those observed in classical optics, including reflection, refraction and interference. Total reflection of slow neutrons was first reported by Fermi and co-workers and has since been extensively applied to a diversity of problems. For example the propagation and attenuation characteristics of surface acoustic waves have been experimentally investigated by neutron diffraction . To our knowledge, however, this method has not yet been applied to studies of the surfaces of quantum fluids, probably on account of the difficulty of combining a neutron reflectometer (e.g. CRISP at ISIS RAL) with the necessary ultra-low temperature sample environment. The investigation of the formation of Andreev's quantum states of 3He atoms on free surface of liquid 4He is another challenge of this research. We will also use neutron scattering to investigate wave turbulence on the surfaces of quantum fluids. The analogous optical experiment has already been carried out for a liquid hydrogen free surface, but no results have yet been reported for either He4 or He3.


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Charlton T (2008) Neutron reflection from a liquid helium surface in Low Temperature Physics

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Charlton T (2009) Neutron reflection from the surfaces of liquid 4 He and a Dilute 3 He- 4 He solution in Journal of Physics: Conference Series

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Kirichek O (2012) Neutron reflection from the surface of a liquid 4 He- 3 He mixture in Journal of Physics: Conference Series

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Kirichek, O. (2013) Experiment RB1220291 report

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Vasilev N (2012) A dynamically adjustable wavelength-sensitive neutron filter in Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment

Description The research involved the use of neutrons from the ISIS facility at the Rutherford Appleton Laboratory to study the properties of liquid and gaseous helium down to very low temperatures, including both of its isotopes He-3 and He-4.
At low temperatures, the properties of He-3 and He-4 are utterly different. The reason involves quantum mechanics, and is associated with the difference in symmetry of their atomic wavefunctions, which causes them to be described by different forms of quantum statistics. When cooled to a few degrees Kelvin above the absolute zero of temperature, they each condense into a colourless liquid of exceptionally low density. Liquid He-4 becomes superfluid (with zero viscosity, i.e. "infinitely thin") below 2.17 K, whereas liquid He-3 does not, at least not within the temperature range of the present experiments above 0.3 K. Neutrons can be scattered (bounced) off both isotopes of helium, but in the case of He-3 they are far more likely to absorbed than to be scattered.
Naturally occurring helium is almost pure He-4, but it also contains about 0.2 parts-per-million of the lighter isotope He-3. For most purposes, the presence of the He-3 is of no importance. Sometimes, however, and especially at very low temperatures as in the present research, these tiny traces of He-3 can play a very important role.
In the first part of the research programme, the absorption probability of neutrons was measured as they passed through a container of He-3, for a very wide range of temperatures. The results could be related to the density of the He-3. At low temperatures, the He-3 formed two phases, and the absorption was measured in the gaseous phase above the liquid; beyond the critical temperature, only one phase was present. The results agreed well with earlier capacitance-based measurements, except in the close vicinity of the critical point. The latter discrepancy is of great interest: it is probably attributable to critical fluctuations in the density near the phase transition, but a detailed theory is not yet available. In the course of these experiments, it was appreciated that there was an interesting potential application of the work: our container of He-3 gas can serve as a neutron filter whose wavelength sensitivity can be adjusted by variation of the gas density, which can conveniently be effected by adjustment of the temperature in the range 5-300 K. We showed that it exhibits high wavelength resolution (~0.5%) over the broad wavelength range 0.2 - 5.2Å. In principle, the range of application could be extended to encompass neutron energies corresponding to production through nuclear fission reactions, or for non-proliferation treaty verification, or for security applications e.g. at airports.
In the second part of the research programme, we sought evidence to test the theoretical prediction by Andreev that, in superfluid He-4 containing traces of He-3 (like commercial helium), the He-3 atoms at low temperatures occupy so-called Andreev levels just below the surface. The idea was tested by measurement of the temperature dependence of the neutron intensity in small-angle reflection from the surface. Reflectometry data from very dilute He-3/He-4 solutions strongly implied the occupation of Andreev levels as the temperature decreased, and this tentative conclusion was vindicated by reflection measurements from isotopically purified He-4. We conclude that it will be of immediate interest to extend the study to polarised neutrons (and in a magnetic field), which will give us information about the spin dynamics of 2-D He-3 complementary to that from NMR measurements.
Exploitation Route It would be of interest to extend the study to polarised neutrons (and in a magnetic field), which will give us information about the spin dynamics of 2-D He-3 complementary to that from NMR measurements.

Although this was basic research that advanced understanding of quantum fluids and their interactions with neutrons, there is also some possibility of a cryogenic wavelength-sensitive neutron filter based on the research, which could perhaps be useful in various contexts, e.g. security scanners for airports.
Sectors Education,Other

Description Beam time
Amount £100,000 (GBP)
Funding ID RB1510035 
Organisation ISIS Neutron Source Facility 
Sector Learned Society
Country United Kingdom
Start 04/2018 
End 06/2018
Description Lancaster Helium Ltd is a spin-out company of Lancaster University. It supplies the isotopically pure He-4 gas needed for a diversity of applications including - •Coolant gas in a nuclear reactor •The down-scattering medium for ultra-cold neutron (UCN) production •Measurement of the Landau critical velocity •Experiments on quantum turbulence •Cyclotron resonance of ions below the superfluid surface •Production of excited helium molecules (long-lived excimers) •Ultra-low-temperature experiments on solid He-4 The gas has many other possible uses. Isotopic separation is effected by heat flush in liquid helium below its superfluid transition temperature at 2.17 K. The He-4 isotopic purity achieved within the company's present machine is believed to be perfect. Thus, any He-3 in the product must arise from subsequent contamination, e.g. by the compressor or pipework or containers. The gas may contain traces of air, water and oil vapour but isotopically it is of extremely high purity. 
Year Established 2016 
Impact Sale of 12 kg of isotopically purified He-4 to Technical University of Munich (2018) for use in a nuclear reactor forming the core of their new ultra-cold neutron (UCN) source.