Critical and surface phenomena of quantum fluids

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.