Title:

Some properties of liquid helium

The theoretical picture of liquid helium 3 which is currently accepted is due to Landau (1957 a). According to this theory, the propagation of sound in He^{5} should show a new phenomenon, called zero sound, if the liquid is excited at a high acoustic frequency and at low temperatures. This thesis describes theoretical and experimental investigations into this phenomenon. We have attempted a measurement of the acoustic impedance of liquid He^{5} at a frequency of 10 000 Mo/s. In the method of measurement adopted, a travelling sound wave is reflected up and down inside a quarts crystal immersed in liquid He^{5}. The acoustic impedance of the liquid is found by measuring the loss of energy from the crystal due to the radiation of sound out into the liquid. In order to obtain useful accuracy, it is necessary to obtain a crystal in which the sound wave can be reflected bank and forth at least 250 times. Preliminary experiments performed with various crystals showed that it was not hard to obtain a crystal which would give 100 echoes, but that obtaining a larger number presented unexpected difficulties. Various attempts were made to improve the performance of the apparatus, but the experiment was eventually abandoned as our theoretical analysis appeared to be more promising. For the theoretical work, we have analysed measurements of the acoustic impedance of liquid He^{5} at a frequency of 1000 Mo/s which have been made by Keen, Matthews, and Wilks (1965). The theoretical expressions used are an extension of those given by Bekarevich and Khalatnikov (1961), who give expressions related to the acoustic impedance as part of a calculation of the Kapitza thermal boundary resistance. Using the same assumptions as Bekarevich and Khalatnikov we find that the acoustic impedance Z divided by the density ρ should rise from 183 m/s to about 190 m/s when the temperature is reduced through 0.09°K. The experimentally observed rise in Z/ρ is 19 ± 6 m/s, so the theory appears to underestimate the change in Z/ρ, and we have considered how the theory should be modified to account for the discrepancy. In the theory of a Fermi liquid due to Landau (1957 a), the forces of interaction between the particles of the liquid are taken into account by introducing certain parameters F_{0}, F_{1}, F_{2}, … which are determined from experimental measurements. Bekarevich and Khalatnikov include only two parameters (F_{0}, F_{1}) as these are the ones most easily derived from experiment. We have been able to estimate a third parameter (F_{2}), and have used this to obtain revised values of the acoustic impedance. These values of Z/ρ are still a little smaller than the experimental points, but we regard the agreement as satisfactory. We conclude that the experimental results of Keen, Matthews, said Wilks are consistent with Landau's theory of a Fermi liquid, and provide valuable support for the existence of zero sound.
