Helium three

The importance of research on superfluid helium is emphasized by two Nobel Prizes. In 1978, P.L. Kapitza reccived the prize for his discovery of superfluidity in 'He. The work was done in Cambridge and Moscow 40 years before it was finally recognized. In 1972, David Lee, Douglas Osheroff, and Robert Richardson observed two new phases in liquid ³ He, which were soon found to be superfluids. The Cornell team received the Nobel Prize in 1996, again a long time after their discovery.

Research on ³ He has been very active since the book of Wilks was published. There are several reasons for this. First, the properties of normal and superfluid ³ He are textbook examples of many-body systems in condensed matter physics, because ³ He provides the best theory and the most clear-cut experimental results. Since the order parameter of superfluid ³ He is very multidimensional, many more phenomena were discovered in ³ He than in the simple superfluid of ⁴ He. For example, eight different types of vortices have been detected in rotating superfluid ³ He, instead of just one in ⁴ He. Secondly, the Fermi superfluid ³ He is a very intriguing system theoretically, because its properties can be explained by means of the formalism developed by Bardeen, Cooper, and Schrieffer for superconductivity in metals.

Thirdly, it is fortunate that the ³ He nucleus has a non-zero spin which makes it possible to use the powerful method of nuclear magnetic resonance in studies of ³ He. In ⁴ He, because I = 0, this versatile technique cannot be employed. And finally, an additional reason for such a large amount of excellent research on ³ He over the last ³5 years is that three new methods of refrigeration were developed during the period 1960-75. These are Pomeranchuk cooling, which was used in the discovery of the new phases of³ He, dilution refrigerators, which quickly became the versatile workhorse in ³ He research, and adiabatic nuclear demagnetization, which opened up temperatures in the low millikelvin region for research on ³He.

Low-temperature physicists working on superfluid ³He now have one important wish: The discovery of superfluidity in the dilute 6.4 % mixture of ³He in superfluid ⁴ He. It is already known that the transition temperature will be in the low microkelvin region or below. Who will get there first?

Contents

• Thermal expansivity of liquid helium. 3
• Properties of liquid helium 3
• Landau parameters for liquid helium 3
• Zero-temperature parameters of liquid ³He from thermal conductivity data
• Transport coefficients for liquid ³He from viscosity and spin diffusion data
• Energy and distance parameters for some interatomic potentials of helium
• Theoretical ground state energy of ³He-⁴ He in kelvin at a density 22 mn^-3
• Pressure dependence of the hydrodynamic mass of 3He in mixtures
• Limiting solubility X_s and coefficient ß of ³He in liquid 4He under pressure
• Coefficients of the Baym and Ebner (1968) potential
• Properties of ³He-⁴He mixtures at s.v.p.
• Landau parameters for ³He-⁴He mixtures at s.v.p.
• Coefficients of the quasiparticle interaction V(q) and s-wave ammplitude a
• Phase diagrara parameters of superfluid helium 3
• BCS coherence length in superfluid helium 3
• Fourth-order invariants for unitary p-states with their strong-coupling parameters
• Ginzburg-Landau ß parameters on Sauls-Serene theory
• Experimental Ginzburg-Landau ß parameters
• Critical velocity and Landau velocity for ³He-B
• Order parameter collective modes of the B phase
• Order parameter collective modes of the A phase