Abstract
The Landau theory of a Fermi fluid is applied to the calculation of low temperature equilibrium properties of liquid helium three and the dilute hard-sphere Fermi gas (DHSFG) model. Parameterized forms of the quasiparticle energy-momentum relation ϵ k and the Landau interaction energy f kk′ are postulated, based on exact microscopically-derived results for the DHSFG model, and the chosen parameters appear in all calculated thermodynamic temperature coefficients. A calculational method due to Richards is used by means of which logarithmic terms of the form T n ln T, whose origins arise in corresponding logarithmic terms in ϵ k and f kk′, are found in all calculated thermodynamic quantities. In particular, terms with n = 2 and with n = 3 are derived for the magnetic susceptibility χ and the heat capacity C, respectively, in agreement with the most recent experiments on liquid 3He. By comparing with empirical fits to 3He data at 0.28 atm, for χ, C and the speed of sound, eight numbers are estimated for the parameterized Landau functions. Exact DHSFG solutions for all thermodynamic quantities studied are derived and checked for internal consistency, both thermodynamically and by using identities which exist within the Landau theory.
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