Transverse Spin Diffusion in a Dilute Spin-Polarized Degenerate Fermi Gas

Abstract

We re-examine the calculation of the transverse spin-diffusion coefficient in a dilute degenerate spin-polarized Fermi gas, for the case of s-wave scattering. The special feature of this limit is that the dependence of the spin diffusion coefficient on temperature and field can be calculated explicitly with no further approximations. This exact solution uncovers a novel intermediate behaviour between the high field spin-rotation dominated regime in which D_⊥ ∝ H⁻², D_∥ ∝ T⁻² , and the low-field isotropic, collision dominated regime with D_⊥ = D_∥ ∝ T⁻². In this intermediate regime, D_{⊥, ∥} ∝ T⁻² but D_⊥ ≠ D_∥. We emphasize that the low-field crossover cannot be described within the relaxation time approximation. We also present an analytical calculation of the self-energy in the s-wave approximation for a dilute spin-polarized Fermi gas, at zero temperature. This emphasizes the failure of the conventional Fermi-liquid phase space arguments for processes involving spin flips. We close by reviewing the evidence for the existence of the intermediate regime in experiments on weakly spin-polarized ³ He and ³ He– ⁴ He mixtures.