Spin diffusion and spin echoes in liquid³He at low temperature

Spin diffusion in a degenerate Fermi liquid is studied, taking into account the effects of the 'molecular field' resulting from the interactions between quasiparticles. It is shown that even in the hydrodynamic limit no equation of the conventional form delta M/ delta t=Dgrad 2 M exists in general; the true equation is nonlinear and depends on the strength of the interactions. Substantial new effects are therefore predicted when lambda Omega 0 tau D > approximately 1, where Omega 0 is the Larmor frequency, tau D the spin diffusion lifetime and lambda a dimensionless parameter which measures the strength of the molecular field. Specifically, it is predicted that the spin-echo attenuation in a ' phi -180-180' experiment will in general not be exponential and will depend on the external field and the initial pulse angle phi . The new effects should lie in the experimentally accessible region both for pure 3 He and for mixtures.