ANISOTROPIC SPIN-DIFFUSION AND MULTIPLE SPIN ECHOES IN HE-3-HE-4 SOLUTIONS

We propose a theta(1)-t(1)-theta(2) pulse-NMR experiment to detect the spin-diffusion anisotropy, Delta D=D-parallel to-D-perpendicular to, in degenerate spin-polarized He-3-He-4 mixtures, where D-perpendicular to and D-parallel to are the transverse and longitudinal spin diffusi on coefficients. In such an experiment the nonlinearity of the dynamic s produces multiple spin echoes (MSE). At the He-3 concentration x(3) approximate to 4% the spin-rotation parameter vanishes (mu M-->0), so that the nonlinearity of the equations of motion is entirely due to th e anisotropy. In this situation, detection of MSE amounts to observati on of Delta D. For slight anisotropy, i.e. Delta D/D-<parallel>less th an or similar to 0.25, we use a perturbation scheme similar to that de veloped by Einzel et al. (in that case, for small mu M and small demag netizing field) to calculate the second and third echo heights. For la rger anisotropy we numerically calculate the echo heights. We find tha t for Delta D/D-parallel to = 0.5 the heights are approximate to 2% of the first echo, and should be detectable. The (theta(1), theta(2)) ti p-angle dependence of the Delta D echoes is different from that of the mu M and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-ro tation and demagnetization effects are present, the theta(1)-t(1)-thet a(2) experiment provides a sensitive means of detecting the anisotropy .