Spin modes in polarized 3He clusters

The transverse-spin modes in clusters of He-3 are considered. These excitations correspond to a gapless Goldstone mode which comes along due to the broken symmetry in the spin space, and can exhibit themselves in polarized He-3. These modes can be interpreted as weakly damped fluctuations of the transverse spin components, which propagate through He-3. The dispersion law of such spin waves is calculated by means of a semiclassical variational method and compared with the results obtained on the basis of the Fermi-liquid theory. The finite sizes of the clusters lead to quantization of the spectra and result in a series of excited states. The number of long-living excited states is strongly affected by the Landau damping. The orthogonality relations and energy-weighted sum rule are formulated. The collective spin modes for l=0 and several cluster sizes are computed.