Dispersion corrections to the collective mode spectrum in axial and planar phases of superfluid He[sup 3]

Using the path integration technique developed by Brusov and Popov earlier, the authors have calculated for the first time the dispersion corrections to the collective mode spectrum in A- and 2D- phases of superfluid He[sup 3] for arbitrary directions of the collective excitation momentum k, taking the damping of collective modes into account. In axial-phase clapping (cl) mode remains six fold degenerate for k [parallel] l, while for other directions a three fold splitting takes place, which reaches a maximum for k [perpendicular] l. The pairbreaking modes remain degenerate even taking the dispersion induced corrections into account. In the planar phase the degeneracy of clapping (cl) and quasi-Goldstone (qGd) modes depends on the direction of the collective mode momentum k with respect to the external magnetic field H: the mode degeneracy remains the same as in the case of zero momentum k for k [parallel] H only, and for any other directions two fold splitting of these modes takes place. The dispersion induced splitting of collective modes could be observed (at least in the A-phase) in sound absorption experiments.