Dispersion corrections to the collective mode spectrum in axial and planar phases of superfluid He3

Abstract

Using the path integration technique developed by Brusov and Popov earlier, we have calculated for the first time the dispersion corrections to the collective mode spectrum in A- and 2D- phases of superfluidHe3 for arbitrary directions of the collective excitation momentumk, taking the damping of collective modes into account. In axial-phase clapping (cl) mode remains six fold degenerate fork ∥l, while for other directions a three fold splitting takes place, which reaches a maximum fork ⊥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 momentumk with respect to the external magnetic fieldH: the mode degeneracy remains the same as in the case of zero momentumk fork ∥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.