Dynamical Spin Susceptibility of Anisotropic Superfluid in He3

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Abstract
Making use of a model Hamiltonian which includes besides the kinetic energy and the BCS like pairing energy, the spin exchange interaction as well as the dipole interaction, we calculated the dynamical spin susceptibility in the anisotropic superfluid state in He3. The fluctuation of the spin couples strongly with the fluctuation of the order parameter and a consistent treatment of these fluctuations is essential in obtaining a correct result. In the absence of the dipole interaction, we find that the dynamical spin susceptibility in the anisotropic superfluid state is identical to the one in the normal state in the uniform limit. In the presence of the dipole interaction, on the other hand, the dynamical susceptibility develops resonance poles, with the resonant frequency slightly shifted from the one in the normal state to the higher frequency side. In the case of the transverse susceptibility, the shift obtained is similar to that given by Leggett. We also predict the appearance of the resonance poles in the longitudinal susceptibility.

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