Analytic vortices and magnetic resonances in rotating superfluidHe3-A. III

We study variationally the circular-hyperbolic vortex-pair free energy. This bound pair yields a free energy much lower than that from a pair of isolated analytic vortices. The satellite resonance frequency of the pure $\hat{l}$ vortex pair and that of the vortex pair with nonuniform $\hat{d}$ are analyzed. We find that the pure $\hat{l}$ vortex pair gives the observed transverse satellite frequency as well as the observed intensity of the satellite, while the vortex pair with nonuniform $\hat{d}$ gives a satellite frequency that is somewhat lower than observed experimentally. It is puzzling why the pure $\hat{l}$ vortex with higher free energy than that from the vortex with nonuniform $\hat{d}$ is more consistent with experiment.