Resonant Pulse Propagation of Sound in SuperfluidHe3-B

Superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$B$ offers a unique example of level crossing, that of the zero-sound mode and the internal "real squashing" mode of the gap parameter. A full treatment of this classic problem is given which compares well with observations at 1.2 bars and 45 MHz. The characteristic beat pattern seen on-resonance is identified is identified as a "$0\pi$-area" pulse, first discussed by Crisp. The present findings for the signal velocity agree with Brillouin's well-known predictions.