Group-Velocity Spectroscopy of Collective Modes in Superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$B$

The group velocity of high-frequency sound for $T\ll T_c$, and the group velocity and attenuation of sound at higher temperatures, have been measured and analyzed to give the frequencies and coupling strengths of two order-parameter collective modes in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$B$. For the squashing mode at 13.1 bars and $T\to 0$, $\frac{{\omega }_{\mathrm{sq}}}{{\Delta }_{\mathrm{BCS}}}=1.501\mathrm{}$ and the coupling constant ${\lambda }_{\mathrm{sq}}=0.010\mathrm{}\pm 0.001$. The recently discovered collective mode at $\frac{{\omega }_{\nu }}{{\Delta }_{\mathrm{BCS}}}=1.075\mathrm{}$ ($T\to 0$) has a coupling constant determined from the group velocity to be ${\lambda }_{\nu }=5.8\mathrm{}\times {10}^{-6\mathrm{}}$.