The transverse acoustic impedance of normal ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is calculated within the framework of Landau's theory of Fermi liquids. Fermi-liquid parameters $F_l^s$ with $l\le 2$ are included in the theory and a two-time relaxation-time approximation is used for the collision integral. It is shown that the impedance is sensitive to the value of $F_2^s$ but insensitive to the ratio of the two relaxation times. This is in contrast to the attenuation of transverse zero sound which is sensitive to both these parameters. Expressions are given for the collective and single-particle contributions to the impedance and they are shown to have comparable magnitudes in the zero-sound regimes. The theory is compared with recent observations of the impedance at 23 bar and it is shown that the real part of the observed impedance implies $F_2^s=-1.0\mathrm{}\pm 0.5$, where the indicated uncertainty does not include that due to the uncertainty in the values of other Fermi-liquid parameters. The observed imaginary part of the impedance cannot be reconciled with the theory.

• Received 10 December 1976

DOI:https://doi.org/10.1103/PhysRevB.17.1238