Comment on the Coupling of Zero Sound to the $J=1^-$ Modes of $^3$He-B

TL;DR

This paper critically examines the claimed coupling between zero sound and $J=1^-$ collective modes in superfluid $^3$He-B, demonstrating that proper accounting for gap distortion negates the previously suggested direct coupling.

Contribution

The authors show that when gap distortion effects are correctly included, zero sound does not directly couple to the $J=1^-$ modes, challenging prior interpretations.

Findings

No direct coupling of zero sound to $J=1^-$ modes when gap distortion is considered

Previous features attributed to $J=1^-$ modes are not conclusively identified

Clarifies the interpretation of attenuation features near the pair-breaking edge

Abstract

Features in the zero sound attenuation near the pair-breaking edge in superfluid $^3$He-B have been observed in large magnetic fields. Schopohl and Tewordt [{\sl J. Low Temp. Phys.} {\bf 57}, 601 (1984)] claim that the $J=1^-, M=\pm 1$ order-parameter collective modes couple to zero sound as a result of the distortion of the equilibrium order parameter by a magnetic field; they identify the new features with these modes. However, we show that, when the effect of gap distortion on the collective modes is properly taken into account, the collective mode equations of Schopohl and Tewordt yield no direct coupling of zero sound to the $J=1^-$ modes. Thus, the identification of the absorption features reported by Ling, Saunders and Dobbs [{\sl Phys. Rev. Lett.} {\bf 59}, 461 (1987)] near the pair-breaking edge with the $J=1^-$ modes is not clearly established.