Landé factors of collective mode multiplets in³He-B and coupling strengths to sound waves

Abstract

In a previous paper we predicted a linear splitting of collective modes in³He-B with magnetic field, in particular, a fivefold splitting of the (8/5)^1/2 Δ mode. A fivefold splitting of about the same size has been recently observed by Avenel, Varoquaux, and Ebisawa for the new sound attenuation peak. In this paper all 18 collective modes are classified in terms of total angular momentumJ=0, 1, 2, andJ _z by means of a unitary transformation to the nine eigenstates¦J, J _z〉. The Landé factors for the field splitting of the real and imaginary mode triplets and quintuplets [including the (12/5)^1/2Δ mode quintuplet] are calculated for all temperatures. We also determine the sound dispersion relation. The angular dependence of the coupling constants of theJ=2 quintuplets is given by vY ²_{2 J z} (θ)v, in agreement with the results of Avenel, Varoquaux, and Ebisawa for the new mode. We find a coupling constant of the (8/5)^1/2 Δ mode to sound which is an order of magnitude smaller than that given by Koch and Wölfle. By comparing this with the experimental strengths we conclude that the particle-hole asymmetry parameter is about four times larger than that derived from the free-particle density of states.