Single-Particle Coupling to Collective Excitations; Sound inHe3

Abstract

In order to test the hypothesis that the observed anomalous behavior of the low-temperature specific heat of ${\mathrm{He}}^3$ is due to the interaction of ${\mathrm{He}}^3$ atoms with sound, the coupling of the single particles to the collective excitations must be calculated. Based on an infinite-order perturbation theory, a technique is introduced for finding the effective coupling at long wavelengths. Within this approximation scheme the coupling is found to be of the deformation-potential kind. Vertex corrections make the expression used for the single-particle self-energy exact. A singular vertex function, which is ruled out if perturbation theory is valid but which is required in order to change the coupling from deformation-potential to piezoelectric, leads to an inconsistency. All approximation schemes treated result in a deformation-potential coupling between ${\mathrm{He}}^3$ atoms and sound. Treatments of this coupling have not so far led to results which can explain the observed specific heat.