Scattering length of Andreev reflection from quantized vortices in $^3$He-$B$

TL;DR

This paper provides an exact calculation of the scattering length for Andreev reflection from isolated vortices in superfluid helium-3 B, analyzing its dependence on impact parameter and temperature.

Contribution

It introduces precise calculations of scattering lengths for quasiparticle flux and energy flux in superfluid helium-3 B, enhancing understanding of quantum turbulence visualization techniques.

Findings

Exact scattering length as a function of impact parameter

Temperature dependence of scattering lengths

Analysis of energy flux scattering lengths

Abstract

Andreev reflection of thermal quasiparticles from quantized vortices is an important technique to visualize quantum turbulence in low temperature $^3$He-$B$. We revisit a problem of Andreev reflection from the isolated, rectilinear vortex line. For quasiparticle excitations whose impact parameters, defined as distances of the closest approach to the vortex core, do not exceed some arbitrary value, $b$, we calculate exactly the reflected fraction of the total flux of excitations incident upon the vortex in the direction orthogonal to the vortex line. We then define and calculate exactly, as a function of $b$, the scattering length, that is the scattering cross-section per unit length of the vortex line. We also define and calculate the scattering lengths for the flux of energy carried by thermal excitations, and for the net energy flux resulting from a (small) temperature gradient, and analyze the dependence of these scattering lengths on temperature.