Calculated cross sections for elastic scattering of neutrons from vortex rings in liquidHe4

A theory of elastic scattering of neutrons from vortex rings in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is presented, and a study is made of the dependence of the differential cross section on the parameters that characterize the vortices. The sensitivity of the cross section to the details of the density profile in and near the vortex core is examined with the aid of numerical calculations based on simple models. The usefulness and significance of these calculations with regard to recent theoretical work on liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ near the $\lambda$ point and also with regard to liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ turbulence produced by intense heat fluxes or ion beams is discussed.