  We study the sensitivity of Yu-Shiba-Rusinov states, bound states that form
around magnetic scatterers in superconductors, to the presence of nonmagnetic
disorder in both two and three dimensional systems. We formulate a scattering
approach to this problem and reduce the effects of disorder to two
contributions: disorder-induced normal reflection and a random phase of the
amplitude for Andreev reflection. We find that both of these are small even for
moderate amounts of disorder. In the dirty limit in which the disorder-induced
mean free path is smaller than the superconducting coherence length, the
variance of the energy of the Yu-Shiba-Rusinov state remains small in the ratio
of the Fermi wavelength and the mean free path. This effect is more pronounced
in three dimensions, where only impurities within a few Fermi wavelengths of
the magnetic scatterer contribute. In two dimensions the energy variance is
larger by a logarithmic factor because impurities contribute up to a distance
of the order of the superconducting coherence length.
