In the case of metals, this complexity is so enhanced by the presence of conduction electrons that things become relatively simple again (in the spirit of classical thermodynamics): whatever excitations of the medium the muon's passage may produce are quickly dissipated and the electronic structure "heals" by the time the muon reaches thermal energies. It is probably a safe assumption that the muon "sees" a pristine environment in metals, except of course for the local distortion of the lattice produced by the muon's charge and its screening cloud of conduction electrons.
In insulators and semiconductors this assumption is dangerous. Whenever a high energy charged particle passes through matter, it leaves behind a trail of positive ions and free electrons (a process generally referred to as radiolysis), and these ubiquitous ions often have a lifetime more than long enough to affect the µSR results.
This is particularly significant because of the large number of µSR applications that exploit the similarity between muonium (Mu) and the hydrogen atoms (H). In many cases the whole point of the experiment is to shed light on the behaviour of H in systems where it is known to exist but cannot easily be observed. Here is the essence of the problem: