  Conduction electrons interacting with a dynamic impurity can give rise to a
local Fermi liquid. The latter has the same low energy spectrum as an ideal
Fermi gas containing a static impurity. The Fermi liquids's elementary
excitations are however not bare electrons. In the vicinity of the impurity,
they are dressed by virtual particle-hole pairs. Here we study this dressing.
Among other things, we construct a mode-resolved measure of dressing. To
evaluate it in position representation, we have to circumvent the limitations
of the Numerical Renormalization Group, which discretizes the conduction band
logarithmically. We therefore extend Natural Orbital methods, that successfully
characterize the ground state, to describe excitations. We demonstrate that the
dressing profile shows nontrivial powerlaw decay at large distances. Our
Natural Orbital methodology could lay the foundation for calculating the
properties of local Fermi liquid quasiparticles in nontrivial geometries such
as disordered hosts or mesoscopic devices.
