  A neutral scalar meson interacting with a fixed isoscalar nucleon is evolved
according to the similarity renormalization group. The fixed source ends up
being too singular and an appropriately dressed static source arises from the
similarity flow. The fixed source is dressed by a virtual cloud of mesons
extending out past the inverse meson mass according to the Yukawa potential.
For low energies the source produces a Yukawa mean field which decouples from
the remaining meson field fluctuations. The renormalization group procedure for
effective particles is also illustrated for this fixed-source model.
