  The problem of a single down spin particle interacting with a Fermi sea of up
spin particles is of current interest in the field of cold atoms. The Hubbard
model, appropriate to atoms in an optical lattice potential, is considered in
parallel with a gas model. As the strength of an attractive short-range
interaction is increased there is a crossover from "polaron" behaviour, in
which the Fermi sea is weakly perturbed, to "molecule" behaviour in which the
down spin particle is bound to a single up spin particle. It is shown that this
is a smooth crossover, not a sharp transition as claimed by many authors.
