  We consider a single \down atom within a Fermi sea of \up atoms. We elucidate
by a full many-body analysis the quite mysterious agreement between Monte-Carlo
results and approximate calculations taking only into account single
particle-hole excitations. It results from a nearly perfect destructive
interference of the contributions of states with more than one particle-hole
pair. This is linked to the remarkable efficiency of the expansion in powers of
hole wavevectors, the lowest order leading to perfect interference. Going up to
two particle-hole pairs gives an essentially perfect agreement with known exact
results. Hence our treatment amounts to an exact solution of this problem.
