  The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are
calculated numerically. The ground states of both systems are calculated with
the FAIR (Friedel artificially inserted resonance) theory. The ground state in
the interacting systems is compared with a nullstate in which the interaction
is zero. The different multi-electron states are expressed in terms of Wilson
states. The use of N Wilson states simulates the use of a large effective
number N_{eff} of states. A plot of ln(F) versus N\proptoln(N_{eff}) reveals
whether one has an Anderson orthogonality catastrophe at zero energy. The
results are at first glance surprising. The ln(F)-ln(N_{eff}) plot for the
Kondo impurity diverges for large N_{eff}. On the other hand, the corresponding
plot for the symmetric FA impurity saturates for large N_{eff} when the level
spacing at the Fermi level is of the order of the singlet-triplet excitation
energy. The behavior of the fidelity allows one to determine the phase shift of
the electron states in this regime. PACS: 75.20.Hr, 71.23.An, 71.27.+a,
05.30.-d
