  Quantum impurity models are prevalent throughout many body physics, providing
some prime examples of strongly correlated systems. Aside from being of great
interest in themselves they can provide deep insight into the effects of strong
correlations in general. The classic example is the Kondo model wherein a
magnetic impurity is screened at low energies by a non interacting metallic
bath. Here we consider a magnetic impurity coupled to a quantum wire with
pairing interaction which dynamically generates a mass gap. Using Bethe Ansatz
we solve the system exactly finding that it exhibits both screened and
unscreened phases for an antiferromagnetic impurity. We determine the ground
state density of states and magnetization in both phases as well as the
excitations. In contrast to the well studied case of magnetic impurities in
superconductors we find that there are no intragap bound states in the
spectrum. The phase transition is not associated to a level crossing but with
quantum fluctuations.
