Kondo screening in gapless magnetic alloys

The low-energy physics of a spin-1/2 Kondo impurity in a gapless host, where a density of band states $\rho_0(\epsilon)=|\epsilon|^r/(|\epsilon|^r+\beta^r)$ vanishes at the Fermi level $\epsilon=0$, is studied by the Bethe ansatz. The growth of the parameter $\Gamma_r=\beta{\rm g}^{-1/r}$ (where ${\rm g}$ is an exchange constant) is shown to drive the system ground state from the Kondo regime with the screened impurity spin to the Anderson regime, where the impurity spin is unscreened, however, in a weak magnetic field $H$, it exceeds its free value, $S_i(H)>{1/2}$, due to a strong coupling to a band. It is shown also that a sufficiently strong potential scattering at the impurity site destroys the Anderson regime.