Kondo screening in gapless magnetic alloys

The low-energy physics of a spin- {1}/{2} Kondo impurity in a gapless host, in which the density of band states ρ₀( ɛ)=| ɛ| ^r/(| ɛ| ^r+ β^r) vanishes at the Fermi level ɛ=0, is studied by the Bethe ansatz. It is shown that the growth of the parameter Γ_r= βg ^{-1/ r} (where g is an exchange coupling constant) drives the ground state of the system from the Kondo regime with a screened impurity spin to the Anderson regime, where the impurity spin is unscreened. However, in a weak magnetic field H, the impurity spin exceeds its free value, S _i(H)> {1}/{2}, due to a strong coupling to a band.