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We present a Wilson renormalization group study of the Konda problem in a pseudo-gap Fermi system with density of states p(f -B F ) = CIS -6 ~1 ~. For initial couplings Jo c J, % -2 the impurity spin is quenched, but we find that the model exhibits unusual low-temperature pmpedes unique to pseudo-gap systems. For r < 0.5 the ground stme is characterized by the J = -a fixed point, with a residual magnetic moment and non-vanishing entropy. The magnetic susceptibility is shown to fit the universal curve,, where f (x) is the universal function for the ordinary Kondo pmbiem For I > 0.5 we also find the quenching of the impurity spin, yet there is no Kondo effect exhibited in the mal m w e t i c susceptibility.Many interesting materials can be described with Fermi systems with a pseudo-gap, i.e. a gapless energy spectrum with a vanishing density of states at the Fermi level. This situation arises, for example, in bulk semiconductors and (quasi-) two-dimensional metals when the conduction and valence bands touch at the symmetry points of the Brillouin zone. Some single-particle excitations in anisotropic superconductors also exhibit pseudo-gap spectra.The interaction of magnetic ions with the electrons .of such systems can lead to different properties from those in normal Fermi systems. Obviously interesting questions involve the Kondo effect, generally believed to be a phenomenon associated with the existence of a sharp Fermi surface: does the Kondo effect persist in systems with a small energy gap or a pseudo-gap? If it does, what are the universal properties in the Kondo regime? In this article we present our study of the Kondo model in pseudo-gap Fermi systems. We confine our attention to pseudo-gap Fermi systems partly because we can apply Wilson's RG method using a diagonalization scheme we have developed. The RG calculation permits us to obtain physical intuition about the low-temperature properties as well as some 'almost exact' results.The problem of magnetic impurities in pseudo-gap Fermi systems was first investigated by Withoff and Fradkin 111, who studied the Kondo model with the density of states p ( t ) = Clsl' (with band cut-off Do and Fermi energy set to zero) using perturbative~ scaling and the 1/N expansion to leading order. They argued that, with r > 0, there is a transition as ,the coupling constant J is varied across the critical value Jc c ( -r&: for a weak initial coupling (J, c J c 0), there is no Kondo effect, while for strong initial coupling J < .Ic, there is a Kondo effect with the Kondo temperature vanishing at . I , as TK M IJ -Jcll/r. Thermodynamic properties were nor computed and differences from the Kondo effect in~normal Fermi systems were not investigated. We use Wilson's RG

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