Friedel oscillations and the Kondo screening cloud

We show that the long-distance charge-density oscillations in a metal induced by a weakly coupled spin-1/2 magnetic impurity exhibiting the Kondo effect are given, at zero temperature, by a universal function F(r/xi(K)), where r is the distance from the impurity and xi(K) is the Kondo screening cloud size hv(F)/(k(B)T(K)), where vF is the Fermi velocity and T(K) is the Kondo temperature. F is given by a Fourier-like transform of the T matrix. Analytic expressions for F(r/xi K) are derived in both limits r << xi(K) and r >> xi(K) and F is calculated for all r/xi K using numerical methods.