Quantitative Calculation of the Spatial Extension of the Kondo Cloud

The internal s-electron polarization in the ground state of a Friedel-Anderson and a Kondo impurity is calculated. The Wilson basis with exponentially fine energies close to the Fermi level is used and expressed in terms of free electron waves with linear energy-momentum dispersion. It is found that in the singlet state the magnetic moment of the d-electron is screened by an s-electron cloud. The linear extension of the cloud is inversely proportional to the Kondo energy. When the singlet state is destroyed the polarization cloud is absent.