FERMI-THOMAS RESPONSE OF A METAL SURFACE TO AN EXTERNAL POINT CHARGE

The dielectric response of a semi-infinite metal to a point charge a short distance outside its surface is calculated in the linearized Fermi-Thomas approximation. The general form of the potential in the metal and vacuum is discussed. A generalization of the classical image theorem is given. The energy change on bringing up the charge to the surface is calculated, and found to be in good agreement with a previous approximation due to Gomer and Swanson.