Enhancement of Electron Density around Positive Point Charges in Metals and Lifetimes of Positrons

By means of approximate self-consistent field calculations using a model of a finite metal with ∼2000 electrons, it is shown that over the range of densities appropriate to metals under normal conditions, the density at the position of a single positive charge varies by a factor of about 2, whereas the variation in the mean electron density ($\frac{3}{4\pi {r_s}^3}$) is an order of magnitude greater. In a simple Hartree calculation of the type reported here, a bound state occurs when $r_s>4\mathrm{}$ atomic units. Some brief remarks are made on the application of these results to the calculation of the lifetimes of positrons in various metals.