The Hall coefficient and resistivity of germanium single crystals bombarded with slow neutrons were measured between 1.2 and 300°K. Slow neutron capture and subsequent nuclear transmutation produce majority impurities, gallium atoms, and compensating impurities, arsenic and selenium atoms. p-type samples with a gallium concentration ranging from 8×1014 to 5×1017 per cc with a fixed compensation ratio of 0.40 were thus prepared and the impurity conduction was studied as a function of the average distance between the majority impurities. The effective radius a of the acceptor ground-state wave function is 90.1 A according to Miller's theory of impurity conduction, whereas a=40 A according to Twose's theory. The latter value agrees well with the effective radius of the Kohn-Schechter acceptor wave function. The activation energy of impurity conduction changes slowly with impurity concentration from 3.5×10-4 to 5.9×10-4 ev and agrees well with the predictions of Miller's theory for gallium concentration below 5×1015 per cc. Measurements on samples which contain different dislocation densities but identical impurity concentrations show that up to 104 dislocations per cm2 do not affect impurity conduction.

The Coulomb interaction between localized electrons is shown to create a 'soft' gap in the density of states near the Fermi level. The new temperature dependence of the hopping DC conductivity is the most important manifestation of the gap. The form of the density of states within the gap is discussed.

In this paper we consider the properties of the disordered systems, when the mean free path of electrons is more or comparable with its wave length, i.e. some higher the localization edge. It is shown that the electron-electron interaction in this situation leads to an anomaly in the density of states near the Fermi level. We argue that this anomaly causes that of the tunnel resistance. The minimum in the temperature dependence of the resistivity in the disordered metals may also be due to a similar mechanism.