In the stable jellium model, inelastic scattering of positrons by vacancies of a metal is considered. This results in the expression for positron’s positioning probability dependence in a vacancy vs of its energy before localization and temperature of the metal. The calculations are performed using self-consistent profiles of vacancy potentials and wave functions of positrons in Al, Cu and Zn. After energy averaging of thermalized positrons, the rate value of positron localization in a vacancy at a fuse temperature, such as Al, ∼ 1011 s−1, which is less than the annihilation rate, but by magnitude order coincides with it. The formula for the velocity of localization can increase the accuracy of the vacancies concentration values in the testsample according to the positron radiation annihilation spectroscopy. On the analysis basis of the vacancies concentration and the injection of positrons into 3D-metal, the interpretation of the shift in energy distribution of the positrons during the reverse emission is given. This interpretation is observed in the experiments. Taking into account the near-surface layer of vacancies charged by localized positrons, which creates a two-dimensional barrier for positrons of reverse emission. For Al self-consistently calculated the value of the relative vacancy concentration (∼ 0.2%) in such twodimensional layer, which corresponds to the shift in the energy distribution by 1 eV. Using the scattering length of electrons in vacancies (Born approximation), an analytic theory of the vacancy effect on electron work function from non-transitional 3D-metals and the potential of large clusters ionization, which are containing vacancies, have been developed. Energy displacement of electrons’ ground state in a spherical metallic cluster, which is presented by a series of dimensional corrections, are calculated. The limitations of applicability of the corresponding expansion in series by exponents of the cluster inverse radius are determined: R−1: N ≥ 9.4·103(R > 4.5 nm) and N ≥ 5.46 · 104(R > 6 nm) for sodium and aluminum, accordingly. The obtai20 ned analytical expressions allow to increase the accuracy of concentration values of vacancies in large clusters, which are obtained from the analysis of the results of photoionization experiments. The quantum-dimensional dependences of the ionization potential, electron affinity, electric capacitance, cohesion and dissociation energies for charged small clusters RbN, KN, NaN, LiN, MgN and AlN(N ≤ 270) with and without monovacance (for comparison) are calculated on the basis of the Kohn-Sham method. The dimensional dependences of these quantities are oscillating with approximation to their dimensional asymptotes ∼ R−1 and strive to the corresponding characteristics of infinite 3D-samples. It was found that the magic numbers of atoms for non-defect clusters and clusters with vacancies are different, especially for magnesium and aluminum. The presence of even one vacancy and a single charge in a cluster leads to noticeable changes in all characteristics of it. The Kohn-Sham method is used in calculation of the quantumdimensional dependences of the energy of vacancy formation in charged small clusters by Schottky’s and ’bubble blowing’ mechanisms. Asymptotes of dimensional dependences for these two mechanisms are different from each other and are weakly dependent of the number of atoms in the cluster. The nature of the dimensional dependence of the vacancy formation energy from excess charge in the cluster is entirely determined by the dimensional dependences of the ionization potential of the cluster and the electron affinity.
