Ionization potential of a metal cluster containing vacancies

A consistent procedure for determining the ionization potential of a large metal cluster of radius $R_{N,v}$, consisting of $N$ atoms and $N_v$ vacancies, is proposed. The perturbation theory in small parameters $R_{v}/R_{N,v}$ and $L_{v}/R_{v}$ ($R_{v}$ and $L_{v}$ are average distance between vacancies and the length of electron scattering on vacancies, respectively) is constructed in the effective-medium approximation for the electron ground state energy. The effective vacancy potential profile, the electron scattering phase and length are calculated by the Kohn–Sham method for a macroscopic metal in the stable jelly model. The obtained analytical dependences can be useful to analyze the results of photoionization experiments and to determine the size dependence of the vacancy concentration, including that near the melting temperature.