Sum-rule approach in the theory of charged self-compressed dielectric droplets

The formal density-functional theory for neutral droplets that experience a spontaneous deformation is developed. The perturbative analytical expressions for the size corrections to the chemical potential, surface tension, and atomic density are derived from the condition of mechanical equilibrium, using a power series expansion in the inverse of droplet radius R. In this way, the determination of these corrections is reduced to a calculation of the quantities for a liquid with a flat surface. It is shown that the size compression and tension of density occur in the 1/R and 1/R2 orders, respectively. The sizes of charged, rigid and elastic, the so-called critical clusters, for which the binding energy is close to zero, are calculated for ArN−, KrN−, XeN− and ArN+, NeN+, HeN+. The results show significant contribution of self-compression to the binding energy of excess electron and a negligible influence on the positron binding.