  Analytical expressions for the binding energy of electrons and positrons in
dielectric clusters, analysed in this work, neglect the elastic effects.
Therefore, we present the density-functional theory for neutral liquid clusters
that experience the spontaneous deformation. Using the 1/R -expansion, $R$
being the cluster radius, the exact analytical expressions for the size
corrections to the chemical potential, surface tension, and atomic density are
derived from the condition of mechanical equilibrium. The problem of
calculation of these corrections is reduced to the calculation of the
quantities for a liquid with a flat surface. The size compression and tension
of density occur in the 1/R and $1/R^{2}$ orders respectively. The sizes of
charged rigid and elastic critical clusters, for which the electron or positron
binding energy is close to zero, are calculated for Xe$_{N}^{-}$, Kr$_{N}^{-}$,
Ar$_{N}^{-}$, Ar$_{N}^{+}$, Ne$_{N}^{+}$, He$_{N}^{+}$. The calculations show
significant contribution of self- compression to the binding energy of excess
electron - in contrast to positron.
