Unified scaling theory of the Electron Box for arbitrary tunneling strength

Electron tunneling leads to screening of the charge of small islands. Theeffect is strongest near degeneracy points of the charging energy. In orderto describe the low energy physics of strong tunneling we introduce atwo-stage scaling theory. In this unified theory several contradictingearlier descriptions find a natural interpretation. Nonperturbative expressionsare derived for the energy levels, decay rates, and charge of the island.The strong renormalization of the effective capacitance of the junction isconfirmed by Monte Carlo simulations.