Two-loop approximation in the Coulomb blockade problem

We study Coulomb blockade (CB) oscillations in the thermodynamics of a metallic grain connected to a lead by a tunneling contact with a large conductance g(o) in a wide temperature range, Ecg(o)(4) (-go/2)<T<E-c, where E-c is the charging energy. Using the instanton analysis and the renormalization-group approach we obtain our main result, the temperature dependence of the amplitude of CB oscillations, which differs from the previously obtained results. Assuming that at T<E(c)g(o)(4) e(-) (g0/2) the oscillation amplitude weakly depends on temperature we estimate the magnitude of CB oscillations in the ground-state energy as proportional toE(c)g(o)(4)e(-g0/2).