Two-loop approximation in the Coulomb blockade problem

We study Coulomb blockade (CB) oscillations in the thermodynamics of a metallic grain which is connected to a lead by a tunneling contact with a large conductance $g_0$ in a wide temperature range, $E_Cg_0^4 e^{-g_0/2}<T<E_C$, where $E_C$ is the charging energy. Using the instanton analysis and the renormalization group we obtain the temperature dependence of the amplitude of CB oscillations which differs from the previously obtained results. Assuming that at $T < E_Cg_0^4 e^{-g_0/2}$ the oscillation amplitude weakly depends on temperature we estimate the magnitude of CB oscillations in the ground state energy as $E_Cg_0^4 e^{-g_0/2}$.