Coulomb blockade in metallic grains at large conductance

We study Coulomb blockade effects in the thermodynamic quantities of a weakly disordered metallic grain coupled to a metallic lead by a tunneling contact with a large conductance $g_T.$ We consider the case of broken time-reversal symmetry and obtain expressions for both the ensemble averaged amplitude of the Coulomb blockade oscillations of the thermodynamic potential and the correlator of its mesoscopic fluctuations for a finite mean level spacing $\delta$ in the grain. We develop a method that allows for an exact evaluation of the functional integral arising from disorder averaging. The results and the method are applicable in the temperature range $\delta \ll T\ll E_C.$