Effect of environment capacitance on the charging energy of a single tunnel junction

We investigate the effect of a capacitor in the electromagnetic environment on the charging energy of a single tunnel junction, and find that whether the capacitor contributes to the charging energy is determined by the resistance between the tunnel junction and the capacitor. The charging energy is reduced and given by the total capacitance of the junction and the capacitor if the resistance is small, and is unchanged in the opposite limit. This result is relevant to some recent experiments on single tunnel junction. It can also be experimentally tested on parallel connected tunnel junctions.