A simplified cluster expansion for the classical real gas

Mayer's expansion of the partition function of a classical real gas in terms of irreducible cluster integrals is derived by a simpler and more direct method. The two principal features of this method are the following. 1. (i) The partition function is expanded in an infinite product rather than a series. As a result the exponential form is obtained immediately: there is no need to sum up infinite sets of graphs. Disconnected graphs never enter. 2. (ii) The calculation leads directly to the canonical N-particle partition function. Neither the fugacity nor the reducible cluster integrals are introduced. The same method is also used to find the expansion of the pair-correlation function. Finally it is applied to the partition function of a real gas in an external potential field