Second cluster integral and excluded volume effects for the pion gas - art. no. 044901

The quantum mechanical formula for Mayer's second cluster integral for the gas of relativistic particles with hard-core interaction is derived. The pr oper pion volume calculated with quantum mechanical formula is found to be an order of magnitude larger than its classical evaluation. The second clus ter integral for the pion gas is calculated in quantum mechanical approach accounting for both attractive and hard-core repulsive interactions. It is shown that, in the second cluster approximation, the repulsive pi pi -inter actions as well as the finite width of resonances give important but almost canceling contributions. In contrast, an appreciable deviation from the id eal gas of pions and pion resonances is observed beyond the second cluster approximation in the framework of the Van der Waals excluded-volume model.