State equation for the three-dimentional system of"collapsing"hard spheres

**The Chelyabinsk State Pedagogical University, the Department of Mathematics By Wertheim method the exact solution of the Percus-Yevick integral equation for a system of particles with the “repulsive step potential” interacting (“collapsing”hard spheres) is obtained. On the basis of this solution the state equation for the “repulsive step potential” is built and determined, that the Percus-Yevick equation does not show the Van der Waalse loop for “collapsing” hard spheres.