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We investigate the phase transition of Bose-Einstein particles with thehard-core repulsion in the grand canonical ensemble within the Van der Waalsapproximation. It is shown that the pressure of non-relativistic Bose-Einsteinparticles is mathematically equivalent to the pressure of simplified version ofthe statistical multifragmentation model of nuclei with the vanishing surfacetension coefficient and the Fisher exponent $\tau_F = \frac{5}{2}$, which forsuch parameters has the 1-st order phase transition. The found similarity ofthese equations of state allows us to show that within the present approach thehigh density phase of Bose-Einstein particles is a classical macro-cluster withvanishing entropy at any temperature which, similarly to the classical hardspheres, is a kind of solid state. To show this we establish new relationswhich allow us to identically represent the pressure of Fermi-Dirac particlesin terms of pressures of Bose-Einstein particles of two sorts.

Bose-Einstein Condensation of Quantum Hard-Spheres as a Deposition Phase Transition and New Relations Between Bosonic and Fermionic Pressures