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Equation of state with quantum statistics corrections is derived for amulti-component gas of particles interacting through the repulsive andattractive van der Waals (vdW) forces up to first few orders over a smallparameter $\delta \approx \hbar^3 n(mT)^{-3/2}[g(1- bn)]^{-1}$, where $n$ and$T$ are the particle number density and temperature, $m$ and $g$ the particlemass and degeneracy factor. The parameter $b$ corresponds to the vdW excludedvolume. For interacting system of Fermi nucleon and Bose $\alpha$ particles, asmall impurity of $\alpha$ particles to the nucleon system at leading firstorder in both $\alpha $ particle and nucleon small parameters $\delta $ doesnot change much the basic results for the symmetric nuclear matter. Theparticle number fluctuations $\omega$ determined by the isothermalin-compressibility $\mathcal{K}(n,T)$ can be obtained analytically at the samefirst order quantum-statistics approximation for symmetric nucleon matter. Ourapproximate analytical results appear to be in good agreement with the accuratenumerical calculations.

Quantum statistics effects and fluctuations of particle numbers near the critical point of nuclear matter