The equation of state and phase diagram of isospin-symmetric chemically equilibrated mixture of alpha particles and nucleons are studied in the mean-field approximation. The model takes into account the effects of Fermi and Bose statistics for nucleons and alphas, respectively. We use Skyrme-like parametrization of the mean-field potentials as functions of partial densities, which contain both attractive and repulsive terms. Parameters of these potentials are chosen by fitting known properties of pure nucleon- and pure alpha matter at zero temperature. The sensitivity of results to the choice of the alpha-nucleon attraction strength is investigated. The phase diagram of the alpha-nucleon mixture is studied with a special attention paid to the liquid-gas phase transitions and the Bose-Einstein condensation of alpha particles. We have found two first-order phase transitions, stable and metastable, which differ significantly by the fractions of alpha particles. It is shown that states with alpha condensate are metastable.
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