  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.
