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The method of lowest-order constrained variational calculations,
which predicts semiempirical data for nuclear matter reasonably
well, is used to calculate the equation of state of beta -stable
matter at finite temperature. The Reid soft-core potential, with
and without N- Delta interactions, as well as the $UV_{14}$
potential which fit the N-N scattering data, are considered in the
nuclear many-body Hamiltonian. In the total Hamiltonian, the
electron and muon are treated relativistically at given
temperature and density, in order to neutralize the fluid
electrically and stabilize it against beta decay. The calculation
is performed for a wide range of baryon densities and temperatures
which are of interest in astrophysics. The free energy, entropy,
proton abundance, etc., of nuclear beta -stable matter are
calculated. It is shown that by increasing the temperature, the
maximum proton abundance is pushed towards lower densities while
the maximum itself increases as the temperature is increased. The
proton fraction is not sufficient to produce any gas-liquid phase
transition. Finally, we obtain an overall agreement with other
many-body techniques, which are available only at zero
temperature.
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