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 ${\mathrm{UV}}_{14}$ 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.

• Received 31 January 2000

DOI:https://doi.org/10.1103/PhysRevC.62.044308