On the accuracy of the single-nucleus approximation in the equation of state of hot, dense matter

An analytical formalism is developed for determining the errors committed in the entropy, free energy, pressure, and abundances of hot, dense matter in stellar collapse when it is assumed that all nuclei can be presented by a single isotope. This single-nucleus approximation is the standard Ansatz. A comparison is conducted of the properties of a mixture that contains a realistic spread of nuclei with those that contain a single nucleus and it is shown that despite the wide spread of nuclei possible, thermodynamic functions deviate little from their single-nucleus counterparts. Further, it is shown that a sensible comparison must account for the variations in the free-baryon abundances due to the added degrees of freedom of the ensemble approach. It is found that the fractional deviations of the free-particle abundances never exceed about 12 percent, that the realistic entropy is only 4 - 7 percent higher than that of the simple approach, and that pressures, in the considered density range, are accurate to better than 0.8 percent. The general results of this paper can be easily used to correct the single-nucleus approximation preditions.