Lattice gas model with isospin-dependent interactions

In this paper we continue the investigation of the lattice gas model. The main improvement is that we use two strengths for bonds: one between like particles and another between unlike particles to implement the isospin dependence of nuclear force. The main effect is the elimination of unphysical clusters, such as the dineutron or diproton. It is therefore a better description of a nuclear system. The equation of state in mean field theory is obtained for nuclear matter as well as for $N\ne Z$ systems. Through numerical and analytical calculation we show that the new model maintains all the important features of the older model. We study the effect of the Coulomb interaction on multifragmentation of a compound system of $A=86\mathrm{}$, $Z=40\mathrm{}$, and also for $A=197\mathrm{}$, $Z=79\mathrm{}$. For the first case the Coulomb interaction has small effect. For the latter case the effect is much more pronounced but typical signatures of the lattice gas model such as a minimum (maximum) in the value of $\tau$ ${(S}_2)$ are still obtained but at a much lower temperature.