Exploring proton rich systems and Coulomb induced instabilities

The thermodynamic properties of proton rich systems are explored in a mean field approach which is generated from a Skyrme interaction. The addition of Coulomb interactions result in asymmetries which modify the chemical and mechanical instability of the system and its equilibrium properties. These properties are studied for systems with proton fraction $y$ on the proton richer side of the valley of $\beta$-stability as well as the neutron rich side. Coulomb induced instabilities lead to proton diffusion processes on the proton richer side and also large asymmetries in chemical and mechanical instabilities and coexistence curves. Considering the whole range of $0 \le y \le 1$, we can study how the symmetry about $y=1/2$ is broken by asymmetric interaction and we can also explicitly show that the role between proton and neutron is exchanged around $y_E$. It is shown that there are two asymmetric coexistence surfaces in $(y, P, T)$ space, one for $y < y_E$ and another for $y > y_E$ and touching each other at $y_E$. These asymmetries in instabilities show up as new branches, one for $y < y_E$ and one for $y > y_E$, and thus form a closed loop in pressure versus $\rho$ for both chemical instability and coexistence regions. The branch of $y > 1/2 > y_E$ was not previously investigated since only the $y < 1/2$ region is usually considered. In our simplified model, mechanical instability is still symmetric around a point $y_E \ne 1/2$ even with Coulomb forces present.