Isoscaling in the lattice gas model

Isoscaling behavior is investigated using the isotopic and isobaric yields from an equilibrated thermal source which is prepared by the lattice gas model (LGM) for lighter systems with $A=36$. The isoscaling parameters $\alpha$ and $\beta$ are observed to drop with temperature for the LGM with the asymmetric nucleon-nucleon potential. However, the isoscaling parameters do not show a temperature dependence for the LGM with the symmetric nucleon-nucleon potential. The relative neutron or proton density shows a nearly linear relation with the $N∕Z$ (neutron to proton ratio) of the system.

Figure 1

(Color online) Isoscaling behavior of $R_{21}\left(N\right)$ (the upper panel) and $R_{21}\left(Z\right)$ (the lower panel) at $T=5.0\mathrm{MeV}$.

Figure 2

(Color online) Isoscaling parameter $\alpha$ and $\beta$ extracted in fixed $Z$ from Fig. 1a and $N$ from Fig. 1b, respectively.

Figure 3

(Color online) The absolute value of the isoscaling parameters $\alpha$ and $\beta$ as a function of $T$ from the yield ratios from the sources of ${}^{36}\mathrm{S}$ and ${}^{36}\mathrm{Ca}$. The scattering points are the calculation results for the LGM with asymmetrical nucleon-nucleon potential [Eq. (4)] and the lines represent the results for the LGM with the same nucleon-nucleon potential for unlike and like nucleon pairs [Eq. (5)]. See text for details.

Figure 4

(a) (Color online) The absolute value of the difference of neutron and proton chemical potential ($\Delta {\mu }_n$ and $\mid \Delta {\mu }_p\mid$) as a function of $T$. (b) $(\Delta {\mu }_n-\Delta {\mu }_p)∕2$ as a function of temperature. Solid points are calculated results and line is its second polynomial fit. See text for details.

Figure 5

(Color online) (a) The relative free neutron (solid symbols) or proton (open symbols) density as a function of $N∕Z$ of the system at $T=5\mathrm{MeV}$ for the isoLGM case (squares) and noisoLGM case (circles). (b) The solid and dashed lines represent the ratio ${\rho }_n∕{\rho }_p$ for the isoLGM case and noisoLGM case, respectively. The dotted line shows the initial ${\rho }_n∕{\rho }_p$ assuming neutrons and protons homogeneously distributed in a volume proportional to the nucleon number.