Isoscaling: Geometry, correlations and symmetry energy

This work uses a simple model to understand the properties of isoscaling. Using a generalized percolation model, it is first shown that isoscaling is a general property of fragmenting systems. In particular, it is found that the usual isoscaling property can be seen as a limit case of bond percolation in lattices in D dimensions, with N colors, with independent probabilities for each color, and for any regular topology. The effect of introducing correlations is also studied.

Figure 1

(Color online) Typical result of the calculation of the quotients in $R_{21}$.

Figure 2

(Color online) Mean number of nearest neighboring protons to a proton. Black circles for a 16X16 lattice and 128 protons. Red square for a 20X20 lattice with the same number of protons.

Figure 3

(Color online) α (black circles) and absolute value of β (red squares) coeficients as a function of temperature, dashed lines correspond to the values of the coefficients for the homogeneous percolation problem or to the infinite temperture limit.

Figure 4

(Color online) Isoscaling deppendence on a. Open symbols stand for $a=0$, full symbols represent $a=-4$.

Figure 5

(Color online) Binding energies for different values of a for $Z=50$ and $40<N<60$. Blue circles stand for results with $a=0$, red squares for $a=-3$ and brown diamonds for $a=-4$.