Temperature effects in nuclear isoscaling

The properties of the nuclear isoscaling at finite temperature are investigated and the extent to which its parameter $\alpha$ holds information on the symmetry energy is examined. We show that, although finite temperature effects invalidate the analytical formulas that relate the isoscaling parameter $\alpha$ to those of the mass formula, the symmetry energy remains the main ingredient that dictates the behavior of $\alpha$ at finite temperatures, even for very different sources. This conclusion is not obvious as it is not true in the vanishing temperature limit, where analytical formulas are available. Our results also reveal that different statistical ensembles lead to essentially the same conclusions based on the isoscaling analysis, for the temperatures usually assumed in theoretical calculations in the nuclear multifragmentation process.

Figure 1

Apparent symmetry energy coefficient $C_{\mathrm{sym}}^{\mathrm{Unc}}/\mathrm{Cor}$ for different systems (with $\Delta (Z/A){}^2=0.147$) calculated with the G.C. ensemble for the LDM1 formula. The dashed lines correspond to $a_v{k}_v=22.39$ MeV. For details, see the text.

Figure 2

Same as Fig. 1 for the LDM2 formula. The dashed lines correspond to $a_v{k}_v=27.80$ MeV. For details, see the text.

Figure 3

Isoscaling parameter $\alpha$ calculated with the LDM1 formula. For details, see the text.

Figure 4

Uncorrected apparent symmetry energy coefficient $C_{\mathrm{sym}}^{\mathrm{Unc}}$ calculated from the LDM2 formula for ${\epsilon }_0=4$ MeV (upper panel). The bottom panel shows a comparison between the results obtained with ${\epsilon }_0=4$ MeV and ${\epsilon }_0=16$ MeV. For details, see the text.

Figure 5

Isoscaling parameter $\alpha$ calculated with the M.C., G.C., and canonical ensembles for the LDM1 and LDM2 formulas. For details, see the text.