Finite-size effects in isobaric ratios

The properties of isobaric ratios, between nuclei produced in the same reaction, are investigated using the canonical and grand-canonical statistical ensembles. Although the grand-canonical formulas furnish a means to correlate the ratios with the liquid drop parameters, finite size effects make it difficult to obtain their actual values from fitting nuclear collision data.

Figure 1

isobaric ratios calculated for odd-$A$ nuclei and for different system sizes in the framework of the canonical ensemble at $T=6.0$ MeV. The fit to the linear behavior shown in the figure gives $\Delta \mu /T=0.55$, 0.95, 1.52, and 2.00, while $a_c^{*}/T=0.420$, 0.280, 0.178, and 0.057 for the $(48,20)$, $(72,30)$, $(96,40)$ and $(384,160)$ nuclei, respectively. Results obtained with the grand-canonical ensemble (solid line) as well as ratios calculated with the experimental data of Ref. [20] (full circles symbols) are also shown.

Figure 2

Size dependence of the fit parameters obtained with the canonical model. The dashed lines show the values predicted by the grand-canonical approach, i.e., $a_c^{*}/T=0.0368$ and $\Delta \mu /T=2.091$. For details, see the text.