Influence of the density of states on the odd-even staggering in the charge distribution of the emitted fragments in nuclear heavy-ion collisions

The fragmentation of thermalized sources is studied using a version of the Statistical Multifragmentation Model which employs state densities that take the pairing gap in the nuclear levels into account. Attention is focused on the properties of the charge distributions observed in the breakup of the source. Since the microcanonical version of the model used in this study provides the primary fragment excitation energy distribution, one may correlate the reduction of the odd-even staggering in the charge distribution with the increasing occupation of high-energy states. Thus, in the framework of this model, such staggering tends to disappear as a function of the total excitation energy of the source, although the energy per particle may be small for large systems. We also find that, although the deexcitation of the primary fragments should, in principle, blur these odd-even effects as the fragments follow their decay chains, the consistent treatment of pairing may significantly enhance these staggering effects on the final yields. In the framework of this model, we find that odd-even effects in the charge distributions should be observed in the fragmentation of relatively light systems at very low excitation energies. Our results also suggest that the odd-even staggering may provide useful information on the nuclear state density.

Figure 1

Charge distribution from the breakup of the ${}^{40}\mathrm{Ca}$ nucleus at different excitation energies, showing primary (a) and final (b) yields, respectively. The standard SMM state density, Eq. (16), is used in all the cases. For details see the text.

Figure 2

Comparison of different observables, from the breakup of the ${}^{40}\mathrm{Ca}$ nucleus, obtained with the standard state density given by Eq. (16) and the improved formula, Eq. (22). For details see the text.

Figure 3

Same as Fig. 1 but the state density is replaced by Eq. (22). For details see the text.

Figure 4

Same as Fig. 3 for the ${}^{80}\mathrm{Zr}$ nucleus. For details see the text.

Figure 5

Average excitation energy of the primary fragments produced in the breakup of ${}^{40}\mathrm{Ca}$ and ${}^{80}\mathrm{Zr}$ nuclei. The vertical dotted lines represent $E_x$ for ${}^{24}\mathrm{Mg},{}^{28}\mathrm{Si}$, and ${}^{32}\mathrm{S}$, as indicated by the arrows and labels. For details see the text.

Figure 6

(a) Comparison between different pairing energies used in this work. (b) and (c) Comparison between the final charge distributions for the fragmentation of ${}^{40}\mathrm{Ca}$ obtained with different symmetry energy parametrizations. For details see the text.