Properties of the largest fragment in multifragmentation: A canonical thermodynamic calculation

Many calculations for the production of light and intermediate particles resulting from heavy ion collisions at intermediate energies exist. Calculations of properties of the largest fragment resulting from multifragmentation are rare. In this paper we compute these properties and compare them with the data for the case of gold on carbon. We use the canonical thermodynamic model. The model also gives a bimodal distribution for the largest fragment in a narrow energy range.

Figure 1

Experimental points (from Fig. 1(f) of [6]) are joined by a dotted line to guide the eye. The calculations are exploratory: these are done for a fixed freeze-out density (solid line for $\rho /{\rho }_0=0.25$ and dashed line for $\rho /{\rho }_0=0.39)$. A higher freeze-out density produces a higher value of $\langle Z_{max}\rangle$. In the figures $Z_{max}$ stands for this average value. The calculations shown here include the composites of set 1. See the discussion following Eq. (7) for enumeration of composites included in set 1 and set 2.

Figure 2

It is expected that the freeze-out density will decrease with excitation energy in this energy range. The calculations here use a parametrization $\rho /{\rho }_0=a+b\exp (-c(E^{*}/A_0))$ where $a=0.17,b=0.83$ and $c=0.417$ MeV${}^{-1}$. The solid line uses set 1, the dashed line uses set 2. Experimental data are joined by a dotted line.

Figure 3

Top panel compares experimental data for ${\gamma }_2$ (Fig. 2 of [6]) with calculations. For definition of ${\gamma }_2$, see the text. The solid curve uses set 1 and the dashed curve uses set 2. The bottom panel compares experimental values of RMS of $Z_{max}$ with the canonical calculation. As explained in the text, without an afterburner evaporation calculation, RMS values from theory will significantly overestimate actual RMS. Evaporation will bring the population much closer to the line of maximum stability. For an estimate of effects of evaporation see Fig. 19 of [5]. It is not surprising that with set 2 (dashed curve) calculated values of RMS exceed those calculated with set 1. As more nuclei further from the line of maximum stability are included the effects of evaporation will be stronger.

Figure 4

Theoretical values of the probability of occurrence of a $Z_{max}$ plotted as a function of $Z_{max}$ [see Eq. (8)]. In a small window of $E^{*}$ (equivalently $T$ as shown here) a bimodal distribution is seen. Similar plot of probability of $A_{max}$ against $A_{max}$ also shows bimodality. The plots here use set 1.