Isotope yields from central ${}^{112,124}\mathrm{Sn}+{}^{112,124}\mathrm{Sn}$ collisions: Dynamical emission?

Isotopic yields for light particles and intermediate mass fragments have been measured for central ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$, ${}^{112}\mathrm{Sn}+{}^{124}\mathrm{Sn}$, ${}^{124}\mathrm{Sn}+{}^{112}\mathrm{Sn}$, and ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions at $E∕A=50\text{MeV}$ and compared with predictions of stochastic mean field calculations. These calculations predict a sensitivity of the isotopic distributions to the density dependence of the asymmetry term of the nuclear equation of state. However, the secondary decay of the excited fragments modifies significantly the primary isotopic distributions and these modifications are rather sensitive to theoretical uncertainties in the excitation energies of the hot fragments. The predicted final isotope distributions are narrower than the experimental data and the sensitivity of the predicted yields to the density dependence of the asymmetry term is reduced.

Figure 1

(Color) Efficiency corrected differential multiplicity $dM∕dyd{p}_{\perp }$ for ${}^{12}\mathrm{C}$ fragments. The cut $70°⩽{\theta }_{\text{c.m.}}⩽110°$ is indicated by the dashed lines in the figure. The color scale in the right side of the figure indicates the relationship between the colors and the values for $dM∕dyd{p}_{\perp }$ in units of $\text{GeV}∕c^{-1}$.

Figure 2

Average differential multiplicities at $70°⩽{\theta }_{\text{c.m.}}⩽110°$ for Li, Be, B, C, N, and O isotopes as a function of neutron excess $(N–Z)$ of the isotope. The solid circles (connected by solid lines to guide the eye) are the data for the ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ system with $N∕Z=1.48$. The solid squares are data for the lightest system ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ with $N∕Z=1.24$. The open diamonds are the averaged values from the two mixed systems, ${}^{124}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ and ${}^{112}\mathrm{Sn}+{}^{124}\mathrm{Sn}$. The dashed and dot-dashed lines are predictions from Eq. (1). See text for more details.

Figure 3

The solid curve and dashed curves indicate the density dependencies for the super stiff and soft asymmetry terms, respectively.

Figure 4

Differential multiplicities for ${}^{112}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions (upper panel) and ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ collisions (lower panel) as a function of the fragment charge (left panels) and the fragment mass (right panels). The points are the data. The dashed and solid lines are the calculated primary and final fragment differential multiplicities, respectively. Statistical uncertainties are shown for the calculations; the corresponding uncertainties in the data are smaller than the data points.

Figure 5

Left panels: Calculated primary (upper panel), calculated final (lower panel), and measured (lower panel) carbon isotopic yields for $\text{Sn}+\text{Sn}$ collisions. Right panels: Calculated primary (upper panel), calculated final (lower panel), and measured (lower panel) mean isospin asymmetries as a function of the fragment charge for Sn+Sn collisions. The lines and data points are further explained in the text.

Figure 6

Upper panel: $R_{21}$ values obtained from the ratios of the primary isotopic distributions for ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions divided by those for ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ collisions. Lower panel: Corresponding $R_{21}$ values obtained from the ratios of the final isotopic distributions. Each line in the two panels corresponds to ratios for a given element. Elements with $Z=2–8$ $(Z=1–8)$ are represented from left to right in the upper (lower) panel. The lines are the result of fitting $R_{21}$ with Eq. (1); the dependencies on neutron number for the best fits are given in each panel.

Figure 7

Upper panel: Dependence of the primary distributions for carbon (left panel) and oxygen (right panel) upon the density dependence of the asymmetry term. Middle panel: Dependence of the final distributions for carbon (left panel) and oxygen (right panel) upon the density dependence of the asymmetry term. The data are also shown as the solid points. The various lines in the figure are described in the text. The excitation energies for the fragments are taken directly from the SMF calculations. Lower panel: The data are the same as in the middle panels. The curves are the calculations obtained when the excitation energies of the primary fragments are reduced by a factor of 2.

Figure 8

Dependence of the scaled function $S\left(N\right)$ on the density dependence of the asymmetry term. The left panel provides a comparison between values for $S\left(N\right)$ computed from the data (solid line) and the calculated primary (points about the dashed line) and final (points about the dotted-dashed line) distributions obtained for the superstiff asymmetry term. The right panel provides a comparison between values for $S\left(N\right)$ computed from the data and the calculated primary and final distributions obtained for the soft asymmetry term.