Isoscaling of fragments with $Z=1\text{−}17$ from reconstructed quasiprojectiles

In heavy-ion collisions, isoscaling provides a method for studying the evolution of nuclear symmetry energy as a function of excitation energy. One challenge in using isoscaling is to accurately determine the neutron-to-proton ratio ($N/Z$) of the fragmenting source. Isoscaling results are presented for the reactions of ${}^{86,78}\mathrm{Kr}+{}^{64,58}\mathrm{Ni}$ at 35 MeV/nucleon taken on the NIMROD-ISiS array at Texas A&M University. The $N/Z$ of the source was calculated from the isotopically identified fragments and experimentally measured neutrons emitted from reconstructed quasiprojectiles. These data exhibit isoscaling for elements with $Z=1\text{−}17$ over a broad range of isotopes. The isoscaling parameter $\alpha$ is shown to increase with increasing difference in the neutron composition (Δ) of the compared sources. For a selected Δ, the ratio $\alpha$/Δ is also shown to decrease with increasing excitation energy. This may reflect a corresponding decrease in the nuclear symmetry energy.

Figure 1

Left: Raw data from $\Delta E\text{−}E$ with Si-CsI detectors. Right: Projected, linearized data for $Z=4$ isotopes. The $x$ axis is $L_X$.

Figure 2

Isotopic yield ratios. Top: System-to-system isoscaling ${}^{86}\mathrm{Kr}+{}^{64}\mathrm{Ni}$, ${}^{78}\mathrm{Kr}+{}^{58}\mathrm{Ni}$. Middle: Isoscaling using neutron-rich and neutron-poor bins on the reconstructed, bound $N/Z$ of the quasiprojectile. Bottom: Isoscaling using neutron-rich and neutron-poor bins on the reconstructed, neutron-corrected $N/Z$ of the quasiprojectile (see text).

Figure 3

Neutron-corrected $N/Z$ of the quasiprojectiles obtained from the ${}^{86}\mathrm{Kr}+{}^{64}\mathrm{Ni}$ (triangles), ${}^{78}\mathrm{Kr}+{}^{58}\mathrm{Ni}$ (squares) reacting systems. The total yield of each system was normalized to unity. The neutron-corrected $N/Z$ of the quasiprojectiles obtained from the combined systems are plotted as stars. The total yield was normalized to 4 for this distribution. Five zones are defined with $N/Z_{\mathrm{QP}}=0.9\text{−}0.96$ (bin 1), 1.0–1.06 (bin 2), 1.1–1.16 (bin 3), 1.2–1.26 (bin 4), and 1.3–1.36 (bin 5).

Figure 4

Left: $S(N)$ as a function of particle neutron number. The error bars are smaller than the size of the point. Elemental symbols are the same as shown in Fig. 2. Right: Isoscaling parameter $\alpha$ from the fitting of the yield ratios of each $Z$. The global fitting $\alpha$ is depicted by the solid line.

Figure 5

Global $\alpha$ fits to combinations of the five bins in $N/Z$ (0.90–0.96, 1.0–1.06, 1.1–1.16, 1.2–1.26, and 1.3–1.36) as a function of the calculated average $\Delta (Z/A){}^2$ of the sources. An additional point (triangle) is added from the isoscaling of ${}^{86}\mathrm{Kr}+{}^{64}\mathrm{Ni}$ and ${}^{78}\mathrm{Kr}+{}^{58}\mathrm{Ni}$ using a single $N/Z$ bin 2 for each system. The propagated error on these values, where not visible, are smaller than the size of the points.

Figure 6

Isoscaling $\alpha$ parameter as a function of the $E^{*}/A$ (MeV) of the reconstructed source. The source $N/Z$ bins were chosen as 2 and 4. The propagated errors, based on yield as described in the text, are smaller than the size of the points.