Light charged clusters emitted in 32 MeV/nucleon ${}^{136,124}\mathrm{Xe}+{}^{124,112}\mathrm{Sn}$ reactions: Chemical equilibrium and production of ${}^3\mathrm{He}$ and ${}^6\mathrm{He}$

Background: The isovector part of the nuclear equation of state remains partly unknown and is the subject of many studies. The degree of equilibration between the two main collision partners in heavy ion reactions may be used to study the equation of state since it is connected to isospin ($N/Z$) transport properties of nuclear matter.

Purpose: We aim to test chemical equilibrium attainment by measuring isotopic characteristics of emitted elements as a function of impact parameter.

Method: We study four ${}^{136,124}\mathrm{Xe}+{}^{124,112}\mathrm{Sn}$ reactions at 32 MeV/nucleon. The data were acquired with the INDRA detector at the GANIL (Caen, France) facility. Combined (projectile+target) systems are identical for two studied reactions, therefore it is possible to study the path towards chemical equilibrium from different neutron to proton ratio ($N/Z$) entrance channels. The study is limited to identified isotopes detected in the forward part of the center of mass in order to focus on the evolution of projectile-like fragment isotopic content and the benefit of excellent detection performances of the forward part of the apparatus.

Results: Light charged particle productions, multiplicities, and abundance ratios dependence against impact parameter are studied. It is measured to almost identical mean characteristics for the two ${}^{124}\mathrm{Xe}+{}^{124}\mathrm{Sn}$ and ${}^{136}\mathrm{Xe}+{}^{112}\mathrm{Sn}$ systems for central collisions. Comparing all four studied systems it is shown that mean values evolve from projectile $N/Z$ to projectile+target $N/Z$ dependence. Those identical mean characteristics concern all light charged particles except ${}^3\mathrm{He}$ whose mean behavior is strongly different.

Conclusions: Our inclusive analysis (no event selection) shows that $N/Z$ equilibration between the projectile-like and the target-like is realized to a high degree for central collisions. The light charged particle production mean value difference between ${}^{124}\mathrm{Xe}+{}^{124}\mathrm{Sn}$ and ${}^{136}\mathrm{Xe}+{}^{112}\mathrm{Sn}$ systems for central collisions is of the order of a few %. This slight difference could be explained by pre-equilibrium particle emission whose intensity may differ for the two reactions. This point is demonstrated using ${}^3\mathrm{He}$ mean characteristics whose production takes place before chemical equilibrium attainment. The realized $N/Z$ balance between projectile-like and target-like does not imply a pure two-body mechanism. Indeed a midrapidity production of light charged particle does exist and its $N/Z$ is different as compared to the projectile-like one: it is $n$ enriched. This point is touched using ${}^6\mathrm{He}$ midrapidity production which is favored by the drift phenomenon.

Figure 1

Top: sum of light charged particle transverse energy distribution for the four studied reactions. Light charged particles refer to H and He isotopes detected in the forward part of the center of mass (minimum bias sample). Bottom: zoom of the left part of the top figure.

Figure 2

Relationship between the impact parameter evaluator and the reduced impact parameter for the four studied reactions (minimum bias samples).

Figure 3

${}^2\mathrm{H}$ Galilean invariant center of mass velocity contour plots for different impact parameter evaluator ranges ($z$ scale: counts per ${\mathrm{cm}}^2/{\mathrm{ns}}^2$, bin size: $0.32\times 0.72 {\mathrm{cm}}^2/{\mathrm{ns}}^2$). The ${}^{124}\mathrm{Xe}+{}^{124}\mathrm{Sn}$ minimum bias sample was used.

Figure 4

${}^2\mathrm{H}$ Galilean invariant center of mass velocity contour plots for different impact parameter evaluator ranges ($z$ scale: counts per ${\mathrm{cm}}^2/{\mathrm{ns}}^2$, bin size: $0.32\times 0.72 {\mathrm{cm}}^2/{\mathrm{ns}}^2$). The ${}^{124}\mathrm{Xe}+{}^{124}\mathrm{Sn}$ minimum bias sample was used.

Figure 5

Ratio between ${\left(\mathrm{\Sigma }{E}_t\right)}_{\mathrm{fw}\mathrm{c}.\mathrm{m}.}^{lcp}$ distributions of $M_{\mathrm{trigger}}^{\min }=4$ (off-line condition) and $M_{\mathrm{trigger}}^{\min }=1$ for the four studied reactions. The minimum bias samples were used.

Figure 6

Forward center of mass light charged isotope productions for each studied reaction as a function of the impact parameter evaluator (minimum bias samples).

Figure 7

Forward center of mass light charged isotope mean multiplicities for each studied reaction as a function of the impact parameter evaluator (mixed samples).

Figure 8

Ratios of mean light charged isotope multiplicities between the ${}^{124}\mathrm{Xe}+{}^{124}\mathrm{Sn}$ and ${}^{136}\mathrm{Xe}+{}^{112}\mathrm{Sn}$ systems. In order to present the data in two pictures, a constant value (1 or 2) is added to certain ratios (mixed samples).

Figure 9

Forward center of mass cluster abundance ratios for each studied reaction as a function of the impact parameter evaluator (mixed samples). Particles emitted forward ($0^{\circ }–{30}^{\circ }$).

Figure 10

Forward center of mass cluster abundance ratios for each studied reaction as a function of the impact parameter evaluator (mixed samples). Particles emitted perpendicular to the beam direction (${60}^{\circ }–{90}^{\circ }$).

Figure 11

Forward center of mass ${}^3\mathrm{He}$ mean multiplicities for each studied reaction as a function of the impact parameter evaluator (mixed samples). Top: particles emitted forward ($0^{\circ }–{30}^{\circ }$). Bottom: particles emitted perpendicular to the beam direction (${60}^{\circ }–{90}^{\circ }$).

Figure 12

Forward center of mass ${}^3\mathrm{He}$ mean abundance ratios for each studied reaction as a function of the impact parameter evaluator (mixed samples). Abundance ratio values are in %. Top: particles emitted forward ($0^{\circ }–{30}^{\circ }$). Bottom: particles emitted perpendicular to the beam direction (${60}^{\circ }–{90}^{\circ }$).

Figure 13

Forward center of mass ${}^2\mathrm{H}, {}^3\mathrm{H}, {}^3\mathrm{He}, {}^4\mathrm{He}, {}^6\mathrm{He}$ fractions for each studied reaction as a function of the impact parameter evaluator (mixed samples). lcp fractions are ${60}^{\circ }–{90}^{\circ }$ divided by $0^{\circ }–{30}^{\circ }$ lcp abundance ratios. In order to present the data in two pictures, a constant value (1 or 2) is added to certain fractions.