Transverse collective flow and midrapidity emission of isotopically identified light charged particles

The transverse flow and relative midrapidity yield of isotopically identified light charged particles (LCPs) has been examined for the 35 MeV/nucleon ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$, ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$, and ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ systems. A large enhancement of the midrapidity yield of the LCPs was observed relative to the yield near the projectile rapidity. In particular, this enhancement was increased for the more neutron-rich LCPs demonstrating a preference for the production of neutron-rich fragments in the midrapidity region. Additionally, the transverse flow of the LCPs was extracted, which provides insight into the average movement of the particles in the midrapidity region. Isotopic and isobaric effects were observed in the transverse flow of the fragments. In both cases, the transverse flow was shown to decrease with an increasing neutron content in the fragments. A clear inverse relationship between the transverse flow and the relative midrapidity yield is shown. The increased relative midrapidity emission produces a decreased transverse flow. The stochastic mean-field model was used for comparison to the experimental data. The results showed that the model was able to reproduce the general isotopic and isobaric trends for the midrapidity emission and transverse flow. The sensitivity of these observables to the density dependence of the symmetry energy was explored. The results indicate that the transverse flow and midrapidity emission of the LCPs are sensitive to the denisty dependence of the symmetry energy.

Figure 1

Reduced rapidity ($Y_r$) distribution for (a) ${}^1\mathrm{H}$, (b) ${}^2\mathrm{H}$, (c) ${}^3\mathrm{H}$, (d) ${}^3\mathrm{He}$, (e) ${}^4\mathrm{He}$, and (f) ${}^6\mathrm{He}$ fragments from the 35 MeV/nucleon ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ reaction. The experimental data are shown as the solid black circles and the stiff-SMF calculation is shown as the open red squares. The detector thresholds have been applied to the SMF simulation. Each distribution has been normalized such that the yield at $Y_r=0.0$ equals unity.

Figure 2

$R_{\mathrm{yield}}^{\mathrm{mid}}$ values are shown as a function of the charge times mass ($\mathit{ZA}$) for ${}^1\mathrm{H}$ ($\mathit{ZA}=1$), ${}^2\mathrm{H}$ ($\mathit{ZA}=2$), ${}^3\mathrm{H}$ ($\mathit{ZA}=3$), ${}^3\mathrm{He}$ ($\mathit{ZA}=6$), ${}^4\mathrm{He}$ ($\mathit{ZA}=8$), and ${}^6\mathrm{He}$ ($\mathit{ZA}=12$) particles.

Figure 3

Comparison of the $R_{\mathrm{yield}}^{\mathrm{mid}}$ values from the experimental data (solid black circles) with the stiff (open red squares) and soft (solid green triangles) SMF calculation. The results from the three reaction systems are shown [panels (a)–(c)] and are plotted as a function of the charge times mass ($\mathit{ZA}$) of the LCPs.

Figure 4

Average in-plane momentum, $\langle P_x/A\rangle$, as a function of the reduced rapidity for (a) ${}^1\mathrm{H}$, (b) ${}^2\mathrm{H}$, (c) ${}^3\mathrm{H}$, (d) ${}^3\mathrm{He}$, (e) ${}^4\mathrm{He}$, and (f) ${}^6\mathrm{He}$ particles. The results shown are from the midperipheral collisions of the ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ system. The solid black line represents a linear fit from $-0.35⩽Y_r⩽0.35$.

Figure 5

The experimental flow parameters ($F$) for the $Z=1$ and $Z=2$ fragments are shown as a function of the $N/Z$ of the colliding system, $(N/Z){}_{\mathrm{sys}}$, for the midperipheral collisions. The SMF model results are shown for the $Z=1$ fragments for a stiff and soft $E_{\mathrm{sym}}(\rho )$. The ${}^{64}\mathrm{Zn}$ and ${}^{64}\mathrm{Ni}$ systems, $A_{\mathrm{sys}}=128$, are connected by a solid line.

Figure 6

The extracted flow parameters ($F$) per nucleon (panel a) and inverse $R_{\mathrm{yield}}^{\mathrm{mid}}$ values (panel b) for the ${}^1\mathrm{H}$, ${}^2\mathrm{H}$, ${}^3\mathrm{H}$, ${}^3\mathrm{He}$, ${}^4\mathrm{He}$, and ${}^6\mathrm{He}$ particles are shown as a function of the charge times mass ($\mathit{ZA}$) of the particle. Results are presented from ${}^{64}\mathrm{Ni}$, ${}^{64}\mathrm{Zn}$, and ${}^{70}\mathrm{Zn}$ systems for midperipheral collisions as shown by the legend.

Figure 7

Flow parameter ($F$) per nucleon is shown as a function of the charge times mass ($\mathit{ZA}$) for the midperipheral collisions. The experimental data (black circles) is shown in comparison to the SMF model results, for both a stiff (red squares) and soft (green triangles) parametrization of the symmetry energy. The free neutron flow from the SMF model is offset with a $\mathit{ZA}=0.1$ for clarity.

Figure 8

$R_{{}^3\mathrm{He}{-}^3\mathrm{H}}$, from Eq. (3), is calculated from the ${}^{64}\mathrm{Ni}$, ${}^{64}\mathrm{Zn}$, and ${}^{70}\mathrm{Zn}$ systems for the midperipheral collisions. The results from the experimental data, including the fit error, are represented by the faded blue (gray) region. The estimated systematic error in the experimental results is represented by the red dashed line. The SMF results are shown with (black circles) and without (gray circles) applying the detector thresholds. As described by the legend, results with a soft and stiff density dependence of the symmetry energy are shown from the SMF model.