Exploiting neutron-rich radioactive ion beams to constrain the symmetry energy

The Modular Neutron Array (MoNA) and 4 Tm Sweeper magnet were used to measure the free neutrons and heavy charged particles from the radioactive ion beam induced ${}^{32}$Mg+${}^9$Be reaction. The fragmentation reaction was simulated with the constrained molecular dynamics model (CoMD), which demonstrated that the $\langle N/Z\rangle$ of the heavy fragments and free neutron multiplicities were observables sensitive to the density dependence of the symmetry energy at subsaturation densities. Through comparison of these simulations with the experimental data, constraints on the density dependence of the symmetry energy were extracted. The advantage of radioactive ion beams as a probe of the symmetry energy is demonstrated through examination of CoMD calculations for stable and radioactive-beam-induced reactions.

Figure 1

(a) Average $N/Z$ as a function of the charge of the fragments. Linear fits to the experimental (dashed black line) and CoMD (solid colored [gray] lines) results are shown to guide the eye. (b) Yield of the different elements produced in the ${}^{32}$Mg+${}^9$Be reaction normalized to the $Z=11$ fragments. (c) Hit multiplicity distribution measured in MoNA in coincidence with the $Z=9$ fragments normalized to the multiplicity $=$ 1 events. In each panel, the experimental results are shown as solid black circles and the open data symbols represent the filtered CoMD simulations with different values of $L$, as described by the legend. In panels (a) and (b), lines are only shown for the $Z=4–9$ fragments denoting the region used to extract constraints on $E_{\mathrm{sym}}\left(\rho \right)$. In the insert of panel (c) the unfiltered average neutron multiplicity is shown as a function of the charge of the residue from the CoMD simulation.

Figure 2

θ and velocity distributions for the neutron hits within MoNA in coincidence with $Z$ $=$ 4 fragments. The experimental distributions are shown as the solid circles and the filtered $L$ $=$ 78 MeV CoMD simulations are shown as the filled green (gray) contours.

Figure 3

The solid blue (gray) area represents the constraints extracted from the present work on the slope ($L$) and magnitude at ${\rho }_0$ of the symmetry energy. The gray hashed region indicates the heavy-ion collisions constraints from Ref. [22]. Additional constraints from heavy-ion collisions are shown from Refs. [26], [2], [53], and [28] as a lower limit, solid circle, open circle, and solid square, respectively. The $E_{\mathrm{sym}}\left({\rho }_0\right)$ of the open circle was offset by 0.1 MeV for clarity. The dotted red (gray) line box [10], long-dashed red (gray) line box [54], and solid red (gray) line lower limit [55] represent recent constraints extracted from neutron star properties.

Figure 4

(a) Average $N/Z$ as a function of the charge of the residue fragment. (b) Average $N/Z$ of $Z$ $=$ 4–11 fragments as a function of the collision time. The results are shown from the ${}^{32}$Mg+${}^9$Be and ${}^{24}$Mg+${}^9$Be CoMD simulations for different slopes of the symmetry energy.