5th International Symposium on Nuclear Symmetry Energy NuSYM15, June 29 - July 2, 2015 Kraków, POLAND

Akira Ono
Tohoku University Sendai, JAPAN

### Cluster formation within transport theory

Abstract
It has been known that light clusters, such as $\alpha$ particles and deuterons, are copiously formed in heavy-ion collisions in various conditions. For example, in Au + Au central collisions at several hundred MeV/nucleon, about 80\% of protons in the system are bound in clusters and heavier fragments. This fact suggests that cluster correlations may play important roles during the dynamical evolution of heavy-ion collisions. Understanding of clusters may be also very important when we try to get information on symmetry energy from heavy-ion collisions. Transport models should be carefully constructed in order to allow the appearance of cluster correlations with the correct probabilities during the time evolution of reactions. In the case of the AMD approach, the two-nucleon collision process has been generalized by allowing one or both of the colliding nucleons $N_1$ and $N_2$ to form clusters with surrounding particles as $N_1+N_2+B_1+B_2\rightarrow C_1+C_2$. We consider clusters ($C_1$ and $C_2$) up to $\alpha$ particles, and they are represented by placing Gaussian wave packets at the same phase space point. In this presentation, I will discuss the effects of cluster correlations in heavy-ion collision dynamics. For neutron-rich reaction systems, a typical effect of cluster formation, in particular $\alpha$-cluster formation, is to enhance the neutron-proton asymmetry of the rest of the system, i.e., $(N-2n_\alpha)/(Z-2n_\alpha) > N/Z$ when $N>Z$. This is at least partly responsible for the enhancement of the neutron-proton (or triton-${}^3\mathrm{He}$) spectrum ratio at low velocities in the center-of-mass frame of expanding and fragmenting neutron-rich systems. Another effect of cluster correlations in expanding systems is that nucleons and clusters cease interacting with each other earlier than in the case without cluster correlations where nucleons continue to interact until a relatively late time. As a consequence, the spectra of emitted particles carry direct information at an earlier time in the case of strong cluster correlations. In central collisions of neutron-rich nuclei at 300 MeV/nucleon, the AMD calculation with cluster correlations shows that the symmetry energy effect on the neutron-proton dynamics at the compression stage is rather directly reflected in the neutron-proton spectra in the final state.