Searching for Solitons in Heavy-Ion Reactions near the Fermi Energy

Solitons are special shape-conserving hydrodynamical solutions that appear in many areas of physics. Here, we explore the existence of such solutions in microscopic descriptions of the heavy ion reaction ¹²C + ²⁸Si → ¹²C^* + 7$α$ in the range E/A=10-65 MeV/u. After recognizing the centrality of the collision and time-reversibility as fundamental requirements for the presence of solitonic ¹²C, we utilize the Hybrid $α$-Cluster model for our analysis with a novel methodology. Our results suggest soliton production for E/A=25-45 MeV/u in the forward direction, with a total cross section being at least in the order of a few $μ$b. This, apart from being encouraging for possible experimental studies, maybe connected to possible toroid states of ²⁸Si at low angular momenta.