From wave-function to fireball geometry: the role of a restored broken symmetry in ultra-relativistic collisions of deformed nuclei

Abstract: In the traditional Monte Carlo Glauber modeling of relativistic collisions involving deformed nuclei, the nuclear shape is interpreted classically; that is, each nucleus in an event is described by a configuration with fixed deformation parameters and orientation (collective coordinates). However, quantum mechanically, a valid ground state must be a superposition, at the amplitude level, of these deformed configurations to preserve rotational and other symmetries. This leads to significant entanglement in the nucleon wave function. For collisions with a moderate number of participants, we show that accounting for this quantum superposition -- particularly in the orientation of deformed nuclei -- can substantially alter the geometric shape of the quark-gluon plasma fireball at the early stage of the collision. By modifying the Monte Carlo Glauber model to approximately incorporate these quantum superposition effects, we find that the second-order eccentricity in Ne-Ne collisions is reduced by approximately $6\%$ compared to classical treatments of nuclear orientation. Even larger impacts are expected for Ne-Pb collisions and for symmetric cumulant observables. These results indicate that quantum entanglement in nuclear structure plays a measurable role in heavy-ion collisions and should be considered when using such collisions to probe nuclear deformation.