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

Abstract

Traditional Monte Carlo (MC) Glauber models treat the shapes of deformed nuclei classically; that is, in a collision event, each nucleus is randomly assigned a configuration with fixed deformation parameters and orientation (collective coordinates). Quantum mechanically, however, a valid nuclear ground state must be a superposition of these configurations to preserve rotational symmetry, creating entanglement in the nucleon wave function. We show that for collisions with a moderate number of participants, this quantum superposition -- particularly in the orientation of deformed nuclei -- has non-negligible impacts on the initial geometry of the quark-gluon plasma fireball. We propose a minimal extension to the MC Glauber model to approximately incorporate these superposition effects and find a $6$-$8\%$ reduction in the second-order eccentricity in central Ne-Ne and Ne-Pb collisions relative to results from classical treatments of nuclear orientation. Though these effects are expected to be small for large collision systems such as U-U, this study demonstrates the importance of properly accounting for quantum superposition and the associated off-diagonal information when studying nuclear deformation in ultra-relativistic nuclear collisions.