Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions

Most atomic nuclei are deformed with a quadrupole shape described by its overall strength β2 and triaxiality γ. The deformation can be accessed in high-energy heavy ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity 2 and the density gradient d in the initial state. Using an analytical estimate and a Glauber model, I show that the variances (22) or ((δd/d)2) and skewnesses (22δd/d) or ((δd/d)3) have a simple analytical form of a′+b′β22 and a′+[b′+c′cos(3γ)]β23, respectively. From these, I constructed several normalized skewnesses to isolate the γ dependence from that of β2 and show that the correlations between a normalized skewness and a variance can constrain simultaneously β2 and γ. Assuming a linear relation with elliptic flow v2 and mean-transverse momentum [pT] of final-state particles, v2∝2 and δ[pT]/[pT]∝δd/d, similar conclusions are also expected for the variances and skewnesses of v2 and [pT], i.e., a+bβ22 for (v22) and ((δ[pT]/[pT])2) and a+[b+ccos(3γ)]β23 for (v22δ[pT]/[pT]) or ((δ[pT]/[pT])3). My findings motivate a dedicated system scan of high-energy heavy ion collisions at RHIC and LHC to measure triaxiality of atomic nuclei: one first determines the coefficients b and c by collisions of isobaric near prolate nuclei, cos(3γ)≈1, and near oblate nuclei, cos(3γ)≈-1, with known β2 values, followed by collisions of other species of interest with similar mass number. The (β2,γ) values for this species can be inferred directly from the measured variance and skewness observables from these collisions. The results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.