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 beta(2) and triaxiality gamma. 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 epsilon 2 and the density gradient d(perpendicular to) in the initial state. Using an analytical estimate and a Glauber model, I show that the variances <epsilon(22)> or <(delta d(perpendicular to)/c(perpendicular to))(2)> and skewnesses <epsilon(2)(2)delta d(perpendicular to)/d(perpendicular to))> or <(delta d(perpendicular to)/d(perpendicular to))(3)> have a simple analytical form of a' + b'beta(2)(2) and a' + [b' + c' cos (3 gamma)]beta(3)(2), respectively. From these, I constructed several normalized skewnesses to isolate the y dependence from that of beta(2) and show that the correlations between a normalized skewness and a variance can constrain simultaneously beta(2) and gamma. Assuming a linear relation with elliptic flow v(2) and mean-transverse momentum [p(T)] of final-state particles, v(2) alpha epsilon(2) and delta[p(T)]/[p(T)] alpha delta d(perpendicular to)/d(perpendicular to), similar conclusions are also expected for the variances and skewnesses of v(2) and [P-T], i.e., alpha + b beta(2)(2) for < v(2)(2)> and <(delta[p(T)]/[p(T)])(2)) and a + [b + c cos(3 gamma)]beta(3)(2). for < v(2)(2)delta[p(T)]l[p(T)])> or ((delta[p(T)]/[p(T)])(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(3 gamma) approximate to 1, and near oblate nuclei, cos(3 gamma) approximate to -1, with known beta(2) values, followed by collisions of other species of interest with similar mass number. The (beta(2, )gamma) 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.