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 β 2 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 ε 2 and the density gradient d ⊥ in the initial state. Using an analytical estimate and a Glauber model, I show that the variances $\langleε^{2}_{2}\rangle$ or $\langle$(δd ⊥ /d ⊥ ) 2 $\rangle$ and skewnesses $\langleε^{2}_{2}δd_{⊥}/d_{⊥}\rangle$ or $\langle(δd_{⊥}/d_{⊥})^{3}\rangle$ have a simple analytical form of a'+b'β$^{2}_{2}$ and a'+[b'+c' cos(3γ)]β$^{3}_{2}$, respectively. From these, I constructed several normalized skewnesses to isolate the γ dependence from that of β 2 and show that the correlations between a normalized skewness and a variance can constrain simultaneously β 2 and γ. Assuming a linear relation with elliptic flow v 2 and mean-transverse momentum [p T ] of final-state particles, v 2 ∝ ε 2 and δ [p T ] / [p T ] ∝ δd ⊥ /d ⊥ , similar conclusions are also expected for the variances and skewnesses of v 2 and [p T ], i.e., a + bβ$^{2}_{2}$ for $\langle v^{2}_{2}\rangle$ and $\langle(δ[p_{T}] / [p_{T}])^{2}\rangle$ and a + [b + c cos (3γ)] β$^{3}_{2}$ for $\langle v^{2}_{2}δ [p_{T}] / [p_{T}]\rangle$ or $\langle(δ[p_{T}] / [p_{T}])^{3}\rangle$. 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 β 2 values, followed by collisions of other species of interest with similar mass number. The (β 2 , γ) values for this species can be inferred directly from the measured variance and skewness observables from these collisions. Finally, the results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.