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 ${\varepsilon }_2$ and the density gradient $d_{\perp }$ in the initial state. Using an analytical estimate and a Glauber model, I show that the variances $\langle {\varepsilon }_2^2\rangle$ or $\langle {(\delta d_{\perp }/d_{\perp })}^2\rangle$ and skewnesses $\langle {\varepsilon }_2^2\delta d_{\perp }/d_{\perp }\rangle$ or $\langle {(\delta d_{\perp }/d_{\perp })}^3\rangle$ have a simple analytical form of $a^{\prime }+b^{\prime }{\beta }_2^2$ and $a^{\prime }+[b^{\prime }+c^{\prime }cos\left(3\gamma \right)]{\beta }_2^3$, respectively. From these, I constructed several normalized skewnesses to isolate the $\gamma$ 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 $\left[p_{\mathrm{T}}\right]$ of final-state particles, $v_2\propto {\varepsilon }_2$ and $\delta \left[p_{\mathrm{T}}\right]/\left[p_{\mathrm{T}}\right]\propto \delta d_{\perp }/d_{\perp }$, similar conclusions are also expected for the variances and skewnesses of $v_2$ and $\left[p_{\mathrm{T}}\right]$, i.e., $a+b{\beta }_2^2$ for $\langle v_2^2\rangle$ and $\langle {(\delta \left[p_{\mathrm{T}}\right]/\left[p_{\mathrm{T}}\right])}^2\rangle$ and $a+[b+ccos\left(3\gamma \right)]{\beta }_2^3$ for $\langle v_2^2\delta \left[p_{\mathrm{T}}\right]/\left[p_{\mathrm{T}}\right]\rangle$ or $\langle {(\delta \left[p_{\mathrm{T}}\right]/\left[p_{\mathrm{T}}\right])}^3\rangle$. 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, $cos\left(3\gamma \right)\approx 1$, and near oblate nuclei, $cos\left(3\gamma \right)\approx -1$, 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.

• Received 3 January 2022
• Accepted 25 March 2022

DOI:https://doi.org/10.1103/PhysRevC.105.044905