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Most atomic nuclei are deformed with a quadrupole shape described by itsoverall strength $\beta_2$ and triaxiality $\gamma$. The deformation can beaccessed in high-energy heavy-ion collisions by measuring the collective flowresponse of the produced quark-gluon plasma to the eccentricity $\varepsilon_2$and the density gradient $d_{\perp}$ in the initial state. Using analyticalestimate and a Glauber model, I show that the variances,$\langle\varepsilon_2^2\rangle$ or $\langle(\deltad_{\perp}/d_{\perp})^2\rangle$, and skewnesses, $\langle\varepsilon_2^2\deltad_{\perp}/d_{\perp}\rangle$ or $\langle(\delta d_{\perp}/d_{\perp})^3\rangle$,have a simple analytical form of $a'+b'\beta_2^2$ and$a'+(b'+c'\cos(3\gamma))\beta_2^3$, respectively. From these, I constructedseveral normalized skewnesses to isolate the $\gamma$ dependence from that of$\beta_2$, and show that the correlations between any normalized skewness andany variance can constrain simultaneously the $\beta_2$ and $\gamma$. Assuminga linear relation with elliptic flow $v_2$ and mean-transverse momentum$[p_{\mathrm{T}}]$ of final state particles, similar conclusions are alsoexpected for the variances and skewnesses of $v_2$ and $[p_{\mathrm{T}}]$. Ourfindings motivate a dedicated system scan of high-energy heavy ion collisionsto measure triaxiality of atomic nuclei. This is better done by collisions ofprolate, $\cos(3\gamma)=1$, and oblate nuclei, $\cos(3\gamma)=-1$, with wellknown $\beta_2$ values to calibrate the coefficients $b'$ and $c'$, followed bycollisions of species of interest especially those with known $\beta_2$ butunknown $\gamma$. The results demonstrate the unique opportunities offered byhigh-energy collisions as a tool to perform interdisciplinary nuclear physicsstudies.

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