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

Abstract

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 $\varepsilon_2$ and the density gradient $d_{\perp}$ in the initial state. Using analytical estimate and a Glauber model, I show that the variances, $\langle\varepsilon_2^2\rangle$ or $\langle(δd_{\perp}/d_{\perp})^2\rangle$, and skewnesses, $\langle\varepsilon_2^2δd_{\perp}/d_{\perp}\rangle$ or $\langle(δd_{\perp}/d_{\perp})^3\rangle$, have a simple analytical form of $a'+b'β_2^2$ and $a'+(b'+c'\cos(3γ))β_2^3$, respectively. From these, I constructed several normalized skewnesses to isolate the $γ$ dependence from that of $β_2$, and show that the correlations between any normalized skewness and any variance can constrain simultaneously the $β_2$ and $γ$. Assuming a linear relation with elliptic flow $v_2$ and mean-transverse momentum $[p_{\mathrm{T}}]$ of final state particles, similar conclusions are also expected for the variances and skewnesses of $v_2$ and $[p_{\mathrm{T}}]$. Our findings motivate a dedicated system scan of high-energy heavy ion collisions to measure triaxiality of atomic nuclei. This is better done by collisions of prolate, $\cos(3γ)=1$, and oblate nuclei, $\cos(3γ)=-1$, with well known $β_2$ values to calibrate the coefficients $b'$ and $c'$, followed by collisions of species of interest especially those with known $β_2$ but unknown $γ$. The results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.