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 ${\beta }_2$ 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 $d_{\perp }$ in the initial state. Using analytical estimate and a Glauber model, I show that the variances, $⟨{\epsilon }_2^2⟩$ or $⟨(\delta d_{\perp }/d_{\perp }{)}^2⟩$, and skewnesses, $⟨{\epsilon }_2^2\delta d_{\perp }/d_{\perp }⟩$ or $⟨(\delta d_{\perp }/d_{\perp }{)}^3⟩$, have a simple analytical form of $a^{\prime }+b^{\prime }{\beta }_2^2$ and $a^{\prime }+(b^{\prime }+c^{\prime }\cos (3\gamma )){\beta }_2^3$, respectively. From these, I constructed several normalized skewnesses to isolate the $\gamma$ dependence from that of ${\beta }_2$, and show that the correlations between any normalized skewness and any variance can constrain simultaneously the ${\beta }_2$ and $\gamma$. 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, $\cos (3\gamma )=1$, and oblate nuclei, $\cos (3\gamma )=-1$, with well known ${\beta }_2$ values to calibrate the coefficients $b^{\prime }$ and $c^{\prime }$, followed by collisions of species of interest especially those with known ${\beta }_2$ but unknown $\gamma$. The results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.

Comments: 20 pages, 14 figures, plus 3 appendix, published version