Probing nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in heavy ion collisions

TL;DR

This paper demonstrates that the correlation between elliptic flow and transverse momentum in heavy ion collisions can reveal the quadrupole deformation and triaxiality of atomic nuclei, offering a new method for nuclear shape imaging.

Contribution

It introduces the use of the Pearson correlation coefficient between elliptic flow and transverse momentum as a sensitive probe for nuclear deformation and triaxiality in ultra-central heavy ion collisions.

Findings

Prolate deformation reduces the correlation coefficient $ ho_2$.

Oblate deformation enhances the correlation coefficient $ ho_2$.

Correlation sign and strength indicate nuclear triaxiality.

Abstract

In heavy ion collisions, elliptic flow $v_2$ and radial flow, characterized by event-wise average transverse momentum $[p_{\mathrm{T}}]$, are related to the shape and size of the overlap region, which are sensitive to the shape of colliding atomic nuclei. The Pearson correlation coefficient between $v_2$ and $[p_{\mathrm{T}}]$, $\rho_2$, was found to be particularly sensitive to the quadrupole deformation parameter $\beta$ that is traditionally measured in low energy experiments. Built on earlier insight that the prolate deformation $\beta>0$ reduces the $\rho_2$ in ultra-central collisions (UCC), we show that the prolate deformation $\beta<0$ enhances the value of $\rho_2$. As $\beta>0$ and $\beta<0$ are the two extremes of triaxiality, the strength and sign of $v_2^2-[p_{\mathrm{T}}]$ correlation can be used to provide valuable information on the triaxiality of the nucleus. Our study provide further arguments for using the hydrodynamic flow as a precision tool to directly image the deformation of the atomic nuclei at extremely short time scale ($<10^{-24}$s).