Nuclear shape fluctuations in high-energy heavy ion collisions

Atomic nuclei often exhibit a quadrupole shape that fluctuates around some average profile. We investigate the impact of nuclear shape fluctuation on the initial state geometry in heavy ion collisions, particularly its eccentricity $\varepsilon_2$ and inverse size $d_{\perp}$, which can be related to the elliptic flow and radial flow in the final state. The fluctuation in overall quadrupole deformation enhances the variances and modifies the skewness and kurtosis of the $\varepsilon_2$ and $d_{\perp}$ in a controllable manner. The fluctuation in triaxiality reduces the difference between prolate and oblate shape for any observable, whose values, in the large fluctuation limit, approach those obtained in collisions of rigid triaxial nuclei. The method to disentangle the mean and variance of the quadrupole deformation is discussed.