Systematic investigation of azimuthal anisotropy in Au+Au and U+U collisions at $\sqrt {s}_{NN}$ = 200 GeV

We present a study of azimuthal anisotropy parameter ($v_n$) of produced particles in Au+Au and U+U collisions at top RHIC collision energy. The U+U collisions have been studied with and without including the deformed shape of the uranium nuclei. For this purpose, we have used a multi-phase transport (AMPT) model that includes the implementation of deformed uranium nuclei. It is found that the elliptic flow ($v_2$) is higher in central U+U collisions with deformed uranium nuclei compared to Au+Au and spherical U+U. On the other hand, other higher harmonics ($v_3$, $v_4$, and $v_5$) are found to be almost similar in magnitude for all three systems (Au+Au, deformed U+U, and spherical U+U). We have shown that the magnitude of $v _2$/$\epsilon_2$ is higher (similar) in Au+Au collisions compared to deformed (spherical) U+U collisions at most central collisions. However, we believe $v_2$/$\epsilon_2$ reflect true collectivity and more collectivity is expected in large nuclei (U$^{235}$) compared to the small Au$^{197}$ nucleus. This indicates that in the case of deformed nuclei, eccentricity ($\epsilon_2$) scaled $v_2$ may not reflect true collectivity. On the other hand, magnitudes of $v_3$/$\epsilon_3$, $v_4$/$\epsilon_4$ and $v_5$/$\epsilon_5$ for a given centrality are the same for Au+Au, deformed U+U, and spherical U+U collisions. These are interesting observations and can be checked in experimental data at RHIC. We have also compared Au+Au and U+U results with that of Cu+Cu for a better understanding of our findings.