Flow Distribution Analysis as A Probe of Nuclei Deformity

Abstract

We study the flow harmonic distribution in deformed nuclei. To do this, we use the standard Gram-Charlier method to find the higher-order correction to the well-known Bessel-Gaussian distribution. We find that, apart from the necessity of including a shift parameter $\bar v_n$, the modified flow distribution describes the flow distribution of quadrupole and octupole deformation accurately. Using the shifted radial distribution, arising from this method, we scrutinize the effect of deformation on flow distribution. Assuming a linear relation between observables of spherical and deformed collisions, $\mathcal{O}_D=\mathcal{O}_S+\left(\sum_{m=2}a_{k,m} \beta_m\right)^{2k}$, for events with a fixed centrality, we compare the flow distribution of deformed and spherical nuclei. We also propose a way to measure $\bar{v}_2$ in asymmetric nuclei collisions.