Deformation probes for light nuclei in their collisions at relativistic energies

We have investigated the performance of anisotropic flows $\ensuremath{\langle}{v}_{n}^{2}\ensuremath{\rangle}$, transverse momentum fluctuations $\ensuremath{\langle}\ensuremath{\delta}{p}_{T}^{2}\ensuremath{\rangle}$, and their correlations $\ensuremath{\langle}{v}_{n}^{2}\ensuremath{\delta}{p}_{T}\ensuremath{\rangle}$ in central collisions at relativistic energies as probes of deformation parameters ${\ensuremath{\beta}}_{n}$ of colliding nuclei, if these nuclei are light nuclei with large ${\ensuremath{\beta}}_{n}$ and different configurations of $\ensuremath{\alpha}$ clusters. The effects from higher-order ${\ensuremath{\beta}}_{n}$ terms are illustrated by derived relations based on the overlap of two nuclei with uniform density distributions and by dynamic simulations of collisions of heavy nuclei whose density distributions are of a deformed Woods-Saxon (WS) form. While the linear relations between ${\ensuremath{\beta}}_{n}^{2}, \ensuremath{\langle}{v}_{n}^{2}\ensuremath{\rangle}$, and $\ensuremath{\langle}\ensuremath{\delta}{p}_{T}^{2}\ensuremath{\rangle}$ and that between ${\ensuremath{\beta}}_{n}^{3}$ and $\ensuremath{\langle}{v}_{n}^{2}\ensuremath{\delta}{p}_{T}\ensuremath{\rangle}$ can be violated for extremely large ${\ensuremath{\beta}}_{n}$, they are mostly valid for realistic values of ${\ensuremath{\beta}}_{n}$, as long as the density distribution of colliding nuclei can be described by a deformed WS form. However, these linear relations are generally not valid with more realistic density distributions of light nuclei with $\ensuremath{\alpha}$ clusters, and the amount of deviation depends on the detailed $\ensuremath{\alpha}$-cluster configurations. Care must be taken when one tries to extract the deformation of light nuclei, and specific probes for $\ensuremath{\alpha}$-cluster structures in these nuclei are very much needed.