Lambda polarization in $^{108}$Ag +$^{108}$Ag and $^{197}$Au +$^{197}$Au collisions around a few GeV

Within the framework of Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, we extract the global spin polarization of $\Lambda$ hyperon in $^{108}$Ag + $^{108}$Ag and $^{197}$Au + $^{197}$Au collisions at $\sqrt{s_{\rm NN}} = 2.42 - 62.4$ GeV. We use two different approaches to calculate the $\Lambda$ polarization $P_y$: approach I is based on equilibrium assumption so that $P_y$ is determined by thermal vorticity and approach II assumes a proportional relation between $P_y$ and the system's angular momentum in $\Lambda$'s rest frame. We find that both approaches can describe the experimental data at low energies around a few GeV but only approach I describes well also higher-energy data. This suggests that at higher energies the relativistic effect plays an important role. After taking into such effect properly, the relativity-improved approach II can describe the higher-energy data as well.