A direct probe of $\Lambda$ potential in nuclear medium

Using the Li\`{e}ge intranuclear-cascade model together with the ablation model ABLA, an investigation is conducted into the effects of $\Lambda$ potential in $\Lambda$-nucleus and $\Lambda$-hypernucleus-nucleus collisions across various beam energies. The findings show that the angle and transverse-momentum distributions of scattered $\Lambda$ hyperon, the scattering cross section of the $\Lambda$ hyperon in $\Lambda$-nucleus collisions as well as the rapidity distribution of $\Lambda$ hyperon in $\Lambda$-hypernucleus-nucleus collisions are significantly influenced by the strength of the $\Lambda$ potential in these scattering reactions across various beam energies. These demonstrations, unhindered by the uncertainties of $\Lambda$ and hypernuclei productions in nuclear medium, allow for a direct investigation of the $\Lambda$ potential, especially its momentum dependence. The criticality of probing the $\Lambda$ potential is closely associated with the resolution of the "hyperon puzzle" in neutron stars.