Proton and kaon production in Au+Au collisions at $\sqrt{s_{\rm NN}}=3$ GeV
Within an extended isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck transport model, we study the protons, $K^+$ mesons and $\Lambda$ hyperons production in Au+Au collisions at $\sqrt{s_{\rm NN}}=3$ GeV. For the collision in 0-10% centrality, we study the transverse momentum spectra and rapidity dependent mean transverse momentum for protons. For the collision in 10-40% centrality, we study the directed and elliptic flows for protons and $K^+$ mesons. The results show that the momentum-dependent nuclear mean field with an incompressibility $K_0=230$ MeV can fit fairly the STAR experimental data, while the momentum-independent nuclear mean field with both $K_0=230$ MeV and $K_0=380$ MeV can only partially describe the experimental results. In addition, we also study the directed and elliptic flows for the associated $\Lambda$, observations reveal the same conclusions as for kaons. These findings indicate that the momentum dependence of nuclear mean field plays a significant role in understanding nuclear matter properties in heavy-ion collisions at $\sqrt{s_{\rm NN}}=3$ GeV.