Elliptic flow (v₂) is one of the most important observations for exploring the properties of nuclear matter using heavy-ion collisions. v₂ is not only affected by dynamic processes but is also related to the Fermi momentum of the initial nucleus.

This study aims to quantitatively determine the effect of the initial Fermi momentum on the time evolution of v₂.

First, based on the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model, gold-gold (Au+Au) collisions at beam energies of 0.4A GeV and 0.8A GeV with impact parameter b = 6 fm were simulated. In the initial stage, three cases were considered: without Fermi momentum, with Fermi momentum, and with half-Fermi momentum. Then, by reverse tracing the nucleons that were emitted at mid-rapidity (|y₀|<0.1) throughout the reaction process, the time evolution of v₂ for these traced nucleons was investigated in detail. Finally, the influence of the initial Fermi momentum on v₂ of the nucleons in the mid-rapidity region in heavy-ion collisions at intermediate energies was examined.

The yield of free nucleons calculated by considering the Fermi momentum was much larger than that obtained without the Fermi momentum, owing to the reduction in nucleon-nucleon collisions. However, v₂ shows the opposite effect; it is obtained by considering that the Fermi momentum is much smaller than that in the latter case because of the stronger blocking effect of the spectator nucleons.

Our results indicate that the initialization of the nucleon momentum must be carefully considered in the transport model.