Tracing the Evolution of Nuclear Excitation at the Electron-Ion Collider

We investigate the evolution of nuclear excitation in electron-nucleus (e+A) collisions at the upcoming Electron-Ion Collider (EIC) using the BeAGLE event generator. Leveraging the EIC's unique collider kinematics, we demonstrate the remarkable capability to separate distinct nuclear reaction stages, hard scattering, intranuclear cascade, and nuclear de-excitation, in the laboratory frame. Our systematic analysis reveals that event-by-event fluctuations in the mean transverse momentum (k) are highly sensitive to the intranuclear cascade formation time and nuclear geometry, while minimally affected by variations in electron beam energy. These findings establish k as a robust observable for constraining nuclear excitation mechanisms, providing critical benchmarks for future EIC experiments and guiding theoretical advancements in nuclear transport modeling.