Cascading nuclear excitation of \(^{235}\text{U}\) via inelastic electron scattering in laser-irradiated clusters

Nuclear excitation induced by lasers holds broad application prospects in precision metrology and nuclear energy, such as nuclear batteries and nuclear clocks. In the present work, the nuclear excitation via inelastic electron scattering (NEIES) mechanism in \(^{235}\text{U}\) is investigated by combining the Dirac-Hartree-Fock-Slater method for theoretical calculations with 2D3V particle-in-cell (PIC) simulations for numerical modeling. The excitation cross-sections of \(^{235}\text{U}\) from the ground state to excited states is evaluated and an efficient indirect excitation scheme for generating \(^{235}\text{U}\) isomers is proposed by first exciting the nuclei from ground-state to high-energy excited states and then decays to the isomeric state. The calculations show that laser-tuned multi-channel NEIES can boost isomeric state accumulation efficiency by eleven orders of magnitude over direct excitation. Additionally, PIC simulations reveal that laser polarization significantly alters high-energy electron distributions. At identical intensity, p-polarized lasers generate seven times more electrons with energies sufficient for exciting $^{235}\text{U}$ to the second excited state (and beyond to the fourth state) compared to s-polarization. This work offers a practical and feasible way for efficient isomeric state generation, supporting experimental tests of laser-driven nuclear excitation in sub-TW lasers.