Cascading nuclear excitation by electron capture of ²³⁵U in two-beam laser-cluster interactions

Abstract: Laser-assisted nuclear excitation provides controllable routes to isomer production in compact plasma environments, with important applications in precision metrology and nuclear energy. In the present work, nuclear excitation by electron capture (NEEC) in ²³⁵U is investigated using Dirac--Hartree--Fock--Slater calculations and 2D3V particle-in-cell (PIC) simulations of laser--cluster plasmas under different irradiation conditions. The calculations show that upper-level cascade pathways enhance the isomer yield by more than ten orders of magnitude relative to direct excitation. To connect this cascade enhancement with plasma evolution, a multilevel cascade-NEEC model is coupled in space and time to the PIC dynamics and used to derive a pathway-resolved plasma--resonance coupling relation for the NEEC yield. Based on this relation, cluster effects are investigated, and increasing the cluster radius is found to be more effective than increasing the initial density. Moreover, we propose a sequential two-beam scheme that temporally stages plasma formation and resonance-window electron heating, increasing the yield by over two orders of magnitude at nearly unchanged incident fluence. This work provides a practical route to efficient ²³⁵U production and a basis for experimental studies of cascading NEEC in laser-driven plasmas.