We investigate the contribution of inelastic electron collisions to nonlinear (NL) dynamics in ultraviolet plasmonic nanoparticles, exploring their potential for harmonic generation. Employing the Landau weak coupling formalism to model radiation-driven electron dynamics in sodium and aluminum, we account for both electron-electron and electron-phonon scattering processes by a set of hydrodynamic equations, which we solve perturbatively to obtain third-order NL susceptibilities. Furthermore, we model high harmonic generation enhanced by localized surface plasmons in nanospheres composed of such poor metals, demonstrating their efficient operation for extreme ultraviolet generation.
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