Electronic-Structure Control of Nuclear Excitation by Electron Capture in Finite-Density $^{229}$Th
Nuclear excitation by electron capture (NEEC) provides a unique pathway for coupling electronic and nuclear dynamics, but its description in dense matter commonly relies on electronic structures of isolated ions. Here we show how dense environments reshape the available NEEC capture channels. Using a finite-temperature average-atom model, we assess channel availability by jointly considering electronic localization, resonance energy matching, and vacancy availability. Near solid density, the shallow $6p$ states remain sufficiently localized to support resonant electron capture that drives the 8.356-eV isomeric transition in $^{229}$Th, whereas higher valence-like states merge into the continuum and no longer constitute localized capture channels. Calculations at different temperatures and densities reveal distinct windows of channel availability arising from the interplay among pressure-induced delocalization, shifts in resonance energy, and vacancy formation. Coupling the reconstructed channels to particle-in-cell simulations of laser-driven $^{229}$Th further shows that electronic structure at finite density can substantially alter the predicted cumulative NEEC yield. These results demonstrate how the electronic environment governs resonant capture pathways, highlighting its essential role in nuclear excitation driven by electrons in dense matter.