When the Nucleus Meets the Solid: Nuclear–Electronic Interactions in Thorium-229 Nuclear Solid-State Clocks

Solid-state realizations of the low-energy nuclear transition in thorium-229 offer a promising route toward compact and robust nuclear clocks. They also introduce a rich set of nuclear–electronic interactions that can significantly modify the nuclear dynamics. In this talk, I present a broad theoretical picture of these interactions for a thorium-229 nucleus embedded in a solid-state host. Starting from a multipole-expanded nuclear–electronic Hamiltonian, I discuss how electronic structure in the host material gives rise to nuclear energy shifts, splittings, and broadenings that are critical for clock operation. These interactions connect well-known solid-state effects—such as electric field gradients and inhomogeneous magnetic fields — to spectroscopic observables through various multipole moments. A key component of this discussion will feature our ab-initio calcuations and work regarding the isomer shift. I then focus on the theory of internal conversion of the thorium-229 isomer in solids, emphasizing how the local electronic environment controls the availability and strength of this decay channel. Building on this framework, I show how internal conversion provides a natural explanation for our observation that VUV illumination can quench the excited nuclear state, effectively reducing its lifetime through electronically mediated decay pathways. Finally, I present our direct observation of internal-conversion decay in a lower band-gap host material and discuss how our theoretical model semi-quantitatively accounts for this result. Together, these studies establish a coherent description of nuclear–electronic coupling in solids and clarify its implications for the design and considerations of solid-state thorium-229 nuclear clocks.