Precision Nuclear-Spin Effects in Atoms: EFT Methods for Reducing Theory Errors

Abstract

We use effective field theory to compute the influence of nuclear structure on precision calculations of atomic energy levels. As usual, the EFT's effective couplings correspond to the various nuclear properties (such as the charge radius, nuclear polarizabilities, Friar and Zemach moments etc.) that dominate its low-energy electromagnetic influence on its surroundings. By extending to spinning nuclei the arguments developed for spinless ones in arXiv:1708.09768, we use the EFT to show -to any fixed order in Zα (where Z is the atomic number and α the fine-structure constant) and the ratio of nuclear to atomic size -that nuclear properties actually contribute to electronic energies through fewer parameters than the number of these effective nuclear couplings naively suggests. Our result is derived using a position-space method for matching effective parameters to nuclear properties in the EFT, that more efficiently exploits the simplicity of the small-nucleus limit in atomic systems. By showing that precision calculations of atomic spectra depend on fewer nuclear uncertainties than naively expected, this observation allows the construction of many nucleus-independent combinations of atomic energy differences whose measurement can be used to test fundamental physics (such as the predictions of QED) because their theoretical uncertainties are not limited by the accuracy of nuclear calculations. We provide several simple examples of such nucleus-free predictions for Hydrogen-like atoms.

Influence Through Mixing: Hotspots as Benchmarks for Basic Black-Hole Behaviour

“…Including this coupling is not simply an intellectual exercise because its presence is often required to renormalize divergences that arise because fields like φ diverge at the hotspot position once couplings are turned on there. As is well-known from other contexts [64][65][66][67][68][69][70][71][72][73][74] having fields divergence at the position of a source like this is fairly generic -the simplest example being the Coulomb potential diverging at the position of a source charge. From an EFT perspective the presence of couplings like λ is often compulsory, because the requirement that UV divergences drop out of physical observables causes the couplings to run and λ = 0 need not be a fixed point of this renormalization-group (RG) flow.…”

“…But the example of the Coulomb field for a small charge distribution also suggests that evaluating the 1/r divergence at r = 0 is really an artefact of trying to extrapolate to zero an external solution that is not actually appropriate in the microscopic theory within which the source's structure can be resolved. A general EFT treatment of these issues is possible [10,[68][69][70][71] (and tested in detail calculating nuclear finite-size effects in atoms [72][73][74]), and shows how all such divergences get renormalized by the effective couplings in the action -such as the coupling λ of hotspot action (2.3) -that describes the source's low-energy properties (as we also see in detail below).…”

“…This Appendix summarizes some parts of the renormalization evolution not made explicit in the main text, closely following the discussion in Appendix F of [74].…”