Why laboratory electron-screening potentials exceed the adiabatic limit
In plain words
The electrons around target atoms partly hide the electric repulsion between colliding nuclei, which raises measured low-energy reaction rates. The measured boost is larger than the maximum that atomic physics seems to allow, and nobody knows why.
Precise statement
Low-energy measurements of $3\mathrm{He}(d,p)4\mathrm{He}$, $6,7\mathrm{Li}(p,\alpha)$ and $d(d,p)t$ yield screening potentials $U_e$, defined by $\sigma_{\mathrm{screened}}(E)/\sigma_{\mathrm{bare}}(E)\sim \operatorname{exp}(\pi \eta U_e/E)$ with $\eta$ the Sommerfeld parameter, that exceed the adiabatic limit $U_{\mathrm{ad}}$ (the difference in electron binding between the separated atoms and the united atom) by up to a factor $\sim 2$ in gas targets and by an order of magnitude for deuterons in some metal hosts. Explain the excess quantitatively, and determine whether the error lies in the screening physics, in stopping-power corrections, or in the extrapolated bare S-factors.
What would settle it
A calculation of $U_e$ from atomic and solid-state theory that reproduces gas and metal data for the same reaction, or an independent determination of the bare $S$-factor (for example by the Trojan-horse method) that removes the excess.
Status in the literature
A 2023 palladium measurement found $U_{e}$ up to ten times model values, and a 2023 analysis argued that resonance strengths need no laboratory screening correction at all.