We report precision determinations of the beam-normal single spin asymmetries ($A_n$) in the elastic scattering of 0.95 and 2.18 GeV electrons off ${}^{12}\mathrm{C}$, ${}^{40}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$ at very forward angles where the most detailed theoretical calculations have been performed. The first measurements of $A_n$ for ${}^{40}\mathrm{Ca}$ and ${}^{48}\mathrm{Ca}$ are found to be similar to that of ${}^{12}\mathrm{C}$, consistent with expectations and thus demonstrating the validity of theoretical calculations for nuclei with $\mathrm{Z}\le 20$. We also report $A_n$ for ${}^{208}\mathrm{Pb}$ at two new momentum transfers (${\mathrm{Q}}^2$) extending the previous measurement. Our new data confirm the surprising result previously reported, with all three data points showing significant disagreement with the results from the $Z\le 20$ nuclei. These data confirm our basic understanding of the underlying dynamics that govern $A_n$ for nuclei containing $\lesssim 50$ nucleons, but point to the need for further investigation to understand the unusual $A_n$ behavior discovered for scattering off ${}^{208}\mathrm{Pb}$.

• Received 9 November 2021
• Revised 31 January 2022
• Accepted 4 February 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.142501