Beam-Normal Single Spin Asymmetry in Elastic Electron Scattering off $^{28}$Si and $^{90}$Zr

We report on a new measurement of the beam-normal single spin asymmetry $A_{\mathrm{n}}$ in the elastic scattering of 570 MeV transversely polarized electrons off $^{28}$Si and $^{90}$Zr at $Q^{2}=0.04\, \mathrm{GeV}^2/c^2$. The studied kinematics allow for a comprehensive comparison with former results on $^{12}$C. No significant mass dependence of the beam-normal single spin asymmetry is observed in the mass regime from $^{12}$C to $^{90}$Zr.