Abstract
We studied two-photon exchange for elastic electron-proton scattering at low ${Q}^{2}$. Compact approximate formulas for the amplitudes were obtained. Numerical calculations were done for ${Q}^{2}\ensuremath{\leqslant}0.1\phantom{\rule{0.3em}{0ex}}{\mathrm{GeV}}^{2}$ with several realistic form factor parametrizations, yielding similar results. They indicate that the corrections to the magnetic form factor can visibly affect the cross-section and proton radii. For low-${Q}^{2}$ electron-neutron scattering two-photon exchange corrections were shown to be negligibly small.
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