Test of vacuum polarization by precise investigation of Delbrück scattering

Using sources of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$, differential cross sections for elastic scattering of 2.754 MeV photons have been measured for angles between 60 and 120° and charge numbers of 30, 42, 50, and 58 with an accuracy of 2.8% on the average. For the cases covered by experiment, Delbrück scattering amplitudes have been calculated on the basis of the lowest-order Feynman graphs with an average numerical accuracy of 1%. For the same cases Rayleigh scattering amplitudes have been calculated on the basis of the second-order $S$ matrix using Dirac-Hartree-Fock-Slater wave functions. These investigations confirm the lowest-order Delbrück theory with an accuracy of 5%. This corresponds to a new test of vacuum polarization of the order $\alpha {\left(Z\alpha \right)}^2$.