Possibilities to observe Delbr\"uck scattering at next generation laser facilities

We have previously shown that by using high-flux linearly polarized laser Compton gamma-ray sources the contribution of the vacuum component, Delbr\"uck scattering, to the elastic scattering of the gamma-rays off nuclei could be nearly isolated at photon energies of 1.1 MeV [1]. Since for photon energies below the electron-positron pair creation threshold of 1.022 MeV the complex Delbr\"uck scattering amplitude is real and measures only the contribution from virtual pairs [2], it is of interest to measure it for the properties of vacuum. We present our calculations for sub-MeV photon energies and discuss the possibility of measuring Delbr\"uck scattering at new ultra-high power laser and X-ray Free Electron Laser facilities. [1] J. K. Koga and T. Hayakawa, Phys. Rev. Lett 118, 204801 (2017). [2] H. E. Jackson and K. J. Wetzel, Phys. Rev. Lett. 22, 1008 (1969).