QED has predicted interactions between photon and photon, for example scattering of photon with photon, or photon splitting, but such processes have not been understood well because their cross sections are very small. The Delbruck scattering is one of such interactions. Its cross section is much larger than those of other interactions; however, there is a critical problem that it is, in principle, difficult to measure selectively the amplitude of Delbruck scattering from other coherent gamma-ray scattering. Recently, we have calculated the cross sections of Delbruck scattering with linearly polarized gamma-ray beam. We have found the angle at which we can selectively measure the cross section. When the next generation of gamma-ray beam with energy of several MeV at ELI-NP is used for this measurement with 76 day, we can measure Delbruck scattering amplitude with statistical uncertainty of 1%.The second topic is a theoretical proposal for generation of gamma-ray vortex. One of features of gamma-ray vortex is its angular momentum is higher than or equal to 2 hbar. If a gamma-ray vortex interacts on a 0+ even-even nucleus, the excitation of 1- (1+) states such as GDR should be forbidden. This will be a new probe to explore selectively exited states with spin higher than or equal to 2 hbar. Photon vortexes with energies lower than keV have been generated experimentally, but there is no effective method to generate photon vortex in the MeV energy region. We have proposed a method using non-linear Compton scattering on electron with circularly polarized high intense laser, and found that the higher order gamma-rays are vortexes. RCNP Colloquium