In diffractive interactions of protons or nuclei a violent collision can occur that leaves the forward going particle completely intact -with probability determined by the structure of the proton or nucleus. At very high energies these collisions also occur with both incident particles remaining intact. This is called central exclusive production. If a new particle, such as the Higgs boson, were produced exclusively this process would give a precise measurement of its mass and test for expected properties of the Higgs. Because of its unusual features this process is also a promising discovery tool. In this paper I focus on analogous electromagnetic processes because many aspects apply to both- particularly the role of coherence. Also, topics in diffraction with nuclear beams are based on electromagnetic interactions. I also discuss two proposed measurements in ATLAS with Pb beams and with proton beams (diffractive Higgs production).
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