Formation of two double-strand breaks in the same DNA molecule by a single high-energy photon or ionizing particle

I calculate the probability that a single high-energy ionizing particle or photon makes two widely spaced double-strand breaks in the same DNA molecule. Deletions (or inversions) between two breaks formed by the same incident particle are linear in radiation dose and occur even at extremely low dose-rates; deletions between breaks induced by separate particles are quadratic in dose and are much fewer at very low dose-rate. The calculations show that for a few grays of sparsely ionizing radiations such as fast electrons, X-rays of gamma-rays, the formation of two double-strand breaks in a DNA molecule 1 megabase in size should be nearly entirely quadratic in dose. For heavily ionizing particles such as alpha particles from radon products, the linear and quadratic terms are comparable in size. These conclusions are robust and insensitive to details of the calculations. The results are essentially the same for DNA in a random coil configuration and for DNA uniformly and randomly distributed within a sphere.