The dispersion formula for nuclear reactions

Abstract

Bohr has shown that in a collision between two nuclei of which at least one is heavy, an unstable compound nucleus will be temporarily formed and that the lifetime of such a compound nucleus, measured on a nuclear scale, is usually very large. For this reason these compound nuclei have fairly well-defined energy levels ("virtual“ or "resonance" levels), and the posi­tions of these levels and the properties of the metastable states belonging to them determine the cross-sections for all nuclear reactions. Breit and Wigner (1936) gave a formula for the probability of a nuclear reaction in terms of the virtual state, taking into account only one such state, while Bethe and Placzek (1937) and Bethe (1937) generalized the formula to take account of all possible virtual states. Their formula is usually referred to as the "dispersion formula" owing to its analogy with the formula for the dispersion of light by atomic systems.