We obtain closed form approximate expressions for two-step hadron nucleus excitations. These are cast in the form of data-to-data relations of elastic and inelastic scattering, which in turn allow prediction of one- versus two-step dominance given prior knowledge of the electromagnetic rates. The data-to-data relations also lead to a simple envelope test for determining what number of steps is dominant in a given region of momentum transfer. Besides giving these qualitative results, the data-to-data forms give an excellent quantitative description of the data.

NUCLEAR REACTIONS Closed form eikonal amplitude for two-step excitation processes. Data-to-data relations of elastic and inelastic scattering. Phase rules and envelope tests.

• Received 12 November 1980

DOI:https://doi.org/10.1103/PhysRevC.23.2186