Zero range scattering theory. I. Nonrelativistic three- and four-particle equations

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Abstract
We prove here that by taking the zero range limit of conventional nonrelativistic three-particle theories and restricting the two-particle amplitude in this limit to have no singularities at negative energy other than bound state poles, we can derive unitary three-particle equations depending only on two-particle physical observables. Phenomenological extensions of this theory suitable for data analysis of systems with three-particle final states and two- and three-cluster reaction theories are briefly discussed. The extension of the theory to four-particle systems is sketched. Nonrelativistic and relativistic applications will be discussed in subsequent papers in this series.