Single-cluster formation in the statistical bootstrap model

Abstract

Single-cluster formation in hadronic reactions is discussed, within the context of the statistical bootstrap model. This process is analogous to compound nucleus scattering in nuclear physics, and similar formulas hold for the formation cross section. If the average resonance width should rise indefinitely with energy, the model will eventually run into conflict with unitarity; the trouble is traced to a breakdown of the "narrow-resonance approximation." The effects of angular momentum conservation on the cluster decay are considered, and formulas are presented for the multiplicity and single-particle momentum distribution as a function of the cluster's spin. Brief discussions are given of possible experimental tests of the model, including the annihilation reactions $e^{+}{e}^{-}\to \mathrm{hadrons}$ and $N\overline{N}\to \mathrm{mesons}$, which are particularly favorable cases. In an appendix it is shown how to estimate asymptotic parameters in a "realistic" model by analytic means.