While at the University of Illinois (1957–1967) Jackson initially continued work on weak interactions as well as strange particle interactions at low energy with Wyld and others. On sabbatical leave at CERN in 1963–64, he collaborated with Kurt Gottfried on production and decay of unstable resonances in high-energy hadronic collisions. They introduced the use of the density matrix to connect production mechanisms to the decay patterns and described the influence of competing processes ("absorption") on the reactions.