Identical nuclei in coherent pion production at intermediate energies

Abstract

The formalism for the calculation of constructive, coherent production of pions through the collision of intermediate-energy nuclei now includes for the first time the exchange symmetry due to identical nuclei both in the initial two-body state and in the final three-body state. Of the eight terms that contribute to the pion-energy distributions, four of the amplitudes are equal in pairs, effectively leaving four amplitudes with direct terms in the initial state and direct and exchange terms in the final state. Of these remaining amplitudes, the final-state exchange terms are negligible as far as the calculation is concerned. This holds for pion-energy distributions over the incident energies from 100 MeV/nucleon to 2 GeV/nucleon for pions fixed in the forward direction (θπ = 0°) and the projectile and target, respectively, fixed in the fore and aft directions. This work is also generalized to include schematic solutions for the cases of identical nuclei in the initial state only, identical nuclei in the final state only, and the case of no identical nuclei at all. PACS Nos.: 24.10Cn, 24.30Cz, 25.70-z, 25.80-e