A non-relativistic operator convenient for analysis of pion photoproduction on nuclei in the Δ(1236) region

In view of its application to the analysis of medium energy photonuclear reactions we have obtained an operator valid, to order $\text{(}\text{p}\text{m}\text{)}{}^2$, in any frame of reference. We have started from a model where the pion photoproduction on a nucleon is described by the Born terms and the s-channel Δ(1236) formation amplitude and we have deduced the non-relativistic limit of the corresponding matrix elements. Both pseudo-scalar and pseudo-vector pion-nucleon couplings are compared. The Δ(1236) parameters are chosen so as to lead to a good account of pion-nucleon reaction cross sections. The agreement with the charged photoproduction data is very good from threshold through the Δ(1236) energy region, whereas the addition of ω⁰ exchange in the t-channel is necessary to reproduce the neutral pion photoproduction cross sections. As an example this operator is used to derive the cross section of the γD → ppπ^? reaction in the spectator nucleon model when the undiscernability of the two outgoing protons is taken into account.