Connection between radiative pion capture and axial current in nuclei

Abstract

Our previous conjecture that the soft-pion limit in nuclei is essentially the Baron approximation for the effective Hamiltonian is here proved for threshold pion photoproduction, in analogy to the case of pion charge exchange. This method provides the effective Hamiltonian H eff = (e/2ƒ π) A · ε related to the axial current and independent of the impulse approximation. The finite pion mass introduces two kinds of deviations from the Born approximation of this effective Hamiltonian. (a) corrections to the Hamiltonian itself (for example the ϱ contribution, the nuclear pole and the fermi motion.) (b) deviations from the Born approximation due to the distortion of the pion wave by the strong interaction. The role of the nuclear excited states is to transform the average distorted pion field into an effective field. A numerical application is made to the 3He-t system.