General differences between the impulse approximation and the elementary particle method in the treatment of two-step processes like pion photoproduction and radiative muon and pion capture are discussed. Important numerical differences arise, exemplified by pion photoproduction on ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The reason is that the Born approximation with low-energy theorems leaves terms undetermined in the elementary particle method. In particular it is shown that in pion photoproduction in pseudoscalar coupling the impulse approximation accounts for numerically sizable contributions of intermediate nuclear excited states not contained in the elementary particle method. In pseudovector coupling no unique and unambiguous relation between the pion-nucleus coupling constant and pion photoproduction holds. An earlier calculation of radiative muon capture by ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is improved by including in a semiempirical way exchange contributions to the muon radiating diagram.

[NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\gamma ,{\pi }^{+}){}_{}{}^3{}_{}{}^{}\mathrm{H}$; calculated $\sigma \left(\theta \right)$. ${}_{}{}^3{}_{}{}^{}\mathrm{He}({\mu }^{-},{\nu }_{\mu }\gamma ){}_{}{}^3{}_{}{}^{}\mathrm{H}$; calculated photon spectrum.]

• Received 11 April 1983

DOI:https://doi.org/10.1103/PhysRevC.29.223