An examination is conducted on a commonly used procedure for extracting (un)polarized $\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}n\to {\mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}}^{-}p$ and $\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}n\to {\mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}}^{0}n$ observables from ${}^2\mathrm{H}(\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>},{\mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}}^{-})pp$ and ${}^2\mathrm{H}(\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>},{\mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}}^0)pn$ data, using a model that consists of the impulse term and the final-state interaction (FSI) terms due to nucleon and pion exchange. Recent experimental and theoretical analyses used an extraction method that does not impose a cut on the final $\mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}N$ invariant mass $W$. I demonstrate that the use of this method can result in the $\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}n\to \mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}N$ observables that are seriously distorted by the nucleon Fermi motion, and that one can efficiently avoid this problem by imposing a cut on $W$. It is also shown that the use of kinematical cuts of recent experimental analyses can still leave in the selected samples substantial FSI effects that must be corrected in extracting the $\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}n\to \mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}N$ cross sections. In terms of the nucleon- and pion-exchange mechanisms, I give the first qualitative explanation of the FSI corrections, obtained in a recent Mainz Microtron experiment, for extracting $\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}n\to {\mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}}^{0}n$ cross sections.

• Received 14 August 2018

DOI:https://doi.org/10.1103/PhysRevC.98.042201