Coplanar and noncoplanar nucleon-nucleon bremsstrahlung calculation: A study of pseudoscalar and pseudovectorπNcouplings

The $\mathrm{pp}\gamma$ and $\mathrm{np}\gamma$ processes have been used to study pseudoscalar (ps) and pseudovector (pv) $\pi N$ couplings. We calculate both coplanar and noncoplanar cross sections using a realistic one-boson exchange model in the energy region between 100 and 300 MeV. We find that the difference in cross sections calculated using the two couplings increases as the nucleon scattering angles decrease. Furthermore, this difference becomes greater with increasing incident energy. We show for the $\mathrm{pp}\gamma$ case that this difference will be significantly increased upon the inclusion of electromagnetic form factors. For $\mathrm{pp}\gamma$ with large proton scattering angles (≥30°), cross sections (both ps and pv) calculated using an on-shell $p\gamma p$ vertex are in very good agreement with the data, and they are also extremely close to a recent soft-photon calculation at 157 MeV using the $\mathrm{two}-u-\mathrm{two}-t$ special amplitude. The ps and pv calculations are both in good agreement with the TRIUMF data at 200 and 280 MeV. More accurate data are required to differentiate between these two couplings. Agreement with sparsely available $\mathrm{np}\gamma$ data is good for most cases, but discrepancies do exist for some data points. For large nucleon scattering angles, noncoplanar cross sections for both $\mathrm{np}\gamma$ and $\mathrm{pp}\gamma$ change rapidly with the noncoplanar angle. However, the respective shapes of the noncoplanar $\mathrm{np}\gamma$ and $\mathrm{pp}\gamma$ curves are very different.