Parity-nonconserving effects in thermal neutron capture by protons and the short-range behavior of the strong two-nucleon force

$P_{\gamma }$, the photon circular polarization in $\mathrm{np}$ radiative capture at thermal energies, is calculated for a class of weak-interaction Hamiltonians and several short-range phase-equivalent transformations (PET's) of the Reid soft-core potential. The calculations, which are exact except for the usual first-order approximation in the weak interaction, are facilitated by the use of Green's function techniques. An error in the form of the electromagnetic-interaction Hamiltonian $H_{\mathrm{em}}$ that has appeared in the literature is also corrected. For the Reid soft-core potential and the Cabibbo model $P_{\gamma }=+2.28\mathrm{}\times {10}^{-8\mathrm{}}$. For a given weak Hamiltonian it is found that nonlocal PET's of the Reid potential may increase $P_{\gamma }$ by as much as an order of magnitude. For the PET's considered the enhanced values of $P_{\gamma }$ are all positive. This extreme sensitivity to the short-range two-nucleon potential, and the discrepancy in sign between the experimental value, $P_{\gamma }=-(1.30\mathrm{}\pm 0.45)\times {10}^{-6\mathrm{}}$, and theoretical predictions, greatly complicates attempts to use the study of $P_{\gamma }$ to discriminate among weak-interaction Hamiltonians.