Single Production of Mesons by Gamma-Rays Near Threshold

The cross section for single charged meson production through absorption of a gamma-ray in a gamma-ray-nucleon collision has been calculated to order $e^2{g}^2$ in the charged scalar meson theory (scalar coupling) and charged pseudoscalar meson theory (pseudovector coupling). The nucleon was assumed to be infinitely heavy, thus restricting the validity of the results to gamma-ray energies less than a few times threshold. For a free nucleon the threshold for $\pi$-meson production is at 155 Mev in the rest system of the nucleon. Close to threshold, in the scalar theory the cross section varies as the three-halves power of the energy above threshold and the angular distribution is of the form ${sin}^2\theta$, while in the pseudoscalar theory the cross section varies as the square root of the energy above threshold and the angular distribution of the mesons is approximately isotropic. At energies 50 percent above threshold, the total cross section is of order ${10}^{-28\mathrm{}}$ ${\mathrm{cm}}^2$ in the pseudoscalar theory and of order ${10}^{-29\mathrm{}}$ ${\mathrm{cm}}^2$ in the scalar theory.