Photoneutron reaction kinematics and error of commonly used approximations

Abstract

An exact closed-form classical equation and a transcendental relativistic equation for the energy-angle relationship of the neutrons produced from the photoneutron reaction are derived in the laboratory coordinate system. Additional formulas are derived to describe the restriction on scattering angle in the double-valued photoneutron energy regime for incident photon energies near the kinematic threshold energy of the target nucleus. The full range of photoneutron reaction independent variables (target nucleus mass number, neutron separation energy, and photon energy) encountered in practical photoneutron production applications are explored to give the applicable range of classical kinematics and other approximations in the calculation of the photoneutron energy-angle relationship. A six-way comparison study of classical, relativistic, and approximation equations presented in this work and those implemented in radiation transport codes is performed. The well-known and widely-used approximations presented without derivation by Wattenberg and Hanson in the late 1940s are only applicable to energy spread of neutrons produced from gamma-ray photoneutron sources, the intended application of the approximations. The Wattenberg and Hanson approximations are inappropriate for general purpose radiation transport simulation and give unphysical negative photoneutron energies for incident photon energies near the kinematic threshold. Recent versions of the MCNP code appear to use erroneous equations related to inelastic neutron scattering to describe photoneutron kinematics resulting in the overestimation of photoneutron energy. Simulated photoneutron spectra are significantly hardened and cannot be used in contemporary nuclear science applications such as characterization of accelerator-driven photoneutron sources. The Monte-Carlo code developer and user communities need to exhaustively review, correct, document, verify, and validate photoneutron physics implementations in the codes that are in common use.