Can the Neutron Polarizabilities Be Determined from a Deuteron Compton Scattering Experiment?

Abstract

A calculation of deuteron Compton scattering using non-relativistic diagrammatic perturbation theory is presented, with the primary motivation of investigating the feasibility of determining the neutron polarizabilities from this type of experiment. This calculation is expected to be valid for energies below 100 MeV. Previous theoretical and experimental estimates for the polarizabilities are given. All diagrams are calculated by expanding the photon wavefunctions into partial waves and using realistic deuteron wavefunctions. The Green's function for the intermediate state in the dispersive states is determined numerically. Pion-exchange, relativistic, and recoil corrections are also included. The low-energy theorem is shown to be satisfied. The relative effects of the different terms as well as their effects on the determinations of the polarizabilities are discussed at energies of 49, 69, and 95 MeV. The cross-section is dominated by the seagull, polarizability, and electromagnetic multipole interactions. Relativistic and pion-exchange terms are also important, while recoil corrections and multipoles of L=2 and greater are negligible. The calculation provides a reasonable description of the experimental data points at 49 and 69 MeV, except for the point at the greatest angle. The polarizabilities are difficult to determine at these energies due to the size of the experimental error bars. No data has been published at 95 MeV but a more accurate determination of the polarizabilities is likely at this higher energy. Detailed calculations for all terms can be found in the appendices.