Elastic Compton Scattering from the Deuteron and Nucleon Polarizabilities

Cross sections for elastic Compton scattering from the deuteron were measured over the laboratory angles ${\theta }_{\gamma }=35\mathrm{}°–150°$. Tagged photons in the laboratory energy range $E_{\gamma }=84\mathrm{}–105\mathrm{MeV}$ were scattered from liquid deuterium and detected in the large-volume Boston University NaI spectrometer. Using the calculations of Levchuk and L'vov, along with the measured differential cross sections, the isospin-averaged nucleon polarizabilities in the deuteron were estimated. A best-fit value of $(\overline{\alpha }-\overline{\beta })=2.6\mathrm{}\pm 1.8$ was determined, constrained by dispersion sum rules. This is markedly different from the accepted value for the proton of $(\overline{\alpha }-\overline{\beta }{)}_p=10.0\mathrm{}\pm 1.5\pm 0.9$.