Cross sections for quasifree Compton scattering from the deuteron were measured for incident energies of $E_{\gamma }=236\mathrm{}–260\mathrm{MeV}$ at the laboratory angle ${\theta }_{{\gamma }^{\prime }}=-135\mathrm{}°$. The recoil nucleons were detected in a liquid-scintillator array situated at ${\theta }_N=20\mathrm{}°$. The measured differential cross sections were used, with the calculations of Levchuk et al., to determine the polarizabilities of the bound nucleons. For the bound proton, the extracted values were consistent with the accepted value for the free proton. Combining our results for the bound neutron with those from Rose et al., we obtain 1-sigma constraints of ${\overline{\alpha }}_n=7.6\mathrm{}–14.0$ and ${\overline{\beta }}_n=1.2\mathrm{}–7.6$.

• Received 6 March 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.1388