Small Angle Coherent Scattering of Gammas by Bound Electrons

Franz has shown that for nonrelativistic changes of photon momentum ($q$) the coherent scattering of gammas by bound electrons reduces to the form factor calculation. We consider the near-relativistic region, by an expansion in $\frac{q}{\mathrm{mc}}$. The corrections to the form factor calculation are very small for small atomic numbers, the order of magnitude being $\left(\frac{Z}{137}\right)\left(\frac{q}{\mathrm{mc}}\right)$. Numerical results for scattering by $K$ electrons of tin give an increase of the amplitude of 25 percent above the form factor value for $\frac{q}{\mathrm{mc}}=1.5\mathrm{}$ and a smaller change for smaller values of $q$. Our results are incomplete since we neglect the effects of binding in the intermediate state.