Possible Precise Measurement of Delbrück Scattering Using Polarized Photon Beams

The advent of high-flux-polarized $\gamma$-ray sources makes possible the nearly isolated precise measurement of the vacuum contribution, Delbrück scattering, to the elastic scattering of these photons off nuclei. Because of the fact that the elastic scattering of the photons is a coherent summation of four processes and that up to now unpolarized sources have been used, the isolated measurement of Delbrück scattering has not been performed. We show that for the appropriate choice of scattering angles, photon polarization, and energies this scattering can be measured nearly independently of other scattering processes. This makes possible the precise measurement of the vacuum contribution to scattering and the possibility of the detection of new physics.

Figure 1

Delbrück scattering represented by lowest-order Feynman diagrams. $k$ and $k^{\prime }$ are the 4-vector momenta of the incoming and outgoing photons, respectively, and $i$ and $j$ are their polarization directions, respectively. $\mathrm{\Delta }=k^{\prime }-k$ is the momentum transfer. The $X$ represents the Coulomb field of the nucleus in which $q$ is the field momentum.

Figure 2

The differential cross section $d{\sigma }_{{\parallel }_{R+T+\mathrm{GDR}}}/d\mathrm{\Omega }$ for tin including $R+T+\mathrm{GDR}$ for scattering angles from $40°\le \theta \le 120°$ in the scattering plane. The angular resolution is $\mathrm{\Delta }\theta =0.15°$, and the energy resolution is 1 eV.

Figure 3

The real and imaginary parts of the scattering amplitudes $A_{\parallel }$ for $D$ and $R+T+\mathrm{GDR}$ as indicated in the figures at 1100 keV of tin in units of $r_e$. The angular resolution is $\mathrm{\Delta }\theta =1°$ (excluding 60°) with a relative error of 1% for $D$.

Figure 4

The differential scattering amplitude $d{\sigma }_{\parallel }/d\mathrm{\Omega }$ for $D$ and $R+T+\mathrm{GDR}$ as indicated in the figure for tin at 1100 keV. The angular resolution is $\mathrm{\Delta }\theta =1°$ (excluding 60°) with a relative error of 1% for $D$.

Figure 5

The differential scattering amplitude $d{\sigma }_{\perp }/d\mathrm{\Omega }$ for $D$ and $R+T+\mathrm{GDR}$ as indicated in the figure for tin at 1.1 MeV. The angular resolution is $\mathrm{\Delta }\theta =1°$ (excluding 60°) with a relative error of 1% for $D$.