Delbrück scattering in combined Coulomb and laser fields

We study Delbrück scattering in a Coulomb field in the presence of a laser field. The amplitudes are calculated in the Born approximation with respect to the Coulomb field and exactly in the parameters of the laser field having arbitrary strength, spectral content, and polarization. The case of high initial photon energy is investigated in detail for a monochromatic circularly polarized laser field. It is shown that the angular distribution of the process substantially differs from that for Delbrück scattering in a pure Coulomb field. The value of the cross section under discussion may exceed the latter at realistic laser parameters that essentially simplify the possibility of the experimental observation of the phenomenon. The effect of high order terms in the quantum intensity parameter $\chi$ of the laser field is found to be very important already at relatively small $\chi$.

Figure 1

Feynman diagram for the Delbrück scattering amplitude in combined Coulomb and laser fields calculated in the Born approximation with respect to the Coulomb field. This diagram corresponds to the Furry representation and the thick line denotes the electron propagator (Green’s function) in the laser field. The wavy lines symbolize the external photons, $k_1^{\mu }$ and $k_2^{\mu }$ are the momenta of the initial and final photons, respectively, $k_3^{\mu }$ is the momentum of the Coulomb quantum. The diagram with the permutation $k_2^{\mu }\leftrightarrow k_3^{\mu }$ has to be added.

Figure 2

Ratio $d\sigma /d{\sigma }_D$ in units ${\chi }^2/{\left(Z\alpha \right)}^2$ obtained in the Born approximation.

Figure 3

Ratio $\mathcal{A}\left(\chi \right)/\mathcal{A}\left(0\right)$, where $\mathcal{A}\left(0\right)=139/4050$.

Figure 4

Stokes parameter $S_3$ at small $\rho$ as a function of $\chi$.