Abstract
We consider the scattering of an x-ray free-electron laser (XFEL) beam on the superposition of a strong magnetic field $\bf{B}_{\rm ext}$ with the Coulomb field $\bf{E}_{\rm ext}$ of a nucleus with charge number $Z$. In contrast to pure Delbr\"uck scattering (Coulomb field only), the magnetic field $\bf{B}_{\rm ext}$ introduces an asymmetry (i.e., polarization dependence) and renders the effective interaction volume quite large, while the nuclear Coulomb field facilitates a significant momentum transfer $\Delta\bf k$. For a field strength of $B_{\rm ext}=10^6~\rm T$ (corresponding to an intensity of order $10^{22}~\rm W/cm^2$) and an XFEL frequency of 24 keV, we find a differential cross section $d\sigma/d\Omega\sim10^{-25}~Z^2/(\Delta{\bf k})^2$ in forward direction for one nucleus. Thus, this effect might be observable in the near future at facilities such as the Helmholtz International Beamline for Extreme Fields (HIBEF) at the European XFEL.
Highlights
According to classical electrodynamics, electromagnetic waves in vacuum obey the superposition principle and do not influence each other
As an example for the Quantum electrodynamics (QED) vacuum nonlinearity, we calculate the scattering of x-ray free-electron laser (XFEL) photons at the combined field of a nucleus plus an external magnetic field, see Fig. 1
Our scenario is within the realm of applicability of the Euler-Heisenberg Lagrangian (2) and the picture of a classical electromagnetic field—especially for the coherent superposition of the signal from many nuclei—instead of the particle picture often associated with Delbrück scattering
Summary
Electromagnetic waves in vacuum obey the superposition principle and do not influence each other. The Coulomb field of a nucleus with charge Zq exceeds the field strength (1p) ffivffiffiery close to the nucleus, i.e., on a distance of order Oð ZƛÞ Such a high field strength helps to observe the interaction of electromagnetic fields and the scattering of photons at the nuclear Coulomb field, which can be understood as quantum vacuum refraction (usually referred to as Delbrück scattering [10,11,12]), has been observed in several experiments, see, e.g., [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. All involved field strengths are subcritical, i.e., well below (1)
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