Coherent $\rho^0$ photoproduction in bulk matter at high energies

Understand

The momentum transfer $\Delta k$ required for a photon to scatter from a target and emerge as a $\rho^0$ decreases as the photon energy $k$ rises.

• For $k>3\times10^{14}$ eV, $\Delta k$ is small enough that the interaction cannot be localized to a single nucleus.
• At still higher energies, photons may coherently scatter elastically from bulk matter and emerge as a $\rho^0$, in a manner akin to kaon regeneration.
• Constructive interference from the different nuclei coherently raises the cross section and the interaction probability rises linearly with energy.