Coherent ${\rho }^0$ Photoproduction in Bulk Matter at High Energies

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 $k>3\times {10}^{14}\mathrm{eV}$, $\Delta k$ 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. At energies above ${10}^{23}\mathrm{eV}$, coherent conversion is the dominant process; photons interact predominantly as ${\rho }^0$. We compute the coherent scattering probabilities in slabs of lead, water, and rock, and discuss the implications of the increased hadronic interaction probabilities for photons on ultrahigh energy shower development.

Figure 1

The cross sections for photon interactions to $e^{+}{e}^{-}$ pairs, and for incoherent photonuclear interactions in the Glauber and ERR models, for water (top), standard rock (middle), and lead (bottom).

Figure 2

$\rho$ probability as a function of depth in a slab for a ${10}^{23}\mathrm{eV}$ photon incident on a water target. The two broad peaks around 20 and 40 cm correspond to $\Delta kL=2n\pi$ at the $\rho$ pole mass.

Figure 3

The probability of a ${10}^{24}\mathrm{eV}$ photon interacting electromagnetically (dashed blue line), in an incoherent hadronic interaction (dotted line), or as a coherently produced $\rho$ (solid line), as a function of target depth in a lead target.

Figure 4

The normalized probabilities for a photon to interact as an $e^{+}{e}^{-}$ pair, via incoherent hadronic interaction (“hadron”), or as an elastically produced $\rho$ (“rho”) in a 100 m thick water or standard rock target. This is thick enough for almost total absorption, so these results apply for an infinitely thick target.