Landau-Pomeranchuk-Migdal effect for finite-size targets

A rigorous evaluation of the Landau-Pomeranchuk-Migdal effect for finite-size targets is performed within the path integral approach previously developed in ref. [4]. The bremsstrahlung rate in QED is expressed through a solution of a two-dimensional Schr\"odinger equation with an imaginary potential. The boundary condition for this solution is formulated in terms of a product of the light-cone electron--photon wave function and the dipole cross section for scattering of $e^{+}e^{-}$ pair off an atom. Numerical calculations are performed for homogeneous and structured targets. Our predictions for the homogeneous target agree well with the photon spectrum measured recently at SLAC with 25 GeV electrons. The spectra obtained for the structured two segment targets exhibit the interference minima and maxima.