Scattering of unformed Vavilov-Cherenkov radiation by the rough lunar surface during its emergence into vacuum

The model boundary problem of scattering of unformed Vavilov-Cherenkov radiation by the rough lunar surface during its emergence into vacuum is considered in the Born approximation. The case of the horizontally directed cascade is considered. The point approximation for the shower disk, but taking into account its evolutions along the track, is used. The lunar surface is defined to be sinusoidal or wavy with a wavelength varying along one of the axes, and also is simulated by various spectra of characteristic roughness sizes: Gaussian, exponential, and uniform spectra.