Multiple Scattering of light in shower optical images - an analytical calculation

摘要

One of the method for determining the primary energy of an UHE shower is to measure its instantaneousoptical images as a function of the shower depth in the atmosphere. Such an image is composed of the direct light emittedby the shower towards the detector and of the light emitted by higher parts of the shower, scattered in the atmosphere andarriving at the same time as the direct light. The second component is often called the Multiply Scattered light suggestingthat it is formed by photons scattered many times. We show that , at least in the case of Auger, this is a misnomer: themain contribution to it is made by photons scattered only once. We find analytically the image produced by these photons.We also propose a new parametrization of the ratio of the scattered to the direct light basing on our analytical solutions,separate for Rayleigh and Mie scatterings.