Development of cascade showers in dense media

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Abstract
I have discovered a new way of solving for the evolution of an electromagnetic cascade shower when the cross sections have been altered by the density. This method relies on a set of Green’s-function solutions to the usual diffusion equations of approximation A of Rossi and Greisen. The Green’s functions explicitly account for the energy and density dependence of the cross sections. This technique gives distribution functions for showers in material at any density, and for all incident and final energies. In particular, this method has been used to study the development of cascade showers at the surface of a neutron-star polar cap. Particles emitted by nuclei excited by a cascade shower are thought to be an important plasma source for radio pulsars. Showers computed using the density-suppressed cross sections penetrate much deeper than the usual Bethe-Heitler showers, which reduces the importance of the excited nuclei for pulsar models. The integrated cross sections introduced by the Mellin-transform techniques of approximation A lend themselves to a description of shower evolution in terms of the mean shower properties. The solutions to the mean shower development equations are at best a rough guide to the evolution of the shower as a whole, but they clearly illustrate the increasing penetration depth of the shower caused by the reduced cross sections.

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