Refining the Greisen Profile for Low-Energy Cosmic Gamma-Rays: Quantifying Deviations Across Altitudes and Zenith Angles

This study refines the Greisen formalism by comparing the classical Greisen profile and a modified Greisen profile, which incorporates an empirical correction to the shower age parameter with zenith-angle dependence, aiming to better describe low-energy cascades against CORSIKA simulations of cosmic gamma-ray showers (20-800 GeV). Fittings across altitudes of 5000-5900 m and zenith angles from 0 to 40 degrees quantify deviations in particle numbers, showing that the modified profile yields deviations below 4.7%, compared to up to 12.5% for the classical profile. These improvements address low-energy ionization losses, atmospheric density variations, and zenith-angle effects, enhancing accuracy for high-altitude observatories like HAWC and the proposed CONDOR array. The modified profile offers a computationally efficient alternative, providing precise particle number predictions to advance gamma-ray astrophysics and cosmic-ray research.