Shower Center of Gravity and Hadronic Interaction Characteristics

TL;DR

This paper derives equations for the shower center of gravity caused by high-energy protons in the atmosphere, linking hadronic interaction properties to shower development.

Contribution

It introduces a simplified analytical model connecting hadronic interaction characteristics with the longitudinal development of atmospheric showers.

Findings

Derived explicit equations for shower center of gravity.

Showed how hadronic interaction length influences shower development.

Provided insights into hadronic interaction effects on cosmic ray showers.

Abstract

Equations for the center of gravity of the shower originated by high energy proton in the atmosphere are written and, within certain simplifications, solved for the case of logarithmically decreasing interaction length of hadrons in the air. Obtained expression provides transparent view of the way in which hadronic interaction characteristics determine the longitudinal shower development.