Lateral distribution and the energy determination of showers along the ankle

TL;DR

This paper investigates the optimal distance for measuring signals in extensive air showers to improve energy estimation accuracy, accounting for uncertainties and detector configurations.

Contribution

It introduces the concept of an optimal distance, r_{opt}, for each shower, enhancing energy determination and handling saturated stations more effectively.

Findings

r_{opt} depends on detector separation, energy, and zenith angle

Using r_{opt} improves energy estimates over fixed distances

The method affects the reconstructed cosmic ray spectrum

Abstract

The normalization constant of the lateral distribution function (LDF) of an extensive air shower is a monotonous (almost linear) increasing function of the energy of the primary. Therefore, the interpolated signal at some fixed distance from the core can be calibrated to estimate the energy of the shower. There is, somehow surprisingly, a reconstructed optimal distance, r_{opt}, at which the effects on the inferred signal, S(r_{opt}), of the uncertainties on true core location, LDF functional form and shower-to-shower fluctuations are minimized. We calculate the value of r_{opt} as a function of surface detector separation, energy and zenith angle and we demonstrate the advantage of using the r_{opt} value of each individual shower instead of a same fixed distance for every shower, specially in dealing with events with saturated stations. The effects on the determined spectrum are also shown.