Energy determination of cosmic ray showers in surface arrays using signal inference at a single distance from the core

In most high energy cosmic ray surface arrays, the primary energy is currently determined from the value of the lateral distribution function at a fixed distance from the shower core, r₀. The value of r₀ is mainly related to the geometry of the array and is, therefore, considered as fixed independently of the shower energy or direction. We argue, however, that the dependence of r₀ on energy and zenith angle is not negligible. Therefore, in the present work we propose a new characteristic distance, which we call r_opt, specifically determined for each individual shower, with the objective of optimizing the energy reconstruction. This parameter may not only improve the energy determination, but also allow a more reliable reconstruction of the shape and position of rapidly varying spectral features. We show that the use of a specific r_opt determined on a shower-to-shower basis, instead of using a fixed characteristic value, is of particular benefit in dealing with the energy reconstruction of events with saturated detectors, which are in general a large fraction of all the events detected by an array as energy increases. Furthermore, the r_opt approach has the additional advantage of applying the same unified treatment for all detected events, regardless of whether they have saturated detectors or not.