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In most high energy cosmic ray surface arrays, the primary energy iscurrently determined from the value of the lateral distribution function at afixed distance from the shower core, r0. The value of r0 is mainly related tothe geometry of the array and is, therefore, considered as fixed independentlyof the shower energy or direction. We argue, however, that the dependence of r0on energy and zenith angle is not negligible. Therefore, in the present work wepropose a new characteristic distance, which we call ropt, specificallydetermined for each individual shower, with the objective of optimizing theenergy reconstruction. This parameter may not only improve the energydetermination, but also allow a more reliable reconstruction of the shape andposition of rapidly varying spectral features. We show that the use of aspecific ropt determined on a shower-to-shower basis, instead of using a fixedcharacteristic value, is of particular benefit in dealing with the energyreconstruction of events with saturated detectors, which are in general a largefraction of all the events detected by an array as energy increases.Furthermore, the ropt approach has the additional advantage of applying thesame unified treatment for all detected events, regardless of whether they havesaturated detectors or not.

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