Alternative energy estimation from the shower lateral distribution function

The surface detector technique has been successfully used to detect cosmic ray showers for several decades. Scintillators or Cerenkov water tanks can be used to measure the number of particles and/or the energy density at a given depth in the atmosphere and reconstruct the primary particle properties. It has been shown that the experiment configuration and the resolution in reconstructing the core position determine a distance to the shower axis at which the lateral distribution function (LDF) of particles shows the least variation with respect to different primary particles type, simulation models and specific shapes of the LDF. Therefore, the signal at this distance (600 m for Haverah Park and 1000 m for Auger Observatory) has shown to be a good estimator of the shower energy. Revisiting the above technique, we show that a range of distances to the shower axis, instead of one single point, can be used as estimator of the shower energy. A comparison is done for the Auger Observatory configuration and the new estimator proposed here is shown to be a good and robust alternative to the standard single point procedure.