The secondary electrons produced during the process of ionization by the primary charged particle are conventionally called delta rays, if their energy is large enough so that they themselves can ionize. Many studies focus upon the energy transferred in the vicinity of the primary particle track and therefore exclude interactions that produce delta rays with energies larger than a certain value Δ. This energy limit is meant to exclude secondary electrons that carry energy far from the primary particle track, since a larger energy implies a larger range. This approximation neglects the directional distribution of secondary radiation and the non-linear path of delta rays, but simplifies analytic evaluation.