Incident energy dependence of hadronic activity

Two features of high-energy hadronic cascades have been long known to shielding specialists: (a) in a high-energy hadronic cascade in a given material (incident E ≅ 10 GeV), the relative abundance and spectrum of each hadronic species responsible for most of the energy deposition is independent of the energy or species of the incident hadron, and (b) because π0 production bleeds off more and more energy into the electromagnetic sector as the energy of the incident hadron increases, the level of this low-energy activity rises less rapidly than the incident energy, and in fact rises very nearly as a power of the incident energy. Both features are of great importance in hadron calorimetry, where it is the ''universal spectrum'' which makes possible the definition of an intrinsic e/h, and the increasing fraction of the energy going into π0's which leads to the energy dependence of e/π. We present evidence for the ''universal spectrum,'' and use an induction argument and simulation results to demonstrate that the low-energy activity scales as Em, with 0.80 ≤ m ≤ 0.85