Response of CsI(Tl) scintillators over a large range in energy and atomic number of ions (Part I) : recombination and $\delta$-electrons

A simple formalism describing the light response of CsI(Tl) to heavy ions, which quantifies the luminescence and the quenching in terms of the competition between radiative transitions following the carrier trapping at the Tl activator sites and the electron-hole recombination, is proposed. The effect of the delta rays on the scintillation efficiency is for the first time quantitatively included in a fully consistent way. The light output expression depends on four parameters determined by a procedure of global fit to experimental data.