Ionization model for cosmic ray protons in ionosphere and atmosphere with 5 interval approximation of the ionization losses function

A new ionization model for cosmic ray protons with five interval approximation of the ionization losses function is presented in this paper. The geomagnetic cut-off rigidities and the energy decrease laws for the different intervals are used for creation of intermediate transition energy regions in the corresponding electron production rate model which performs the coupling of the five main intervals in the ionization losses function. This work improves the previous results for four interval model of the ionization losses function and the electron production rate. The case of vertical penetration of cosmic rays is considered. This new approach can be developed for derivation of respective detailed formulas over the full surface "altitude, azimuth angle, zenith angle." They may be then applied in the case of the corresponding 3D integration over azimuth, zenith and kinetic energy.