Ionization model for protons in ionosphere and atmosphere with 4-interval approximation of the ionization losses function

An analytical and numerical approach for penetration of cosmic ray protons in the iono-/atmosphere is considered in this paper. This approach will improve our ionization model for planetary ionospheres and atmospheres. The electron production rates are calculated using new formulas which couple the four main energy intervals in the ionization losses function ( dE/dh ). This is a four-interval function, which performs good approximation of the measurements and experimental data. The geomagnetic cut-off rigidities and the energy decrease laws for the different intervals are used for creation of intermediate transition energy regions which performs the coupling of the four main intervals in the ionization losses function. This work improves the previous results for two and three intervals modeling of the ionization losses function and the electron production rate. (authors)