Generalized model of ionization profiles due to cosmic ray charged particles in planetary ionospheres and atmospheres with 5 energy interval approximation of the ionization losses function

An analytical and numerical approach for penetration and ionization of cosmic ray nuclei with charge Z in the planetary ionospheres and atmospheres is considered in this paper. The electron production rates are calculated using new formulas, which couple the five main energy intervals in the ionization losses function ( dE/dh ). This is a five interval function, which performs better approximation of the measurements and experimental data in comparison with previous results. The geomagnetic cut-off rigidities and the energy decrease laws for the different intervals are used for creation of an intermediate transition energy region, which performs the coupling of the five main intervals in the ionization losses function. A new sixth energy interval for charge decrease in lower energies is taken into account. The case of vertical cosmic ray penetration is considered. (authors)