  Recently an essential progress in development of physical models for cosmic
ray induced ionization in the atmosphere is achieved. Basically, the models are
full target, i.e. based on Monte Carlo simulation of an
electromagnetic-muon-nucleon cascade in the atmosphere. In general, the
contribution of proton nuclei in those models is highlighted, i.e. primary
cosmic ray $\alpha$-particles and heavy nuclei are neglected or scaled to
protons. The development of cosmic ray induced atmospheric cascade is sensitive
to the energy and mass of the primary cosmic ray particle. The largest
uncertainties in Monte Carlo simulations of a cascade in the Earth atmosphere
are due to assumed hadron interaction models, the so-called hadron generators.
In the work presented here we compare the ionization yield functions $Y$ for
primary cosmic ray nuclei, such as protons, $\alpha$-particles, Oxygen and Iron
nuclei, assuming different hadron interaction models. The computations are
fulfilled with the CORSIKA 6.9 code using GHEISHA 2002, FLUKA 2011, UrQMD
hadron generators for energy below 80 GeV/nucleon and QGSJET II for energy
above 80 GeV/nucleon. The observed difference between hadron generators is
widely discussed. The influence of different atmospheric parametrizations,
namely US standard atmosphere, US standard atmosphere winter and summer
profiles on ion production rate is studied. Assuming realistic primary cosmic
ray mass composition, the ion production rate is obtained at several rigidity
cut-offs - from 1 GV (high latitudes) to 15 GV (equatorial latitudes) using
various hadron generators. The computations are compared with experimental
data. A conclusion concerning the consistency of the hadron generators is
stated.
