Analytic calculations of the spectra of ultra-high energy cosmic ray nuclei. I. The case of CMB radiation

Understand

We present a systematic study of different methods for the analytic calculation of ultra-high energy nuclei diffuse spectra.

• Nuclei propagating in the intergalactic space are photo-disintegrated and decrease their Lorentz factor due to the interaction with cosmic microwave background and extragalactic background light.
• We calculate the evolution trajectories in the backward time, that describe how atomic mass number $A$ and Lorentz factor $\Gamma$ change with redshift $z$.
• Three methods of spectra calculations are investigated and compared: {\it (i)} trajectory method, {\it(ii)} kinetic equation combined with trajectory calculations and {\it (iii)} coupled kinetic equations.