The Intergalactic Propagation of Ultra-High Energy Cosmic Ray Nuclei: An   Analytic Approach
  It is likely that ultra-high energy cosmic rays contain a significant component of heavy or intermediate mass nuclei. The propagation of ultra-high energy nuclei through cosmic radiation backgrounds is more complicated than that of protons and its study has required the use of Monte Carlo techniques. We present an analytic method for calculating the spectrum and the composition at Earth of ultra-high energy cosmic rays which start out as heavy nuclei from their extragalactic sources. The results obtained are in good agreement with those obtained using numerical methods. 
Dan Hooper, Subir Sarkar, and Andrew M. Taylor