Results from the Pierre Auger Observatory indicate that nuclei make a sizeable part of the observed flux of ultra-high energy cosmic rays (UHECRs). The theoretical study of both in-source and extra-galactic propagation requires detailed understanding of nuclear interactions with the surrounding photon fields (i.e. CMB, EBL, accretion disk thermal emission, non-thermal emissions) and in particular the resulting nuclear cascades which describe the escaping composition and its evolution over propagation.
This contribution presents a novel treatment of UHECR nuclear cascades as a Continuous Time Markov Chain showing that this process underlies the stochastic photonuclear interactions experienced by UHECRs both within sources and during extra-galactic propagation. As result, expressions for probability distributions are obtained which have closed form and are more efficient to compute than other methods presently employed such as Monte-Carlo or numerical integration of systems of differential equations. Furthermore, this approach allows more nuance in describing compositions without the need of ad-hoc restrictions (such as limiting the number of species by decay lifetime or restricting products to most frequent secondaries) expanding the number of nuclear species that can be included with low cost in computation time.
Using this method, the propagation horizon related to photointeractions is defined precisely and can be quantified to any desired level of confidence using the obtained probability density functions for complete disintegration. The in-source survival fraction is computed in an example of UHECR source previously studied, and the application of this approach for extra-galactic propagation is also discussed.