Charmed mesons may be produced when a primary cosmic ray or the leading hadron in an air shower collide with an atmospheric nucleon. At energies $\ge {10}^8\mathrm{GeV}$ their decay length becomes larger than 10 km, which implies that they tend to interact in the air instead of decaying. We study the collisions of long-lived charmed hadrons in the atmosphere. We show that $({\Lambda }_c,D)$-proton diffractive processes and partonic collisions of any $q^2$ where the charm quark is a spectator have lower inelasticity than $(p,\pi )$-proton collisions. In particular, we find that a $D$ meson deposits in each interaction just around 55% of the energy deposited by a pion. On the other hand, collisions involving the valence $c$-quark (its annihilation with a sea $\overline{c}$-quark in the target or $c$-quark exchange in the $t$ channel) may deposit most of the $D$ meson energy, but their frequency is low (below 0.1% of inelastic interactions). As a consequence, very energetic charmed hadrons may keep a significant fraction of their initial energy after several hadronic interactions, reaching much deeper in the atmosphere than pions or protons of similar energy.

• Received 15 October 2010

DOI:https://doi.org/10.1103/PhysRevD.83.034027