UHE Cosmic Rays and Neutrinos Showering on Planet Edges

Ultra High Energy (UHE) Cosmic Rays, UHECR, may graze high altitude atmosphere leading to horizontal upward air-showers. Also PeVs ν¯ hitting electron in atmosphere may air-shower at W^- boson resonant mass. On the other side ultra high energy muon and electron neutrinos may also lead, by UHE neutrinos mass state mixing, to the rise of a corresponding UHE Tau neutrino flavor; the consequent UHE tau neutrinos, via charge current interactions in matter, may create UHE taus at horizons (Earth skimming neutrinos or Hor-taus) whose escape in atmosphere and whose consequent decay in flight, may be later amplified by upward showering on terrestrial, planetary atmospheres. Indeed because of the finite terrestrial radius R, its thin atmosphere size (h≃10) km, its dense crust, the UHE tau cannot extend much more than ∼Rhπ/2≃360 kilometers in air, corresponding to an energy E≃7.2 EeV, near but below GZK cut-off ones; on the contrary Jupiter (or even Saturn) may offer a wider, less dense and thicker gaseous layer at the horizons where Tau may loose little energy, travel longer before decay and rise and shower at E_{ν_τ}≃4-6ṡ10 eV or ZeV extreme energy. Also solar atmosphere may play a role, but unfortunately tau-showers secondaries maybe are too noisy to be disentangled, while Jupiter atmosphere, or better, Saturn one, may offer a clearer imprint for GZK (and higher Z-Burst) Tau showering, well below the horizons edges.