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Ultra High Energy Cosmic Rays (UHECR) are the most energetic particles observed in Nature, with energies up to few × 1020 eV. As any other observation of Cosmic Rays (CR), UHECR are characterized by three basic observables: spectrum, chemical composition and anisotropy. In this short review we will mainly discuss the first two observables neglecting the discussion about a possible anisotropy in the arrival directions of UHECR.

The behavior of the UHECR spectrum is mainly conditioned by the interaction of such particles with the intervening astrophysical backgrounds and by the cosmological evolution of the Universe. In the energy range E ≃ 1018 - 1019 eV the propagation of UHE particles is extended over cosmological distances with a typical path length of the order of Gpc. Therefore one should also take into account the adiabatic energy losses suffered by particles because of the cosmological expansion of the Universe.

The background affecting the propagation of UHE protons is only the Cosmic Microwave Background (CMB). There are two spectral signatures that can be firmly related to the propagation of protons through this background: pair-production dip [1], which is a rather faint feature caused by the pair production process:

Equation 1 (1)

and a sharp steepening of the spectrum caused by the pion photo-production:

Equation 2 (2)

called Greisen-Zatsepin-Kuzmin (GZK) cut-off [2].

In the case of UHE nuclei the situation changes because, apart from CMB, also the Extragalactic Background Light (EBL) becomes relevant. The interaction processes that condition the propagation of UHE nuclei are pair production, that involves only the CMB background [4], and photo-disintegration. The latter is the process in which a nucleus of atomic mass number A because of the interaction with CMB and EBL looses one or more nucleons:

Equation 3 (3)

the most relevant process is the one nucleon emission (n = 1) as discussed in [4]. The photo-disintegration of nuclei, together with the pair production process, produces a steepening in the observed spectrum. The exact position and behavior of the flux suppression depends on the nuclei species as well as on the details of the cosmological evolution of the EBL which, differently from CMB, is not known analytically being model dependent [5]. In general the nuclei flux steepening is not as sharp as the GZK and it is placed at lower energies respect to the GZK energy scale [4].

The GZK cutoff is the most spectacular feature in the UHECR spectrum. However one must remember that it is defined only for UHE protons interacting with the CMB filed. The cutoff energy position is roughly fixed by the energy where the pair-production (Eq. (1)) and the photo-pion production (Eq. (2)) energy losses become equal, namely at EGZK ≃ 50 EeV [3]. The shape of the GZK flux suppression could also be model-depend: it depends on a possible local over-density or deficit of sources and can be mimicked by low enough values of the maximum energy that sources can provide. In contrast, the pair-production dip is practically model-independent mainly because protons contributing to this energy range arrive from sources lying at cosmological distances.

From the experimental point of view the situation is far from being clear with different experiments claiming contradictory results. The HiRes and, nowadays, the Telescope Array (TA) experiments show a proton dominated composition till the highest energies with a clear observation of the proton pair-production dip and GZK cut-off [6]. Chemical composition observed by HiRes and TA is coherent with such picture showing a pure proton dominated spectrum starting from energies E ≃ 1018 eV till the highest energies. The experimental picture changes taking into account the Auger observations. The spectrum observed by Auger shows a behavior not clearly understood in terms of the proton pair-production dip and GZK cut-off [7]. This spectral behavior could be a signal of a substantial nuclei pollution in the spectrum, which is confirmed by the Auger observations on chemical composition that show a progressively heavy composition toward the highest energies, this tendency starts already at E ≳ 4 × 1018 eV [7]. In this short review we will discuss the main issues in the physics of UHECR presenting a twofold discussion from both experimental as well as theoretical point of view. The paper is organized as follows: in section 2 we will mainly discuss the two observable features connected with protons propagation, i.e. dip and GZK cut-off, presenting a comparison with HiRes and TA data, in section 3 we will focus on the Auger observations of spectrum and chemical composition, discussing the consequences of a nuclei dominated spectrum, in section 4 we will discuss the physics of the transition between galactic and extra-galactic CR, finally conclusions will take place in section 5.

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