Particle Physics Booklet - Particle Data Group - Lawrence Berkeley ...

224 24. Cosmic rays
24. COSMIC RAYS
Written August 2008 by D.E. Groom (LBNL).
At ∼10 GeV/nucleon the primary cosmic rays are mostly protons (79%)
and alpha particles (15% of the cosmic ray nucleons). The abundance
ratios of heavier nuclei follow the solar abundance ratios. The exception
is the Li-Be-B group, which is overabundant by a large factor relative to
solar abundance, probably due to the spallation of heavier nuclei in the
interstellar medium. The intensity from a few GeV to beyond 100 TeV is
proportional to E−2.7 . The spectrum is evidently truncated at a few times
1019 eV by inelastic collisions with the CMB (GZK mechanism).
The primary cosmic rays initiate hadronic cascades in the atmosphere,
whose thickness is 11.5 λI or 28 X0. Most of the energy is converted to
gamma rays via π0 → γγ and deposited by ionization in EM showers; few
hadrons reach the ground. For charged pions, π ± → μ ± + ν competes with
further nuclear interaction. The muon energy spectrum at the surface
is almost flat below 1 GeV, gradually steepens to reflect the primary
spectrum in the 10–100 GeV range, and steepens further at higher energies
because pions with Eπ > ∼ 100 GeV tend to interact before they decay.
Above ∼ 10 TeV, and below ∼ 100 TeV, when prompt muon production
becomes important, the energy spectrum of atmospheric muons is one
power steeper than the primary spectrum.
The average muon flux at the surface goes as cos2 θ, characteristic
of ∼3 GeV muons. The rate in a thin horizontal detector is roughly
1cm−2min−1 ; it is half this in a vertical detector.
The vertical muon flux for E>1 GeV goes through a broad maximum
at an atmospheric depth h ≈ 170 g cm−2 , but for h >
∼ 300 g cm−2 it
can be fairly well represented by I/Isurface =exp[(h−1033 g cm−2 )/
(630 g cm−2 )]. Calculators to convert h to altitude in a ”standard
atmosphere” can be found on the web. At the summit of Mauna Kea
(4205 m = 600 g cm−2 ) the vertical flux is about twice that at sea level.
The vertical p + n flux at sea level is about 2% of the muon flux, but
scales with depth as exp(−h/λI). The pion flux is 50 times smaller. The
e + /e− flux for E>1 GeV averages about 0.004 of the muon flux, but these
EM shower remnants are much more abundant at lower energies.
The energy loss rate for muons is usually written as a(E) +b(E)E,
where a(E) (ionization) and b(E) (radiative loss rate/E) areslowlyvarying
functions of E. Ionization and radiative loss rates are equal at
the muon critical energy Eμc, which is typically several hundred GeV.
If a(Eμc) andb(Eμc) are assumed constant, then the range is given by
ln(1 + E/Eμc). (Straggling is extremely important, but it is also neglected
here.) Furthermore, since the differential muon flux at very high energies
is proportional to E−α (one power steeper than the primary spectrum),
the total vertical flux at depth X is proportional to (ebX − 1) −α+1 .
This function, with b =4.0 × 10−6 cm2g−1 and α =3.6, normalized
to 0.013 m−2s−1sr−1 at X = 1 km.w.e. (km water equivalent), gives a
reasonable fit to the depth-intensity data shown in Fig. 24.5 of the full
Review. The flux at depths >
∼ 10–20 km.w.e., entirely due to neutrino
interactions, is about 2 × 10−9 m−2s−1sr−1 .
For details and references, see the full Review.