Extensive Air Showers and Ultra High Energy Cosmic Rays

Lectures given at a Summer School in Mexico: 2002

  Extensive Air Showers and Ultra High Energy
                  Cosmic Rays

                                         A.A. Watson

          Department of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK,
                                    a.a.watson@leeds.ac.uk

 Abstract. This paper is intended to be pedagogic. The first part is devoted to a brief exposition
 of the physics associated with the development of extensive air showers. This is seen as being
 relevant to any student beginning studies in this field. The latter part of the paper deals with
 methods of detection of extensive air showers, in a general way, and with results on the energy
 spectrum, arrival direction and mass distribution of cosmic rays of energy above 1018 eV. Finally,
 proposals for explaining the anomalous existence of the very highest energy cosmic rays are
 briefly discussed and forthcoming methods of detection through the Pierre Auger Observatory and
 the Extreme Universe Space Observatory (EUSO) are described shortly.

                  AN INTRODUCTION TO COSMIC RAYS
Cosmic rays were discovered by the Austrian physicist, and enthusiastic amateur
balloonist, Victor Hess, as a result of flying ionisation detectors in a series of manned
balloon flights. In 1912, he ascended to over 5300 m and found that the rate of
discharge of his ionisation chambers increased rapidly with altitude after the first
kilometre above the ground. He interpreted this observation as evidence that the earth
was being continuously bombarded by radiation that could cause ionisation. The
story of the early years of the study of this radiation has been told many times and
will be recounted only briefly here. The early workers (and notably R A Millikan)
supposed that the extraterrestrial radiation was gamma rays as these were the most
penetrating radiations then known. It was Millikan who coined the name ‘cosmic
rays’, using it first in a lecture to the British Association at the University of Leeds in
1926. It turns out, however, that only a small fraction of the radiation that causes the
type of effect observed by Hess are gamma rays: in fact most of the incoming cosmic
rays are the nuclei of atoms (from hydrogen to uranium) accelerated in places in the
Universe that we have yet to identify.
  That most of the incoming radiation consisted of charged particles was established
first by Clay who collected measurements of the intensity of ionisation as a function
of geomagnetic latitude on voyages between Amsterdam and the Dutch East Indies.
He found that the intensity fell by about 15% between the geomagnetic latitude of
Amsterdam and the geomagnetic equator. From this set of observations, confirmed

                                             1

through measurements made by Leprince-Ringuet and Auger on a voyage from
Europe to Buenos Aires, it was demonstrated that the major part of the radiation
causing the effects observed at sea level were charged particles. The interpretation
was much helped by calculations of the trajectory of charged particles in the
geomagnetic fields, most notably by Stoermer in Europe and Vallarta in Mexico.
Electrons were tentatively identified as the likely particles.
  Again, as with the initial idea that the incoming radiation was primarily gamma
rays, this proved to be an erroneous deduction. The experiments that clinched the
issue of the charge were carried out, at the invitation of Vallarta, in 1933 in Mexico
City by Johnson and by Compton and Alvarez. It had been recognised, originally by
Rossi, that the sign of the charge of the particles, if one charge dominated, would be
reflected in the ratio of the fluxes coming from easterly and westerly directions.
These definitive experiments showed that there was an excess of particles from the
west, implying that the majority of particles were positively charged. The positron
had been discovered in 1932 so that there was a suspicion that the cosmic rays might
be positive electrons. However, in 1939, using relatively sophisticated counter
systems flown in balloons, Schein and collaborators demonstrated that the bulk of the
particles were probably protons. The gamma ray and electron trails had proved to be
false ones.
  The direct determination of the charge spectrum had to await the development of
the nuclear emulsion technique with which it was established, again using balloons,
that the nuclei of elements from hydrogen to iron were all present in the primary
cosmic rays. The striking excesses of Li, Be and B in cosmic rays above their normal
abundances led to the conclusion that the bulk of the particles had travelled through
an average of 4 g cm-2 of interstellar hydrogen. Subsequently a flux of electrons was
detected at an intensity of only 1% of the charged particle flux. Much later the
presence of primary gamma rays was established but at an intensity of 10-4 of the
nuclear flux. Studies of great sensitivity have been made of the various components in
the decades since their discovery. Perhaps the gamma rays of 100 MeV or so provide
the strongest clues but the question of the origin of even the lowest energy cosmic
rays is still far from settled.
  A further approach to the search for cosmic ray origin, and the one that is the main
topic of this article, is based on the serendipitous discovery, by Auger and
collaborators in 1938, that showers of particles from very high-energy particles can
reach ground level more or less simultaneously. This discovery was made possible
by improvements to the resolving time of coincidence circuits developed by Maze,
who designed a circuit with a resolving time, τ, of 10 µs. One way to measure the
resolving time is to look for the chance coincidence rate between two counters
separated by some reasonably large distance. If the counts in each detector are
independent, then the chance rate is given by: -

                            Chance Rate = 2 N1N2τ,                               (1)

                                      2

FIGURE 1. An event of about 1020 eV recorded by the Volcano Ranch array. The black circles
represent 3.3 m2 scintillation detectors and the numbers near the circles are particle densities in
particles m-2. ‘A’ is the estimated location of the shower core. The full lines are density contours [1].

where N1, N2 are the rates in the two counters. To their great surprise Auger and his
colleagues found that the coincidence rate was much higher than expected even when
distances up to 300 m separated the counters. They concluded that ‘extensive air
showers’ existed which caused the correlated arrival of particles at widely separated
detectors. Using the newly developed cascade theory, and assuming that the showers
were initiated by photons, Auger deduced that the primary energy was about 1015 eV.
This energy was almost 6 orders of magnitude above that deduced for the charged
cosmic rays from analysis of their behaviour in the geomagnetic field. Thus, in a
single step, and as a result of a technological advance coupled with extraordinary
physical insight, the energy scale known to science was extended upwards by a
remarkable amount.
  Study of the extensive air shower phenomenon was pursued to establish the highest
energies carried by cosmic rays and also in the expectation that at a sufficiently great
energy even charged particles would cut through the magnetic fields in interstellar
and intergalactic space and retain a memory of their starting direction when they were
detected at earth. This worked progressed only slowly until the MIT group, headed
by Rossi, developed a technique for measuring the relative arrival times of the shower
particles at dispersed detectors. In pioneering work it was shown that an array of
scintillation detectors could be used to measure the shower direction and the time
spread of the particles in the shower disc. The direction of the incoming primary
cosmic ray was assumed to be perpendicular to the shower disc

                                               3

FIGURE 2. Observed spectrum of primary cosmic rays. Various features are marked. The material
of the present article is mainly concerned with the high energy portion of the spectrum. Figure, by S
Swordy, is similar to a figure in [2].

and was found within about 3°. The technique was developed rapidly and, after
running a prototype project at Agassiz, near Boston, the MIT group led efforts to
study the high-energy cosmic rays at Chacaltaya, Bolivia, and at Volcano Ranch,
New Mexico. This work did not yield the evidence of anisotropies anticipated if the
charged particles were relatively undeflected by magnetic fields, nor have later
studies with very much larger arrays sensitive to the highest energies. However, what
has been measured with high accuracy is the energy spectrum of cosmic rays, which
is now known from 1 GeV to beyond 1020 eV. A very energetic event recorded by
the Volcano Ranch array is shown in figure 1 [1] while the energy spectrum is shown
in figure 2 [2]. How the energy is deduced from the

                                             4

FIGURE 3. Cascade, or shower, from a 10 GeV proton developing in a cloud chamber that contains
lead plates [3]. The first interaction of the proton will most probably have been in one of the lead
plates. Neutral pions feed the cascade, which multiplies in the lead. Charged pions make similar
interactions to protons, or decay into muons. The area of shown is 0.5 m x 0.3 m.

pattern of particle densities and the methods of deriving the energy spectrum will be
discussed below, together with other aspects of the detection techniques.

       THE DEVELOPMENT OF EXTENSIVE AIR SHOWERS
  In this section I aim to give the reader an idea of how an air shower develops. I
believe that it is essential to have a good and intuitive grasp of the important
quantities that drive the development of the cascade and to learn how to be able to
visualise what is going on. This is an important step to take before using, or
developing, the sophisticated Monte Carlo calculations that are increasingly necessary
to interpret shower observations. Additionally, I have found such background
knowledge to be extremely useful when trying to interpret rare events, or when
thinking of methods that might be developed to explore particular aspects of showers.
  In figure 3 a cloud chamber picture of a shower created in lead plates by a cosmic
ray proton of about 10 GeV is shown [3]. The features in this picture, except for
scale, are extremely similar to those present when a high-energy particle enters the

                                             5

earth’s atmosphere and creates an air shower. Each lead plate (the dark bands running
horizontally across the picture) is about two radiation lengths thick and the area of the
picture is 0.5 m x 0.3 m. The gas in the cloud chamber was argon, effectively at
atmospheric pressure, and thus most of the shower development happens within the
lead plates. Little development of the cascade takes place in the gas but it allows a
snapshot of how the particle number increases, and then decreases, as the shower
progresses through more and more lead. This picture will provide a useful reference
in what follows. All of the important features of shower development, such as the rise
and fall of the particle numbers, and the lateral spreading of the shower, are evident,
as are some muons that penetrate much deeper in the chamber than most of the
electrons.
  The incoming particle can be identified as a proton with some confidence. The
level of ionisation excludes a heavier nucleus and the traversal of the particle through
six lead plates (about 88.5 g cm-2 or 13.9 radiation lengths) strongly excludes the
possibility that the incoming particle is an electron. To have the point of interaction,
presumably with a lead nucleus, in 7th plate is very reasonable, as we now know that
the p-air cross-section is around 250 mb (equivalent to 80 g cm-2), and that the
interaction length in lead is about 194 g cm-2 . The interaction with one of the
nucleons of lead can be represented as

                       p + p → p + p + N(π+ + π- + πo),                            (2)

where the first proton is the cosmic ray and the second proton is in the target nucleus.
A very similar equation would correspond to the target nucleon being a neutron. Of
course, charge and all the other familiar quantum numbers must be conserved. Here,
and in what follows, I have ignored the presence of particles such as K, Λ, η, Ω, Σ….
which are undoubtedly created and which are treated correctly in the detailed Monte
Carlo calculations mentioned below.

                The electromagnetic portion of the cascade

  It is convenient to follow first the fate of the πos. At rest, these particles have a
mean lifetime of 10-16s and so will nearly always decay, except at the most extreme
energies. The most common decay mode is into 2 gamma rays, πo→γγ. The decays,
πo→γe+e- and πo→e+e-e+e- are also possible, but can be ignored in a preliminary
discussion. Photons, in the electric field of a nucleus of atomic number Z, will
produce electron pairs with a mean free path

                                λpair = 1/nσpair,                                  (3)

where n is the number density of nuclei of atomic mass A of the material through
which the photon is travelling. The cross-section is given by

                       σpair ≅ ((Z2 re2)/137)(28/9)ln(183/Z1/3) cm2                (4)

                                        6

which, for air, reduces to

                             σpair ≅ 5.7 re2 =6 x 10-26 cm2 ,                         (5)

where re is the classical radius of the electron. Pair production is a catastrophic
process for the photon. The electrons of the pair, however, produced with an angle
between them of, typically, θ~mc2/hν, go on to produce further photons through the
process known as bremsstrahlung. Here, hv is the energy of the photon.
Bremsstrahlung and pair production are very similar processes. Bremsstrahlung can
be thought of classically as the radiation emitted when any charged particle is
accelerated. Here an electron or positron is accelerated in the field of an atomic
nucleus.    The cross-section for pair production and the cross-section for
bremsstrahlung, σbrem, are simply related by

                                  σpair =(7/9)σbrem                                   (6)

which reflects the similarity of the two processes at the quantum mechanical level.
The spectrum of photons emitted in the bremsstrahlung process is a flat one with, to a
reasonable approximation, all energies up to the energy of the electron itself being
emitted with equal probability. The root mean square angle of emission is of the
order of mc2/E, where E is the energy of the radiated photon. Thus, low energy
photons can be emitted at large angles.
  Energy loss by the electron is a stochastic process and it is convenient to
characterise it in terms of the radiation length, Xo, where the energy, E, retained by an
electron is given by

                                  E = Eo exp(-x/Xo),                                  (7)

with Eo being the energy of the electron as it starts to traverse material of thickness x.
Note that for bremsstrahlung the energy loss, -dE/dx, is proportional to E and is thus a
much more important source of loss than ionisation at energies above about 10 MeV.
However, as the electron loses energy, there comes a point where the rate of energy
loss due to bremsstrahlung falls below the rate of energy loss due to ionisation. When

                             -dE/dx)brem = -dE/dx)ionisation                          (8)

the electron is said to be at the critical energy, E = εc.
   Table 1 shows values of the radiation length, critical energy and the Molière radius
for some important materials, with the radiation length expressed in units of g cm-2.
It is useful to recall that the thickness of material x (g cm-2) = ρt, where the density, ρ,
in g cm-3 and the path length, t, in cm.

                                          7

TABLE 1. The radiation length, critical energy and Molière radius for various materials
                Z                    Xo /g cm-2         εc /MeV               Ro
 Air            7.4                  37.8               84.2                  77 m at NTP
 Water          7.2                  37.3               83.8                  9.4 cm
 Lead           82                   5.8                7.8                   1.37 cm

  The direction of propagation of the electron can be changed in a major way by
scattering. The theory of this was worked out in detail by Molière. An important
quantity is the root mean square (rms) scattering undergone by an electron as it
traverses a thickness of material, x. If the electron has an initial momentum of p (in
units of MeV/c) then

                             θrms=(21 MeV/pβ)√(x/Xo).                                   (9)

Thus, at the critical energy, an electron undergoes an rms scatter of about 14° as it
traverses 1 radiation length. An important quantity for appreciating the lateral spread
of extensive air showers comes from the rms scatter. The lateral distance, Ro, in
radiation lengths, by which an electron at the critical energy is scattered as it traverses
one radiation length is given by the Molière unit,

                                  Ro= 21 MeV/εc.                                        (10)

For air, the Molière unit is ~0.25 radiation lengths, or about 77 m at sea-level, the
distance depending on the air density, as dictated by the temperature and pressure.
  A helpful insight into the development of an electromagnetic cascade was given
many years ago by Heitler [4] through a ‘Toy Model’. Assume that after a distance λ,
taken as equal to the mean free path for pair production, an electron pair is created
with each electron taking half of the initial energy, Eo. Approximating the mean free
path for bremsstrahlung as equal to that for pair production (i.e. ignoring the factor
7/9 in equation 6), we can assume that a bremsstrahlung process takes place for each
electron after a further distance λ. The cascade, continues with the energy being
shared equally at each branching node, until that rate of energy loss by
bremsstrahlung equals the rate of energy loss by ionisation, i.e. until the electron
energy has fallen to εc. Suppose that this happens after a depth X, then the number of
branching nodes, n = X/λ. Hence, the number of track segments of electrons and
photons at a depth X is given by

                                       N(X) = 2X/λ.                                     (11)

The energy of the electrons and photons has degraded to E(X) = Eo/N(X) at depth X.
Hence the number of particles at shower maximum (electrons and photons) is
N(Xmax) = Eo/εc and the depth at which the shower reaches maximum is given by

                                  Xmax = λ ln (Eo/εc)/ ln 2.                            (12)

                                          8

This last relation is a useful descriptor of how the depth of shower maximum changes
with energy (see below). These ideas can be used to make a very crude estimate of
the energy of the particle that initiates the cascade in figure 3: it is around 10 GeV.
  The above paragraphs give some basic details about the development of the
electromagnetic cascade. The processes of bremsstrahlung and pair production are
extremely well understood and all cross-sections are accurately calculable from
theory based on quantum electrodynamics (QED). In the 1950s and 1960s extensive
analytical calculations were developed, particularly by Nishimura and Kamata, and
these were followed by Monte Carlo calculations which allow the cascades to be
examined in further detail. In addition to QED-defined processes, account has also to
be taken of the production of pions by photons and is an important factor to consider
when calculating the number of muons present in showers produced by photons.
Note that the γp cross-section is about 1/300 of that for pp interactions.

                               The hadronic cascade

  In extensive air showers initiated by baryons, the hadronic part of the cascade is
crucial for feeding the electromagnetic cascade. The development of the hadronic
cascade is much harder to describe in a simple way as the details of the key
parameters, such as cross-section, inelasticity and multiplicity, are poorly known
from experiment and cannot yet be calculated from theory. In particular, of course,
the energies of interest in the earliest stages of the development of air showers are
well beyond accelerator energies and one has to be alert for surprises. For example
up until the discovery of the rise in the cross-section of proton-proton interactions in
1973, it had been widely expected that the cross-section had reached an asymptotic
limit that would remain to the very highest energies. Similarly, ideas of Feynman
concerning the ‘scaling’ of inclusive cross-sections led to predictions about the
variation of multiplicity of secondaries produced in collisions, at variance with what
was later found by experiment. We have a much more tenuous grasp on several key
aspects of shower development than is desirable.
   The pp interaction of equation 2 is highly oversimplified in that it is assumed that
only pions are produced. However, nearly all that will be said about the role of pions
can be applied, in an obvious way, to the other, less numerous, hadrons that are
created.
  The outgoing nucleon, often called the leading nucleon, will usually carry more
energy than any other particle leaving the interaction region and will interact again
with the characteristic mean free path. If we approximate the mean free path in air by
a constant length of 84 g cm-2, we see that, for a particle entering the atmosphere
vertically, the mean number of interactions of successive leading nucleons before sea-
level is about 12. The fluctuations around this number are one of the major causes of
the differences that are predicted, and observed, between showers produced by
particles of the same primary energy. Another major source of fluctuations is the
inelasticity of the collision, where the inelasticity, κ, is defined as the fraction of the
energy of the incoming particle that is not retained by the leading nucleon. The

                                         9

inelasticity is not a fixed quantity and can vary between 0 and 1. It can be useful for
rough estimates to take κ = 0.5, so that half of the energy is transferred to pions, but
this is a crude approximation (see figure 6 below). Charge independence dictates that
energy is shared equally between the three sets of pions: thus in a collision of a
leading nucleon approximately 0.5 x 0.33 = 0.16 of the energy of the leading nucleon
transfers, through the neutral pions, to the electromagnetic cascade.
  The charged pions, produced in collisions of the leading nucleon or primary cosmic
ray with a nucleon in a nitrogen or oxygen nucleus, will go on to interact or decay,
the two processes being competing mechanisms for their disappearance. The distance
travelled before interaction depends on the cross-section for π-p interactions. Direct
measurement has shown that this cross-section is roughly 2/3 that for p-p collisions,
reflecting to some extent the fact that there are two valence quarks in a pion as
compared with three in a nucleon. The cross-sections vary with the mass of the target
nucleus as

                   σpA(inelastic) = 45A0.691mb and σπA = 28A0.75mb,                    (13)

respectively. The pion cross-section in air, in the GeV range, is about 115 g cm-2.
Both cross-sections rise with energy (see discussion below). Whether a pion will
decay before it interacts depends on the density of air and on the Lorentz factor of the
pion. The probability of the two processes occurring in a given distance interval is
equal when the mean distance travelled before decay,

                                      Γτc = λ/ρ,                                       (14)

the mean distance travelled before interaction. In this equation, Γ, is the Lorentz
factor of the pion which has a rest lifetime, τ = 2 x 10-8s, c is the velocity of light, λ is
the mean free path for interaction and ρ is the density of the material (air in the case
of an air shower). Thus for an air density of 5 x 10-4 g cm-2 (altitude ~ 5000 m) the
Lorentz factor at which decay and interaction will have equal probability is ~380,
corresponding to a pion energy of about 50 GeV. At higher altitudes, the
corresponding Lorentz factor will be enhanced and it is clear that in the early stages
of shower development the pions will tend to interact. These numbers are illustrative
only as the rising cross-section must be taken into account for an accurate estimate.
  The parameters of pion interactions at high energies are poorly known from
machine studies. It is normally assumed that there is a ‘leading pion’ coming from
the collision, just as there is a leading nucleon from a proton collision. The
multiplicity of secondaries produced is also poorly known, as is the case for proton
collisions.
  An important parameter that plays a role in the lateral spread of the shower is the
transverse momentum, pt, of the secondary particles. The distribution is well
described by

                             g (pt)dpt ∝ pt exp(-pt/),                             (15)

                                         10

FIGURE 4. Inelastic p-air cross-sections from measurements and models as at 1997 (upper panel) and
2001 (lower panel), [5].

where the mean transverse momentum,  = 350 MeV/c. Thus it is clear that in
early stages of shower development, before electron scattering becomes important,
the opening angle of the pions coming from pion and proton collisions are much
larger than the corresponding angles associated with pair production and
bremsstrahlung. This reflects the relative strengths of the strong and electromagnetic
interactions.

     The key parameters of the hadronic cascade and Monte Carlo
                             calculations
  These simple ideas are useful for giving an understanding of how the hadronic part
of the shower develops but reality is much more complex and our knowledge about it

                                           11

is very uncertain1. For example, the proton-proton cross-section, and hence the
proton-air cross-section, does vary with energy and in the range beyond accelerator
energies the extrapolation of the cross-section depends on the choice of model used to
FIGURE 5. Mean multiplicity of charged particles produced in inelastic proton-air and pion-air
collisions [6].

describe the hadronic interactions. The model dependence is illustrated in figure 4
[5]. Currently, two of the favoured models are Sibyll 2.1 and QGSjet, the most recent
version of which are ’98 and ’01. The QGSjet models predict the slower rise of
cross-section with energy and at 1020 eV the difference is about 100 mb. There are
similar differences between the cross-sections predicted for π-air collisions. There
are also large differences between the multiplicities predicted by these two models.
In figure 5 the multiplicity of charged particles is shown: at 1020 eV this is about 400
for Sibyll 2.1 while for QGSjet98 the corresponding value is more than twice as large.
The same trends are associated with π-air collisions. The multiplicity is important in
determining the number of muons expected in the shower.

1
  Recently (2004), J Matthews has described a Heitler-type approach to hadronic interactions
that is strongly recommended. This will be published in Astroparticle Physics. See ICRC
(Hamburg) Proceedings p 261 for an early version of this work.

                                             12

A further important quantity is the average longitudinal momentum taken by the
leading baryon from the collision. In figure 6 the average momentum fraction carried
away is shown for p-N14 collisions. This ‘elasticity’ falls from around 0.5 at 1011 eV
to about 0.3 at 1020 eV. There is little guidance about this quantity from accelerator
measurements. In colliding beam experiments, the particles carrying large fractions
of the energy of the incoming particles travel down the accelerator beam pipe and are
not observed. There is a difference here between the interests of the cosmic ray
physicist and those of the accelerator physicist. Just as Rutherford learned nothing

about the structure of the nucleus by studying alpha particles deflected through small
FIGURE 6. Mean elasticity (= 1 - κ) of proton-air and pion-air collisions as predicted by QGSjet98
and SIBYLL 2.1 [6]

angles, the particle physicist is more interested in those interactions reflecting large
angle scatters. The spread of the longitudinal momenta of pions is poorly known.
  In view of the significant differences between the predictions of the two models, it
is, at first sight, remarkable to find that the result of Monte Carlo calculations of the
longitudinal development of showers show only small differences between the Sibyll
and QGSjet models (figure 7). This is, in part, because the larger cross-section
associated with the Sibyll model is associated with the smaller multiplicity (compare
figures 4 and 5) and these factors conspire to give very similar predictions of the
longitudinal development of the shower.

                                           13

The differences between the two models, in their extrapolations, arise from the
different assumptions that are made about the distribution of partons in the protons
and pions. An illuminating discussion of these differences has been given in [6] and
will not be discussed further here. The reader is also directed to the discussion on the
relationship between cross-section and multiplicity given in [7].
  Thus far, nothing has been said about fluctuations in shower development. All of
the key factors just discussed (and summarised in [4], [5] and [6]) relate to average

values. Of importance, as these can be measured rather directly (see below) are the
predictions of the fluctuations to be expected in Xmax. These have been calculated
recently [6] for the two models mentioned here and results are shown in figure 8.
FIGURE 7. Average longitudinal shower development for vertical proton and iron showers of 1019
eV. The dashed vertical line indicates the atmospheric depth of the Auger site [5].

   Charged pions decay into muons and muon-neutrinos (π→ µ+νµ). Muons, having a
lifetime nearly 100 times that of the pion, do not decay until their energies have
become quite low (

It is useful to have, as reference, some numbers to characterise the predicted
behaviour of showers. Values of Nmax and Xmax are listed in table 2, taken from [6].

TABLE 2. Nmax and Xmax as calculated with two models of particle interactions
                                  Nmax                                 Xmax g cm-2
                   Sibyll 2.1         QGSjet98            Sibyll 2.1          QGSjet98
  19                         9                   9
10 eV              7.2x 10            7.1 x 10            799                 785
  20                          10                 10
10 eV              6.9 x 10           6.8 x 10            856                 832

  The most recent QGSjet model (’01) predicts that showers will maximise a few g
cm-2 higher in the atmosphere than is predicted using QGSjet98, further increasing
the discrepancy between the two models.

FIGURE 8. Fluctuations of the position of the shower maximum, σ. The solid line is for the most
recent SIBYLL model (SIBYLL 2.1) while the dotted line is for SIBYLL 1.7. The dashed line is for
the QGSjet98 model [6]

  The total number of muons in showers, as predicted using the two models, is shown
in figure 9. The Sibyll model predicts significantly fewer muons than QGSjet. At

                                          15

1020 eV the discrepancy is a factor of 1.37 for muons of energy above 0.3 GeV, an
energy of importance for the Auger Observatory, as vertical muons of this energy and
above traverse the water tanks of the surface array. The difference predicted in
multiplicity of secondary particles (figure 5) accounts very largely for the differences.
  At quite modest distances from the shower core (> 2Ro), the dominant particles are
photons, electrons and muons in the rough numerical ratio of 100:10:1. The high
energy hadrons (including the surviving leading nucleon) are within in a few metres
of the shower axis though there are low energy nucleons, primarily evaporation
nucleons from the many interactions, that have a much broader lateral spread and that
may be important in some types of detector. The lateral spread of the particles is
crucial for one of the methods of detecting high energy cosmic rays, as will be

discussed below in the context of shower detection.

FIGURE 9. Average number of muons at sea level , obtained in proton showers with zenith
angle θ = 0°. The solid (dotted) line represents the values obtained with SIBYLL 2.1 (SIBYLL 1.7),
while the dashed line is for QGSjet98. The panels are for the different energy thresholds shown [6].

                                            16

Not all showers are produced by protons and it is commonly assumed that the
baryonic primaries creating air showers will lie in the range between protons and iron
nuclei. Details of how an iron nucleus interacts with a nucleus of oxygen or nitrogen
are unclear. Certainly the cross-section is much reduced (equation 13). For an iron-
air nucleus collision the cross-section is about 1.8 b, corresponding to a mean free
path of about 13 g cm-2 at GeV energies. At higher energies the cross-section will
rise, corresponding to the rise in the p-p cross-section. It is commonly presumed that
the A-nucleons of the incoming nucleus behave as A free ‘leading nucleons’
following the first collision, although this is certainly an over-simplification. It
should be immediately clear that the stochastic fluctuations in showers caused by the
relatively long mean free path of the nucleons will be significantly reduced because
of superposition, at some level.
  Showers produced by gamma rays will develop via pair production and
bremsstrahlung in the manner described and their behaviour can be accurately
predicted. At energies above 1019 eV there are further important processes that need
to be taken into account in some situations. Quantum mechanical interference, (the
Landau-Pomeranchuk-Migdal or LPM effect) becomes important and acts to reduce
the cross-sections for pair production and bremsstrahlung. The LPM effect is of little
consequence in proton-initiated showers. Additionally pair production through
photon interactions with the geomagnetic field must be considered [8, 48].

               THE HIGHEST ENERGY COSMIC RAYS
  In this section I will outline why the highest energy cosmic rays are of interest and
describe the techniques that are used to detect them.

         Why are Ultra High Energy Cosmic Rays interesting?
  There is continuing fascination with the origin of ultra high-energy cosmic rays
(UHECR). By these I mean that small fraction of the cosmic ray flux, which has
energies above 1018 eV. The existence of such particles, which in collisions with
stationary nuclei produce centre-of-mass energies of about s = 40 TeV , has been
known for over 30 years, but their origin, and the route by which they acquire this
macroscopic energy, is unknown and indeed presents an extraordinary puzzle. One of
the reasons why the highest energy cosmic rays are of interest is because the places
where they are produced are probably astrophysical sites containing unusually large
energies in their magnetic field structures. This statement can be justified by a very
general argument due to Greisen [9]. Assume that the acceleration region must be of
a size to match the Larmor radius of a particle being accelerated and that the magnetic
field within it must be sufficiently weak to limit synchrotron losses. Analysis with
these constraints shows that the energy of the magnetic field in the source grows as
Γ5, where Γ is the Lorentz factor of the particle. For 1020 eV this energy must be >>
1057 ergs and the magnetic field must be < 0.1 Gauss. Such putative cosmic ray
sources are also likely to be strong radio emitters with radio power >> 1041 ergs s-1,

                                      17

unless protons or heavier nuclei are being accelerated and electrons are not. Thus we
expect that the accleration of the most energetic cosmic rays will take place in well-
known objects.
  Such energetic sources are relatively rare and are mostly very far from earth.
Particles travelling to us from the more distant of them can have their initial energy
significantly reduced for the following reason. Almost immediately after the 2.7 K
radiation was discovered, it was recognised independently by Greisen [10], and by
Zatsepin and Kuzmin [11], that if the highest energy cosmic rays were of universal
origin then interactions of the particles with this radiation field would severely
modify the energy spectrum observed at earth from what it was at the source. The
high-energy particles ‘see’ the microwave photons strongly blue shifted by a factor of
about 2Γ, where Γ is the Lorentz factor of the particle. The important reaction is

                      γ + p → ∆+ → p + π0 or n + π+ .                           (16)

Photo-pion production sets in with such dramatic effect above 4 x 1019 eV that
Greisen’s paper [10] was entitled ‘End to the Cosmic Ray Spectrum?’ When the
proton has energy above a few times 1019 eV the energy of the blue-shifted photon is

                                      18

FIGURE 10. Calculation of the mean energy of protons, as they travel through the 2.7 K radiation, as
a function of distance for various energies [12]

sufficient to excite the ∆+-resonance thus draining the energy of the proton through
pion production and, coincidentally, producing a source of ultra high-energy gamma
rays and neutrinos. Using relativistic kinematics it can be shown that the proton, in
its rest frame, ‘sees’ a photon of energy ε/ = εΓ(1 + βcos θ), where θ is the angle
between the directions of travel of the photon and proton, β is v/c, with the usual
notation, and ε is the energy of the microwave background photon. The threshold for
photo-pion production in the laboratory system is 145 MeV so that for a head-on
collision between a proton and a microwave photon of average energy ~6 x 10-4 eV,
Γ=1011. More detailed calculations show that the spectrum is predicted to steepen at
an energy lower than this because the spread of energies in the black body spectrum
of the photons lowers the threshold value of Γ. The proton losses about 1/6th of its
energy in each collision.
  An elegant demonstration of the importance of this pion production process is
shown in figure 10 [12]. Here the mean energy of a proton as a function of the
distance travelled from a source is shown for initial proton energies of 1020, 1021 and
1022 eV. We see that once the proton has travelled ~100 Mpc through the 2.7 K
radiation field, its energy is independent of its initial value and has become almost
distance-invariant at just below 1020 eV. The implication of this calculation is that
observation of a particle with energy >1020 eV would imply that its source lay within
~100 Mpc of the earth. The sharp fall in the number of particles predicted to occur
above 4 x 1019 eV is known as the GZK cut-off. The energy is lost from the proton in
a stochastic manner. At 1020 eV there is a 50% probability that the proton will have
travelled more than 20Mpc before reaching the earth.
  Nuclei and photons also suffer energy losses through interactions with photons. A
typical reaction is

                               γ + 56Fe→ 55Fe + n.                                           (17)

For heavy nuclei the giant dipole resonance (typically 10 MeV at the peak) is excited
at similar total energies to that at which the ∆+ resonance is excited with protons, and
iron nuclei would be fragmented over distances comparable to the attenuation lengths
for protons. Here the diffuse infrared background plays a role of increasing
importance. However, the density of it is still poorly known and the estimate of the
attenuation is correspondingly uncertain.
  High-energy photons are removed through interaction with radio photons via the
electron-pair production process,

                                    γ + γ→ e+ + e-.                                          (18)

                                            19

Although lack of accurate information about the diffuse flux of radio photons of
around 10 - 100 MHz makes the attenuation difficult to assess accurately, the distance
scale is probably considerably shorter than for protons and nuclei.
  All of these energy loss processes can also take place in the photon fields that very
probably surround the sources of the particles.
  Although it is now over 35 years since the above effects were pointed out, it is still
not established whether the spectrum in the region of 1020 eV contains the modulation
features that are expected. The difficulties in obtaining precise information lie in the
very low flux of the particles and in the fact that observations have usually to be made
many interaction lengths beyond the first interaction point, so that precise energy
estimates are difficult. Approximate flux values are ~100 km-2 y-1 above 1018 eV, ~1
km-2 y-1 at 1019 eV, and ~1 km-2 per century at 1020 eV.

     Detection methods for UHECRs: Detectors past and present
  UHECRs can only be detected through the extensive air showers that they create in
the atmosphere, as was explained above. A primary particle of 1019 eV will have
nearly 1010 particles in the resulting cascade when it reaches ground level (see table
2), while Coulomb scattering of the shower particles (mainly electrons), and the
transverse momentum associated with the strong interactions of protons, nuclei and
mesons (usually described as ‘hadronic interactions’) early in the cascade, spread the
particles over a wide area. A shower from a 1019 eV primary has a footprint on the
ground of over 10 km2. It is useful to keep in mind the picture of the miniature
shower in a cloud chamber (figure 3).
  The generic method of detection of air showers is based on developments of the
technique used by Auger and his colleagues in their discovery work. The procedure
is to spread a number of particle detectors (scintillators and water-Cherenkov
detectors are currently the devices of choice) in a regular array on the ground. The
Volcano Ranch array (figure 1) was the earliest example of such a giant array. The
higher the primary energy the larger can be the spacing between the detectors. To
study showers produced by primaries above 1019 eV the spacing between the
detectors can be over 1 km. At such a distance, the signal comes from muons,
electrons and photons, with the relative contributions depending on the type of
detector. The response is usually expressed in units of the signal produced by a muon
traversing the detector vertically (vertical equivalent muon or VEM) and is about 2
VEM m-2 at 1 km from the centre of a shower produced by a primary of 1019 eV.
Thus with a detector of 10 m2 a strong response is readily measurable. A smaller
spacing between detectors is desirable but is not feasible over large areas for financial
reasons, although portions of a giant array are sometimes constructed with smaller
spacing (figure 14). The direction of the events can be measured to better than 3° by
determining the relative times of arrival of the shower disk at the detectors. The
particle density pattern can be used to infer the number of particles that reach the
ground. To determine the primary energy one must use predictions from a calculation
carried out with assumptions about the development of the shower in the atmosphere
using extrapolations of the properties of interactions studied at accelerators. It is, of

                                       20

course, uncertain, as we have seen, as to what the characteristics of hadronic
interactions are at the centre-of-mass energies of interest that are around
  s = 4 × 1013 eV . Additionally most of the particles in the shower lie within about
100 m of the shower core and are unobservable with a sparse detector array. Methods
have been developed to overcome this limitation. In particular it has become
recognised (principally following the work of Hillas [13]) that the density measured
by scintillators or water-Cherenkov detectors at distances of many hundreds of metres
from the shower axis are closely proportional to the primary energy. However, the
energy estimates remain difficult to make and their systematic accuracy is hard to
quantify even though such densities can be accurately measured at ground level.
Typical measurement errors lead to uncertainties in the ground parameter of about 15
– 20%, but the conversion to primary energy may contain a systematic error of 30%.
An indication of the manner in which fluctuations are reduced at large distances is
shown figure 11 [14]. The small fluctuations make the technique viable.

  Fortunately, another detection method has been developed which does not suffer
from the drawback of model dependence. Shower particles excite the 1+ and 2+ bands
of nitrogen as they traverse the atmosphere. The major component of the resulting
fluorescence is in the 300 - 400 nm range and is emitted isotropically. The emission
FIGURE 11. The fluctuations in the relative densities of S(r) (where the relative density is defined as
the deviation of the density from the average divided by the average density). S(r) is the scintillator
density at r m. The simulations are for different masses at 1017 eV using the COSMOS model [14].

spectrum is shown in figure 12. Although only about 4.5 photons are radiated per
metre of electron track, the light from showers produced by primaries of energy

                                             21

above ~3 x 1017 eV is detectable with arrays of photomultipliers on clear, moonless
nights. In principle, the technique allows a calorimetric measurement of the shower
energy in a manner similar to the method often used at particle accelerators. The
resulting cascade profile gives the particle number as a function of depth and the
energy of the primary can be obtained rather directly from the area under the curve.
The energy of the particle that initiates each cascade is obtained by integrating under
the cascade curve and multiplying the result by the ratio of the critical energy for an
electron in air, about 84 MeV, to the radiation length, about 38 g cm-2 (see table 1).
More details are given below. In extreme cases, the light may originate 30 km from
the photomultipliers and an understanding of attenuation effects of the intervening
atmosphere is very important. The fluorescence yield of photons, as a function of
wavelength in the wavelength range studied, must be known accurately so that
corrections can be made for Rayleigh scattering. Attenuation by the aerosol
component of the atmosphere must be also be understood and continuously
monitored. In addition to the energy inferred from the fluorescence light, a correction
of about 10% must be made to the primary energy estimate for energy that goes into
muon, neutrino and hadronic channels [15]. The angular accuracy achievable with
the fluorescence technique is very similar to that attained with arrays of particle
detectors, particularly when stereo observations are made.
  The surface array technique has been realised on scales > 8 km2 at 5 sites, Volcano

Ranch (USA), Haverah Park (UK), Narribri (Australia), Yakutsk (Russia) and
AGASA (Japan). The fluorescence technique has, until very recently, been
implemented only by the Fly's Eye group from the University of Utah (USA)
FIGURE 12. The relative yield of nitrogen fluorescence as a function of wavelength [22].

                                            22

working in the Dugway desert: this group has thus provided a key set of data. The
Fly’s Eye instrument consisted of two clusters of 880 and 460 photomultiplier tubes
set 3.3 km apart. With these units it was possible to map out the longitudinal
development of individual shower events. The largest event observed by Fly's Eye
was estimated to have an energy of 3 x 1020 eV: its longitudinal profile is shown
figure 13 [16]. At present the only devices taking data above 1019 eV are the AGASA
instrument in Japan, which has an aperture of 170 km2 sr and has been in operation
for over 10 years, and the HiRes detector (a development of Fly's Eye), which started
to observe in 1998. In addition, preliminary data are being taken with the
Engineering Array of the Pierre Auger Observatory (see below).
  It was the array technique that was first used to establish that the cosmic ray
spectrum extends beyond 1019 eV. In the late 1950s Linsley laid out 19 scintillation
detectors (figure 1) on an 884 m hexagonal grid at Volcano Ranch, New Mexico [1].
The first events above 1019 eV were recorded there and one estimated to have been
produced by a primary of energy ~1020 eV was described in 1962, some four years
before the GZK prediction. Energy estimates have been re-assessed over the years as
our knowledge has increased and Linsley’s initial estimate has been found to be
robust.
  The distributed detector concept was further developed by a group from the
University of Leeds who constructed an array at Haverah Park, which differed in a
number of important respects from that at Volcano Ranch. The detector elements
were deep (1.2m) water-Cherenkov detectors of large area (typically 34m²) and sub-
units of these detectors formed arrays tuned to lower energies. The large areas of the
peripheral detectors enabled densities to be measured as far as 3 km from the axis.
The density map of one of the largest events recorded at Haverah Park is shown
figure 14 [17]. The water tanks respond very efficiently to photons and electrons in
addition to muons and, at 1 km, the signal comes from ~40% muons and ~60%

                                      23

FIGURE 13. The cascade curve produced by the largest Fly’s Eye event of 3 x 1020 eV. The x-axis
shows the depth of the cascade in the atmosphere measured from the top. The shower maximum is at a
depth of about 800 g cm-2. In these units, the atmospheric depth in the vertical direction is close to
1000 g cm-2 at sea level [16].

electrons and photons. The tanks are 3.4 radiation lengths thick and most of the
electrons and photons, which have mean energies of about 10 MeV, are completely
absorbed. The photons are 10 times more numerous than the electrons at the
distances of interest. The large number of detectors allowed the size at the ground,
defined by the water-Chernkov density at 600 m, to be found to within 10%. Using a
model of particle interactions (QGSjet98), that appears to describe many properties of
showers rather well up to 1018 eV, the primary energy is estimated to be 8 x 1019 eV
[25]. It is not yet possible to assess the systematic error in this evaluation, or in those
from other ground arrays, because of differences between different models.
  The largest array constructed so far is that known as AGASA (Akeno Giant Air
Shower Array), which is operated by a group led by the Institute of Cosmic Ray
Research of the University of Tokyo. This array comprises 111 scintillation detectors
each of 2.2 m2 spaced on a grid of about 1 km spacing. The scintillators are 5 cm
thick and so respond mainly to electrons and muons. The detectors are connected and
controlled through a sophisticated optical fibre network. The largest events detected
have energies of 2 and 3 x 1020 eV and one of these is shown figure 15 [18]. The

                                             24

FIGURE 14. One of the largest event observed at Haverah Park. The numbers beside the detectors
(indicated by the black dots) are the densities in units of vertical equivalent muons per square metre.
The detector areas vary from 34 m2 at A1 – A4 to 1 m2 for those detectors shown only in the right-hand
portion of the diagram [17].

AGASA instrument has recorded the majority of events reported as having energies
above 1020 eV and, as described below, this work, taken on its own, appears to
provide convincing evidence for trans-GZK particles.
  Since mid-1998 a successor to the Fly's Eye instrument, known as Hi-Res [19], has
started to take data at the Dugway site. In its final form it is expected to have a time-
averaged aperture of 340 km2 sr at 1019 eV and 1000 km2 sr at 1020 eV. This is a
stereo system which will measure the depth of shower maximum to within 30 g cm-2
on an event-by-event basis. This precision is usefully smaller than the expected
difference in the mean depth of maxima for proton or Fe initiated showers. The plans
for the HiRes instrument were in train before the 3 x 1020 eV event was reported and
the aim was to build a detector with 10 times the sensitivity previously achieved in
the region above 1019 eV. As with the stereo Fly's Eye, there are two locations for the
detectors: these are separated by 12.5 km. The increase in aperture and in Xmax
resolution over Fly's Eye comes from the reduction in the aperture of each
photomultiplier from 5° x 5° to 1° x 1° and the increase in the diameter of the mirrors
from 1.5 to 2 m. The enhanced sensitivity will enable showers to be seen above the
noise out to 20 to 30 km. The attainment of either of these reaches will be a
significant achievement and precise monitoring of the atmosphere will be necessary
to reconstruct the shower profiles accurately and to define the aperture, which grows
as the shower energy rises. Each mirror is viewed by 256 close-packed
photomultipliers: there are 42 mirrors at one site and 22 at the other. The first report
of the energy spectrum measured by the HiRes detector has recently been submitted
[52].

                                             25

FIGURE 15. The detector arrangement of the Japanese array, AGASA, together with one of he
highest energy events observed by the array. Dots in the right-hand figure show the detector positions
and open circles are charged particle densities observed by each detector with the radius of the circle
proportional to the logarithm of the density. The left-hand diagram shows the manner in which the
densities fall off with distance [18].

    MEASURING THE ARRIVAL DIRECTION, ENERGY AND
               MASS OF COSMIC RAYS
  The methods of determining the desired parameters of the incoming cosmic rays are
different for the generic ground array method and for the fluorescence technique. The
methods will therefore be considered separately.

                  Direction Measurement with Ground Arrays

  The arrival direction of the incoming cosmic ray is derived from measurement of
the relative arrival times of the shower front at the widely spaced detectors of ground
arrays. The shower front is assumed to move through the atmosphere at the velocity
of light. As a first step, the shower front is taken as a plane perpendicular to the
direction of the incoming particle. After the centre of the shower, the shower core,
has been found a more sophisticated description of the shower front in terms of a
section of a sphere may be appropriate. How the individual relative time
measurements are combined is a matter for careful consideration as the arrival time of
the ‘first particle’ may be difficult to define. Large area detectors will ‘catch’ earlier
particles than small area detectors and Monte Carlo calculations can be a helpful
guide to the most effective procedures. For the giant arrays that have so far reported
data the directions are claimed to be measured to better than 3°.
  It is not usually possible to make independent checks on the direction
determination. When 6 or more detectors are struck, a comparison between directions
determined by independent subsets of times may be useful. The observation of the

                                             26

FIGURE 16. A comparison of the declination distributions observed at Volcano Ranch (all zenith
angles recorded by a scintillator array) and at Haverah Park (zenith angles less than 60° recorded by a
water-Cherenkov array) [21]

shadow of the moon or the sun that has been exploited so successfully at energies
below 1015eV [20] cannot be used at higher energies as the shower rate is too low by
many orders for magnitude. Exceptionally, at Haverah Park, a check was possible in
some instances when high momentum muons (> 45 GeV/c) were recorded in the
tracking detectors of a magnetic spectrograph. It is also important to recognise that
the accuracy of direction measurement will vary from shower to shower and for some
types of anisotropy searches this detail must be taken into account.
  Knowing the direction of the shower in terrestrial coordinates (usually expressed as
the angle from the zenith and the azimuthal angle), and the time of arrival in some
suitable reference system, the celestial (right ascension and declination) and the
galactic coordinates (galactic latitude and longitude) can be found. An advantage of a
ground array, assuming that it operates for several years at high efficiency, is that the
exposure in right ascension will be close to uniform. The distribution in declination
is a function of the latitude of the array, the type of particle detector used and the
zenith angle above which data are accepted. As an illustration, the

                                             27

FIGURE 17. Geometry of an air shower trajectory as seen by Fly’s Eye. The shower detector plane
contains both the extensive air shower and the centre of the Fly’s Eye detector and is specified by fits
to the spatial pattern of hit photomultiplier tubes, which must lie along a great circle on the celestial
sphere. The angle ψ and the impact distance Rp are obtained by fits to observation angles χi vs. time of
observation [22].

declination ranges observed at Volcano Ranch (a scintillator array at 35°N, and for
which all zenith angles were included) and at Haverah Park (a water-Cherenkov array
at 54° N and with the showers restricted to below 60°) are compared in figure 16 [21].

            Direction Measurement with a Fluorescence Detector
  In the case of fluorescence observation of an air shower, the whole sky is viewed by
many photomultipliers. The fluorescence light is emitted isotropically along the
trajectory of the shower and is collected by mirrors. Photomultipliers viewing the
mirrors record the time sequence of arrival of the light and also its quantity. The

                                              28

shower detector plane, defined in figure 17, is reconstructed from the sequence of hit
photomultipliers [22]. The distance to the shower axis (Rp) and the incident angle ψ
in the plane are then determined from a fit of the time sequence of hit
photomultipliers. Details of the fitting procedure are given in [22].
  If a shower is seen simultaneously by two fluorescence detectors, a shower plane
for each one can be determined and the intersection of these planes defines the
direction without timing information. Typically, the uncertainty of the direction in
space measured with the fluorescence technique is ~ 2 – 3°.

                 Energy determination with ground arrays
  The shower energy is inferred by a measurement of the particle signal at a large
distance from the shower core. To find the core, and hence determine the density at
an appropriate distance the fall off of density in the detectors must be known. This is
described by a lateral distribution function (LDF) which is dependent on detector
type, zenith angle, primary energy and the nature of the primary particle. The LDF
must be determined empirically from the observations. How this is done in the case
of arrays of water-Cherenkov tanks has been described recently [23, 24]. Using
minimisation techniques, the shower core is determined and the ground parameter
used to relate observations to primary energy can be obtained. For the Haverah Park
array, the adopted parameter is ρ(600), the water-Cherenkov density at 600 m from
the shower axis. At AGASA, the corresponding parameter was the scintillator
density measured at 600 m (S(600)). For the showers observed at the atmospheric
depth of Haverah Park and AGASA, the measured ground parameter decreases with
zenith angle at fixed energy. To combine observations from different zenith angles
an attenuation length, λ, is measured by comparing the density in showers observed at
the same rate but at different zenith angles. For showers of ~1018 eV observed with
water-Cherenkov detectors λ is found to be ~580 g cm-2, in reasonable agreement
with calculations using the QGSjet model for p or Fe primaries [25].
  To determine the primary energy one must use predictions from a calculation that
has been made with assumptions about the development of the shower in the
atmosphere using extrapolations of the properties of interactions studied at
accelerators. It is, of course, uncertain as to what the characteristics of hadronic
interactions are at the energies of interest, as we have seen. The need to rely on
extrapolations of known particle physics to estimate the primary energy is the major
drawback of the generic method and doubts remain about the systematic errors in the
energy determination arising from the model uncertainties.
  For the detector arrays, Monte Carlo calculations have shown that the particle
density at distances from 400 – 1200 m is closely proportional to the primary energy.
Such a density can be measured accurately (usually to around 15 - 20%) and the
primary energy inferred from parameters found by calculation. The estimate of the
energy depends on the realism of the representation of features of particle interactions
within the Monte Carlo model, at energies well above accelerator energies. A
currently favoured model (QGSJET) is based on QCD and is matched to accelerator

                                       29