Scale breaking model and gammaisation processes for high energies give a correct description of the longitudinal development of extensive air showers (E.A.S.). From the analysis of phenomenological characteristics of E.A.S. at Tien-Shan experiment, it follows that for energies near 10 to the 6 GeV the secondary particle multiplicity increases with energy faster than is predicted by the accepted scale breaking model

Procureur, J.

Stamenov, J. N.

Stavrev, P. V.

Ushev, S. Z.

English

NASA Technical Reports Server

,84
HE 5°4-8
ANALYSIS OF THE ELECTRON AND MUON COMPONENTS OF E.A.S.
--2
AT OBSERVATION LEVEL 700 g.cm WITH A SCALE BREAKING
INTERACTION MODEL AND "GAMMAISATION" HYPOTHESIS.
J, Procureur
Laboratolre de Physique,Universi%_ de Bordeaux I
rue du Solarium
33170 Gradignan (France).
J.N. Stamenov,P.Y. Stavrev,S.Z. Usher
Institute of nuclear research and nuclear energy
Bld. Lenin 72
118_ Sofia (Bulgaria)
ABSTRACT
Scale breaking model and "gammaisation" processes
for high energies give a correct description of the
longitudinal development of E.A.S. From the analysis
of phenomenological characteristics of E.A.S. at
Tien-Shan experiment,it follows that for energies near
I06GeV the secondary particle multiplicity increases
with energy faster than is predicted by the accepted
scale breaking model.
1. Introduction We simulate the muon and electron components
of extensive air showers (E.A.S.) with fixed sizes in the region
104-106 at mountain altitude. In a previous work the same authors
(I) used a scale breaking model (SBM) including parameters in .
accordance with the results from the SPS collider and in good
agreement with KNO scaling model predictions.
The SBM gives a correct description of E.A.S. at Tien-Shan
level but is not able to reproduce the longitudinal development
of showers.
To obtain a correct position of the maximum of E,A,S, develop-
ment,we include,as was first proposed by Sol. Nikolski (2),%he
"gammalsation" hypothesis i.e. a larger emission of _ rays than
predicted by the traditional models.
It has been shown(3) that this model gives a correct descrip-
tion of the longitudinal development of E.AoS.
The aim of this work is to verify if the SBM including
9ammaisation is compatible with the experimental muon component for
showers of fixed size.
_. Method Average values of the electronic and muonic sizes,N e
and N_,and lateral muonic densities _(r) are simulated by a mixed
simulation model including full Monte--_Carlo procedures for the
first interactions of hadrons and analytic approximations for
deeper interactions in the atmosphere.
https://ntrs.nasa.gov/search.jsp?R=19850027806 2020-03-20T17:10:54+00:00Z
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More precisely,the main characteristics are the following :
- p-air cross section increases with energy E
= 269(1.+O.OSln(E/100)) (mb) for E > I00 GeV.
fluctu_ _irzone are determined by an exponenti_l distribution.
- average charge multiplicity : <ns> = 0.57+0.5841ns+O.IST(Ins) 2
fluctuations around <ns> satisfy to the KNO scaling. _
The structure function _Z) is described by a gamma-k relation.
- average value of Pt increases with energy:< pt>= O.0151nE + 0.23
distribution is defined by f(pt)dpt = (pt/p_)exp(-Pt/P O)
- the empirical rule<n_> = <ns> is contradicted by results from
° -- ° I
p-_ collider where the estlmation for <a> = < nT>/< ns> is .4
for Ks = 540 GeV. (4)
Compilation of higher energy observations of cosmic rays jets
and gamma-ray families is made in ref (2). in this publication
the authors estimate that <a> could be near five for very high
energy collisions.
To take into account the "gammaisation" hypothesis we use an
empirical parametrisation of the p-air interactions for EoA.S;
simulations : <a>= I. + 141n(E/105) for E > I05 GeV with the
condition of saturation <a> _ 3. which seems very reasonnable.
- results for showers with fixed sizes are obtained by :
f_ dZ (E)X(No ) = X(E)P(E,No) d--_-_-----dE ,where X(E) is the value of
the observable X for showers with fixed primary energy E.
P(E,No) is the probability for showers initlatedby a given
primary with energy E to obtain the fixed size N o
To obtain a correct comparison with the experimental data we
have taken into account the triggering conditions of the Tien-Shan
array and the algorithm systems for the statistical data treatment.
All distorsions and statistical errors are included in a special
algorithm which allows us to obtain from Nth ,observable obtained
from simulation using SBM,N p the corresponding pseudo-experimental
characteristic (5)°
]. Results
As shown in ref (_),
gammaisation is a serious _ ""/maxl..cm -_}
candidate to restore agreement 700
between phenomenological
predictions and experiment, in
E.A.S. about the absorption
of showers. For exemple 600
maximum's depth T as a _
max
function of the prlmary ener-
gy E is shown fig I for pure
proton,pure iron primaries
and mixed composition (60% p
+ _0% re)
Doffed lines and full lines
are respectively without and E-'o_with gammaisationo 5 i[O 6
It can be noticed that the lid
relatively large proportion
of iron in the mixed composition
186
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iS a consequence of the small saturation value ( <a> = 3.) of
the ratio <nz>/<ns>
The comparlson of the Tien-Shan dependence N_(Ne) with SBM
calculation results shows some serious discrepancies ( fig. 2 )
On this figure are dra_1 for fixed sizes Ne and mean zenith angle
@ = 226 _the much sizes N_ for pure proton and iron primaries.
r _ Dotted lines and full lines
N_ // % are respectively dependences
without (<a>= 1.) andwithgammalsation.As shown in ref. (1) the much
.// { /
• /._,,,- 1-./ P size dependence N_ N N_ simula-ted by the SBM model without .
"//J/ ! /// 9ammaisation is defined in the
! I/// size interval 105-107 by theJ_
f "5_/ parameter _ : 0.67
/ " , ',!/ This value is different fromthe experimental one :
/ ,.// aexp = 0.800 _ 0.008 (6)
/ If we take into account the• gammaisation this situation isworse for the largest values ofN e •
103j Indeed,the production of addit-
/ ional y increases with energy,soimposes a flatter dependence ofN,(Ne) i.e. e = 0.61
_It is possible to obtain results
in better accordance with experim-
tal ones with a mixed primary
composition.However the N_-N e
i10s i1_,,, Ne variation is neve_ steep enough
• - in comparison with the cortes-
fiG. 2 podant experimental results.
If we do not take into account the process of gammaisation
(dotted lines fig.3),in the size interval lO_-iO 6 and in the range
of distance 5-I00 m,a good agreement is obtained for the lateral
distributions of muons (the origin of the experimental points is
given in ref. (I))
However,for large sizes and far from the axis of showers
(R >lOOm),simulated densities become slightly smaller than the
experimental ones. This gives_because the large number of muons
far from the axis,the underestimation of N_(Ne) (see fig. 2)
As expected from results shown in fig. _with production of
additional y,the situation is the same for small showers and
becomes less favorable for large sizes (Ne_ 106 ) (full lines on
fig. 3)
_. Discussion A consequence of the gammaisation hypothesis for
high energies ( E >I05 GeV.) is the decrease of the ratio N_/N e
for showers initiated by primaries with fixed energy. This _mply
for showers registered with fixed sizes a smoother variation of
N_(Ne) than is obtained with the standard SBM model.
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HES._-8
1 i
mixed primary composition, p
However,because the agreement of I _tm- ,
the protonic showers for smallest _ E..>SGeV
sizes (N e_ 104 ) and the important F-
decrease of the primary energy
spectra,the effect of heavy _
primaries remains not large enough°
In any case,the N_-N e dependence _'%
is never steep enough in comparison I. _ \
withresults,the correspondent experimental ______\
The agreement with experiment
can be obtained with help of a
stronger increase of multiplicity
<ns> with energy° This result is 161 _ :_
confirmed by the results of other " _ % _\authors (7) with calculations
Carried out under the assumption of T _'_)_ _ _
coming from accelerators data is
equivalent to <Us> _ E 0.13
However we have to notice that _IO
no experimental arguments from the
accelerator region allow one to
adopt such a strong dependence of
secondary multiplicity on the
_nergy of interactions.
5. Conclusions , . . I0, , . ,100, R{m}
We have analysed E.A.S. electron fig. 3
and muon components in the Tien-Shan
. experiment on the basis of the SBM:model including the
"gammaisation" hypothesis. We have shown that with a correct
description of the longitudinal development,a good agreement
between experimental and calculated results is ontalned if we
use a mixed primary composition rich in proton and a stronger
variation of multiplicity of secondaries with energy than the
one given by accelerators results.
References :
(I) J. Procureur,J.N. Stamenov et alo to be published in
J. Phys. G
(2) S.Io Nikolski (197o) Trudi FIAN 46,100
(3) J.N. Capdevielle,J. Procureur J. Physo G 10 (198_),705
(4) N. Yamdagni (1982) proc. Workshop on Very High Energy Cosmic
Ray Interaction,University of Pennsylvania,p 36
(5) S.I. Nikolski_and J.N. Stamenov,Proco 18th ICCR (1983)0G&-I_
(6) I.No Kirov,S.Io Nikolski et al.,Proc. 7th ESCR (1980),360
(7) AoDo Erlykin et el. Moscow (198_) FIAN n ° 1_


Analysis of the electron component of EAS at observational level 700 g x cm(-2) with a scale breaking interaction model and gammaisation hypothesis

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