The distribution of the number of muons in extensive air showers (EAS) and the equi-intensity curves of EAS are analyzed on the basis of Monte Carlo simulation of various cosmic ray composition and the interaction models. Problems in the two best combined models are discussed

Tanahashi, G.

English

NASA Technical Reports Server

5 HE4.1-3
ANALYSIS OF EQUI-INTENSITY CURVES AND N_ DISTRIBUTION OF EAS
G.TANAHASHI
Institute for Cosmic Ray Research, University of Tokyo
Tanashi, Tokyo, 188 Japan
ABSTRACT
The distribution of the number of muons in EAS and the equi-
intensity curves of EAS are analyzed on the basis of Monte Carlo
simulation of various cosmic ray composition and the interaction
models. Problems in the two best combined models are discussed.
I. Introduction
Many analyses of EAS data have been reported to investigate the cosmic
ray composition and their interaction. For example, the comprehensive
work was reported by Gaisser et al(1) in 1978. After then, the equi-
intensity data of Chacaltaya was revised(2) and the other data of Akeno
experiment was added to it(3). Akeno experiment also gave a distribution
of the number of muons(>IGev) of EAS at fixed shower size with a good
statistics(4). In this report we make an analysis of these data with use
of the Monte Carlo simulation described in 2.
2. One dimensional simulation of EAS
Among the parameters used in the interation model of the cosmic ray
with the air nucleus, the collision m.f.p, is assumed to be
A=_o/(1+0.07(log_(Tev)+1)1"5)gcm-2 where _o=80 and 120 for proton and pion
interaction respectively, and Eo is the cosmic ray energy. The value of
are shown in Fig.1 together with_=290.Eo(Tev)O'O6mb obtained in the
Akeno experiment(5). The assumptions of the other parameters are follow-
ing.
The leading particle carrys the energy Es fluctuated uniformly between
0-Eo. The partition of the rest of the energy between the fragmentation
and the central region is half to half. The energy spectrum of the pro-
duced particles in the fragmentation is exp(-E/E*) where E* is 0.6Es and
p Es for proton and pion incident respectively. In the central region the
spectrum is assumed to be a plateau shaped one whose energy spread is
shown in Fig.2 for various models. Resultant multiplicity-energy relation
, multiplicity distribution, scaling behavior and inclusive rapidity dis-
• tribution are checked to fit the data of accel_rator experiments.
Produced particles are to be pions or kaons, and the proportion of the
kaon production is to increase with the energy as O.051ogE_Gev).
Interation models shown in Fig.2 are used for the EAS calculation.
They are SC(scaling), STD(standard, Which is scaling + the extension of
the central distribution in I014ev to the higher energies), SC1/2(scaling
+ increasin_ multiplicity with E_/2 in the central region above I014ev),
SCM(scaling + particles nearly at rest in CM system above I014ev) and CCM
(no fragmentation particles and all particles nearly at rest in CM system
above I014ev).
We have further two kinds, I and II, in each of the above models. I
includes the generation of the high energy neutral pion as the leading
particle, and the forward and backward symmetry of the produced particles
in CM system. II includes no production of the energetic neutral pion as
the leading , and the enhanced particle production in the backward three
times more than the forward as the effect of target nucleus. The details
https://ntrs.nasa.gov/search.jsp?R=19850027657 2020-03-20T17:18:52+00:00Z
6 HE4.1-3
,,. ,L...... .
8 _z .
Fzg. I LooFRZ_.R_K.E_O_CG_)
01234S67Bg10
Fig.2 LOOPRmARZE_ROY<C_)
of these assumptions
will be described els-
I
where.
, ..
The shower curves
of electrons and muons _z
of STD based on I, II e_ .
are shown in Fig.3. It """
is seen that the
attenuation of particles
between 1000-1600gcm -2
is nearly exponential I
and has almost the same
attenuation length(180-
190gcm -2 in I and 190- _ _i
200gcm -2 in II) irres- _ o_
pective of the primary _ "'"..
energies above I013ev. _ "'.
In the same figure, the ----
shower curves of the _-- 10tSev_o,
constant cross section /_
are also shown for the /
comparision. The reason /
that the attenuations
are almost the same Fig.3 500 10oo 15ooA_OSP_RIC DEPTH(gcm -2)
comes mainly from the ............. ! I I ,
increasing cross sec- / _, "
tions. The other result + HSD
is that the muon con-_ _ __%_ _._
tent in II is almost 3 7
times larger than I's.
In Fig.4 the shower
curves of various
models are shown in _ "_.,'_.._'_
comparison. All of them ! 6i
are based on model I. ___'_ _ ' _ _oNIt is found again the
attenuation byond 1000 (F+_.._*j_X_-- __
gcm -2 are almost para" - ,
E_I017evllel. The difference
among SC, STD and SCI/2 ..... I |,
500 I000 1500
are very small, and this Fig.4 ATMOSPHERIC DEPTH(gcm-2)
7 HE4. I-3
means that the energy distribution in the central region does not affect
much the shower curve except the extreme case like SCM. The crosses in
the figure show the iron shower curve(HSD) based on the superposition of
STD.
3. Nu distribution of fixed Ne
The N_ distributions of EAS _ l
of different primary component
(mass number A=1,4,15 and 50)
are calculated under the con- _
dition of fixed Ne assuming the
primary integral energy spect- _01s_oNs
rum to be E-_. These N_ dis-
tributions include the error ,o00
which comes into N_ in the
course of the data reduction
and also the error due to the
possible fluctuation of muon _
lateral distribution. The dis-_ __ __ L_I._._! I_
tribution of A>_ are almost due = _00
to thee errors. These N_ dis-
tributions of each component
are superposed to fit the ex-
, PROPORTION OF [
periment(5) as shown in Fig.5. I _=0_0_s .
The conclusions obtained from ' P=_" i
this comparision are (i)low Nu ] _H-]
f I
tail requires the existence of ,05 'o6
proton showers more than Fig.5 _0_slzE(N_)
several % (ii)the Nu distri-
bution of the proton shower must be as broad as in STD, that is, the very
high multiplicity models are avoided because o_ their narrow distribution
of N_ (iii)the avrage N_ of each component must be spread over more than
factor 3 for fixed Ne.
4, Equi_intensity curves of EAS
Equi-intensity curves of a mixed composition are related to each shower
curves as follows. Assume that the shower curves are energy independent
in the required energy region, that is N(E,x)=E.N(x) where N(e,x) is the
shower curve of energy E in depth of x. The intensity ratio of the heavy
to the proton shower in fixed shower size is
_(x) = (lh/Ip)N= (lh/Ip) E. (Nh (x)/Np (x))r
where k=(lh/Ip) E zs the intensity ratio in fixed energy and Y is the
integral exponent of the primary energy spectrum. Putting _ =2, _(_) can
be calculated with use of the values of Nh(x), Np(x) as the funtion of k.
Equi-intensity curves _(x) are obtained from
_(x) =Np (x) / (I+_(x) )+Nh (x). _(x) / (I+_(x) )
_(x) and _(x) are calculated for the following combinations of the proton
and the heavy showers.
proton shower STD STD STD SCM
heavy'shower HSD SCM CCM CCM
notation HSD/STD SCM/STD CCM/STD CCM/SCM
The _(x) are sh_n in Fig.6 for k=0.1, 1.0 and 10 together with the ex-
perimental data(2)(3). In general, the attenuation length between 800-1400
gcm -2 are steeper than either prediction, but two cases(HSD/STD and k=10)
8 HE4.1-3
(CCM/SCM and k=0.1) barely fit the experiment as shown in the figure in
dotted curves after the normalization of the intensity. SCM/STD and CCM/
STD do Not fit because of too much _ifferen_ of proton and heavy shower
curves. This different makes the composite curves flat.
5. Discussions and conclusion
Both two selected cases satisfy,the requirement (i) in 3.
As for CCM/SCM, it is not
clear whether (ii)(iii) are
satisfied or not, but seems
to be not. This model is
introduced to approach the ,
one which is proposed by 10_
Kakimoto et al(2) to explain
the rapid development of EAS
in high altitude observed by
them. So the further pro-
gress of this experiment
will test the model.
On the other hand, HSD/
STD satisfys all the require-
ments (i)(ii)(iii) in 3. The
problem_of this model are
the less content o_muons in
EAS and the slow development _ 107C
of the number of muons. The _
model needs about 2 times
more muons. If we adopt
model II instead of I, the
number of muons increases Fig._ 6 7 8 9 10 11 12 •13 I_A_mosphericdepfh(gcm-2)
but the attenuation length _ .i_- • '
also increases apart fur- _XPC6)
ther from the experiment. I I _ HSDCh)
As for_e.slow developmentof muon in this model, we I
can scarcely fit the experi- Fig.7
ment by taking the number
of muons of iron showers in
600 gcm -2 and of proton I
showers in |100gcm-2(Fig.7). If the N_ difference of the proton and the
heavy nucleus shower is larger in some model, such a model is better in
this problem.
Acknowledgements
The EAS simulation are done by FACOM 380 at the computer room, Institute
for Nuclear Study, University of Tokyo.
_eferences
_I) Gaisser, T.K. et al. Rev. Mod. Phys., 50, 859 1978
(2) Kakimoto, F. et al. J. Phys. G; Nucl. Phys. 9, 339 1983
(3) Nagano, M. et al. J. Phys. G; Nucl. Phys. TO, 1295 1984
(4) Hara, T. et al. Proc. 18th ICRC(Banbalor_, I_, 285 1983
(5) Hara, T. et al. Phys. Rev. Lett. 50, 2058 1983
(6) Hara, T. et al. Proc. 18th ICRC(Ba-ngalore), I__[I,281 1983


Analysis of equi-intensity curves and NU distribution of EAS

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