With the use of Akeno calorimeter, the attenuation of particles in concrete is analyzed as the function of the shower size of 10 to the 5th power to 10 to the 7th power. The attenuation length does not depend much on the shower size but depends a little on the shower age. The average value is approx. 150 g/sq cm for s = 0.5 to 0.85 and approx. 40 g/sq cm for s = 0.85 to 1.15. These values and their fluctuations are consistent with the equi-intensity curves of extensive air showers (EAS)

Hara, T.

Hatano, Y.

Hayashida, N.

Kifune, T.

Nagano, M.

Tanahashi, G.

English

NASA Technical Reports Server

HE4.2-9
77
CORE STRUCTURE OF EAS IN I015ev TO I017ev
T.Hara, Y.Hatano, N.Hayashida, T.Kifune, M.Nagano and G.Tanahashi
Institute for Cosmic Ray Research, University of Tokyo
Tanashi, Tokyo, 188 Japan
ABSTRACT
With use of Akeno calorimeter, the attenuation of particles in
concrete is analized as the function of the shower size of 105
to 107 . The attenuation length does not depend much on the shower
size but de_ends a little on the shower age. The average value
is _150gcm -L for s=0.5-0.85 and _140gcm -2 for s=0.85-1.15. These
values and their fluctuations are consistent with the equi-intensi-
ty curves of EAS.
I. Introduction
Akeno calorimeter has an area of about 10mx10m and has the proportional
counter arrays at 5 different depths(0, 115, 230, 345 and 633gcm-2 in con-
crete) with 10cm resolution in one dimension(1). We report the preliminary
result of energy flow or the attenuation length measurement with use of the
calorimeter. In this paper the attenuation length(A) is defined as
Energy flow = _l_x)dx=_ N(xo)j_xp(-x/A)dx
where _ ; the energy loss/particle, unit mass
N(x) ; shower size in the depth x
xo ; observation depth, 930gcm -2 in Akeno
The data are of the latter half of 1982, and about 13,000 vertical
showers are analyzed whose sizes are between 105 and several times of 107 .
Only 3 shower cores hit the calorimeter area above the size of 107 .
2. Average attenuation length of EAS
The analysis is only for the vertical showers with sec@=1.0-1.1. EAS
data are sorted in the shower size(N) bin of 105.0-5.5 , 105.5-6.0 , 106.0-
6.5, 106.5-7.0 and >107.0 , and also in the age(s) bin of 0.50-0.85, 0.85-
1.15 and 1.15-1.50. The average lateral distribution of particles and the
shower sizes in each concrete depth are determined in every combinations
of the above sorting. Fig.1 shows the average local attenuation lengths
° as the function of core distance in N=I06.0-6.5 and in all s. They are
defined in I replacing N(x) by _(x), the particle density in a unit of 10
proportional counters(5mxlm). The average shower sizes in each concrete
depth are obtained by integrating _(x) over the core distance. They are
shown in Fig.2. A systematic difference of the particle densities measured
by the scintillation counters and by the proportional counters are corrected
in the figure_ that is _pc/_ sc is about 1.5 at _=10, 1.3 at _=102 and
1.15 at _=10 . The shower sizes are normalized within eacn size bin. The
error bars only show the uncertainty due to the threshold of the counter
output, and in most cases the true values are considered to be rather close
to the lower limit. The data of size=107 and age=0.85-1.15 are not reliable
because of the poor statistics of the core events.
The attenuation lengths from these transition data are 150_10gcm -2 for
s=0.50-0.85 and 140±10gcm -2 for s=0.85-_.15, and not much depend on the
shower size. These values are smaller than _180gcm -2 predicted for the
proton showers of the standard interaction, and also for the iron showers
https://ntrs.nasa.gov/search.jsp?R=19850027676 2020-03-20T17:06:33+00:00Z
HE4.2-9
78
as shown in Fig.3(2), where "standard" means the increasing cross section
as #_,_E 0"06, Feynman scaling and the extrapolation of the known central
energy distribution to the higher energies.
I I ; I I I I
6001
_oe500 _
_=400_ _ -3 0
"
200 o
o 'Oo_
_ 100 _, : _ 104
I I I I I I
2.5 5 10 20 40 80
CORE DISTANCE(m)
Fig. 1
500 500
Fig.2 DEPTHIN CONCRETE(gcm-2)
3. Relation of 3 attenuation length_ bE, _I, AN
To see the consistency of the result with others, three attenuation
lengths are taken into account. Their definitions are as follows.
(i) AE of the fixed energy shower
_E is obtained from the shower calculation of the fixed energy, and in
the case of the simulation, the average value of many showers is used.
AE is about 180gcm -2 in I016ev and in >950gcm -2 for the standard proton
showers(Fig.3). *
(ii) AI of equi-intensity cut
hi is obtained from the equi-intensity cut of the size spectra in the
different depths. The experimental value is 160-170gcm-2(3) in I016ev o
to I017ev and >950gcm -2.
(iii)/IN of the fixed size in the fixed level
The attenuation length obtained in the calorimeter experiment is /iN.
The experimental value is 140-150gcm -2 as described in 2.
In what follows we make a simple calculation of these As to see how the
cosmic ray composition affects these values. The composition is assumed to
be two components, the proton and the heavy nuclei. Each shower curve is
to be the exponential form, say Np.exp(-x/Ap) for proton and Nh.exp(-x/Ah)
for heavy nuclei. Np=Nh=I09, Ap=180gcm -2 and Ah=140gcm -2 in I016ev as Shown
in Fig.3. The reason to adopt the small value of Ah is that the usual
models of heavy nuclei shower can not give a appreciably smaller attenuation
than the proton's. The fluctuations of the longitudinal development are
ignored. The integral energy spectrum is to be E-2, and the intensity ratio
at the same energy k=Ih/Ip is to be a parameter of the calculation. AE,
AI and AN are given as follows.
19 HE4.2-9
A= (x2-xl)/in (NI/N2) ....
for AE, N1/N2=(exlp+k.exlh)/(ex2p+k.ex2h)
for AI, N1/N2=((ex1_2+k.exlh2)/(ex2p2+k.ex2h2))0"5
for AN, NI/N2= (exlpZ+k. exlh z) / (exlp .ex2p+k.exlh.ex2h)
where NI and N2 are the shower size at the depth of xl and x2 respectively
and exlp=exp(-xl/Ap), exlh=exp(-xl/Ah), ex2p=exp(-x2/Ap), ex2h=exp(-x2/Ah).
The relations between k and As are shown in Fig.4. It is seen that AN has
almost the same value as AI in the whole range of k. This means that the
difference of Al(160-170gcm -2) and .AN(140-150gcm -2) can not be explained by
means of the different response of proton and heavy nuclei showers.
The other possible explanation is to attribute it to the fluctuation of
the shower development. Fig.5 shows two distributions of simulated attenu-
ation lengths of fixed energy and of fixed size for the proton showers.
The positions of the distribution maximum are almost the same, but the
average value of the fixed energy one is larger than that of the fixed size.
As the attenuation length of fixed energy is nearly equal to that of the
equi-intensity cut .in single component showers, this can explain the differ-
ence provided that the primary cosmic rays contain a proper amount of
protons.
N
_ i40 r
6 . 1201-I I' I_ IO0 -* k
_5 HEAVY TO PROTON RATIO Fig.4
I I I
500 I000 1500 Fig.3
ATMOSPHERIC DEPTH(gem -2)
4. Fluctuation of the attenuation length
The attenuation length of each shower can not be directly obtained from
the data, and only "the attenuation length within 10mx10m(A100)" are ob-
tained. The histogram in Fig.6 shows the _I00 distribution(bottom side
, scale) of the showers which hit the central part(5mx5m) of the calorimeter.
This kind of fluctuation decreases with the core distance, and gets remark-
ably smaller beyond 15m down to 80-90gcm -2. So, for the core hitting
showers, we can convert AI00 to the attenuation length assuming the local
attenuation lengths are continuous between 5m and 20m.
The conversion depends on how to interpolate the attenuation between 5m
and 20m. The most gentle one is that the local attenuation lengths fluct-
ate around the average in proportion to the central AIO0 in the region
above 80-90gcm -2 like the two curves in Fig.1. The attenuation lengths
obtained with use of this conversion are shown in the top side scale of
Fig.6. In the same figure, the distribution of the attenuation length is
compared with f_the one simulated for proton showers(the same one in Fig.5).
The observed distribution does not agree with the prediction. Some part
of the disagreement may be the contribution of the heavy nuclei showers,
but the further discussion needs the further detailed analysis, especially
the improvement of AIO0 conversion to the attenuation length.
80 HE4.2-9
Fig.5 = LOG(Ne(1500gcm-2)/Ne(1000gcm-2))
0 -I -2Z
AV
_00 _ _ _.4
® 50
-4
\
300 200 150 IQO(gcm-
Fig.6 CO_ERTED ATTENUATION _NGTH OF EACH SHO_R(gcm-2)
100 150 200 250
I I i I
20 Experiment_ 1 + --
H
z
Simulated A-distribution
_ rs
I0_
1 I_"_1
200 400 600 800 (gcm-2)
A1o0 IN THE SHO_R CORE
Acknowledgements
The author_ are indebted to the technical staffs in _eno crew.
The data reductions and the EAS simulation are done by FACOM 380 at the
computer room, Institute for Nuclear Study, University of Tokyo.
References
(1) Hara, T. et al. Proc. 16th ICRC(kyoto), 8, 135 1979
(2) Tanahashi, G. HE 4.1-3 in this conference
(3) Nagano, M. et al. J. Phys. G; Nucl. Phys. 1._, 1295, 1984


Core structure of EAS in 10(15) to 10(17) eV

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