A primary cosmic ray spectrum was derived which fits both experimental multiple muon rates and the all-nucleon flux derived from the single muon intensities underground. In the frame of the interaction model developed by Gaisser, Elbert and Stanev, it is possible to reproduce NUSEX muon data with a primary composition in which the iron spectrum is only slightly flatter than the proton one. This result rules out the popular idea that the primary composition varies drastically with increasing energy, leading to the dominance of heavier nuclei at energies 10 to the 15th power to 10 to the 16th power eV

Battistoni, G.

Bellotti, E.

Bloise, C.

Bologna, G.

Campana, P.

Castagnoli, C.

Castellina, A.

Chiarella, V.

Ciocio, A.

Cundy, D.

English

NASA Technical Reports Server

158
0G5.1-5
PRIMARY COSMIC RAY SPECTRUM IN THE I013-i0 16 eV
ENERGY RANGE FROM THE NUSEX EXPERIMENT
G. Battistoni I, E. Bellotti 2, C. Bloise l, G. Bologna 3, P. Campana l,
C. Castagnoli 3, A. Castellina _, V. Chiarella l, A. Ciocio I, D. Cundy _,
B. D'Ettorre Piazzoli 3 E. Fiorini 2, P Galeotti 3, E. larocci I
C. Liguori 2, G. Mannocchi s, G. Murtas I, P. Negri 2, G. Nicoletti l,
P. Picchi 3, M. Price _, A. Pullia 2, S. Ragazzi 2, M. Rollier 2,
O. Saavedra 3, L. Satta l, S. Vernetto 3 and L. Zanotti 2.
i Laboratori Nazionali delI'INFN, Frascati, Italy.
2 Dipartimento di Fisica dell'UniversitN and INFN, Milano, Italy•
3 Istituto di Cosmogeofisica del CNR, Torino, Italy•
CERN, European Organization for Nuclear Research; Geneva, Switzerland•
INTRODUCTION
The single muon intensity has been measured in the NUSEX experiment at
various depth up to i0,000 hg/cm 2 s.r..
These intensities have been converted to a sea-level muon energy
spectrum which is used to derive the primary all-nucleon flux•
From these data we are able to determine the slopes of the primary
proton and helium spectra, which are thus used in a model for the
primary composition producing the observed multiple muon rates.
DATA REDUCTION AND PRIMARY SPECTRUM
The NUSEX detector is located in the Mt. Blanc tunnel at a vertical
depth of about 5000 hg cm "2 s.r. It consists of a cube of 150 t mass
and 3.5 side, made of 136 horizontal planes I cm thick, interleaved with
planes of tubes of I cm x I cm cross section, operating in the limited
streamer mode. More details are reported elsewhere [I].
20429 muon events crossing at least I0 layers were recorded in a zenith
angle range 0° - 75° during an effective working time of 18,946 hours
from June 1982 to December 1984. The number of events for different
multiplicities are reported in table i.
The single muon intensity at different depths has been found using the
procedure of Ref. 2. The general relation
l(h,@) = I_'K(h)'G_'K(h,@)+IP(h)'GP(h,e) (I) "
P
has been fitted to the data. Here the _ and K superscripts refer to
conventional muons from _ and K decay, the p superscript to prompt muons
from charmed particle decays•
158 
PRIMARY COSMIC RAY SPECTRUM IN THE 10 13-10 16 eV 
ENERGY RANGE FROM THE NUSEX EXPERIMENT 
OG 5.1-5 
G. Battistoni 1 , E. Bellotti 2, C. Bloise 1 , G. Bologna 3 , P. Campana 1, 
C. Castagnoli 3 , A. Castellina 3 , V. Chiarella 1 , A. Ciocio 1 , D. Cundy~, 
B. D'Ettorre Piazzoli 3 , E. Fiorini 2 , P. Galeotti 3 , E. Iarocci 1 , 
C. Liguori 2 , G. Mannocchi 3 , G. Murtas 1 , P. Negri2, G. Nicoletti 1 , 
P. Picchi 3 , M. Price~, A. Pullia 2, S. Ragazzi2, M. Rollier 2 , 
O. Saavedra 3 , L. Satta 1 , S. Vernetto 3 and L. Zanotti 2• 
1 Laboratori Nazionali dell'INFN, Frascati, Italy. 
2 Dipartimento di Fisica dell'Universita and INFN, Milano, Italy. 
3 Istituto di Cosmogeofisica del CNR, Torino, Italy. 
~ CERN, European Organization for Nuclear Research; Geneva, Switzerland. 
INTRODUCTION 
The single muon intensity has been measured in the NUSEX experiment at 
various depth up to 10,000 hg/cm 2 s.r •• 
These intensities have been converted to a sea-level muon energy 
spectrum which is used to derive the primary all-nucleon flux. 
From these data we are able to determine the slopes of the primary 
proton and helium spectra, which are thus used ~n a model for the 
primary composition producing the observed multiple muon rates. 
DATA REDUCTION AND PRIMARY SPECTRUM 
The NUSEX detector is located in the Mt. Blanc tunnel at a vertical 
depth of about 5000 hg cm- 2 s.r. It consists of a cube of 150 t mass 
and 3.5 side, TIlade of 136 horizontal planes 1 cm thick, interleaved with 
planes of tubes of 1 cm x 1 cm cross section, operating in the limited 
streamer mode. More details are reported elsewhere [1]. 
20429 muon events crossing at least 10 layers were recorded in a zenith ~ 
angle range 0° - 75° during an effective working time of 18,946 hours 
from June 1982 to December 1984. The number of events for different 
multiplicities are reported in table 1. 
The single muon intensity at different depths has been found using the 
procedure of Ref. 2. The general relation 
(1) 
has been fitted to the data. Here the nand K superscripts refer to 
conventional muons from nand K decay, the p superscript to prompt muons 
from charmed particle decays. 
https://ntrs.nasa.gov/search.jsp?R=19850025734 2020-03-20T18:01:38+00:00Z
I 59 OG 5.1-5
The angular enhancement functions have been calculated in Ref. 3 . The
intensity of prompt muons is found < 4% on the considered range of
depths, so that the second term in (I) has been neglected. The muon
intensity is reported in Fig. i. together with the intensity points
measured with the spark chamber apparatus located in the Mt. Blanc tunnel,
garage 27. The agreement is excellent, so giving a unique intensity-depth
set of measurements from 3900 to I0000 hg/cm _ s.r. very well represented
by the relation
l_,K(h) = (7.63±.48),10-_exp[-h/(810.44±.84)]cm-2s-lsr -I
Following the procedure of Ref. 2 we derive the primary all-nucleon
spectrum in the relevant energy range I0 13 . 2"10 l_ eV :
dN (4.8±.2)E_2.79±.03 -2 -IdE ° - .. cm s sr-IGeV -I
The rates of events with exacty n muons have been calculated following
the procedure described in Ref. 4.
= iKi(A) _ Yi(A)Cn _ 5E Pn(E°'A)dE°
where P (E0,A) is the probability to sample n muons of a showern
resulting from the interaction of a primary with energy E0, and mass
A, and the primary spectrum is described as a superposition of single
power spectra
-Yi(A)
d-E0=aN [iki(A ) E0 (i=p,_,CNO,Mg,Fe)
Inputs to P (E0,A) come from the enerBy and radial muon distributionsn
calculated by Gaisser and Stanev (Ref. 5) for our experimental site. We
assume a value of -2.79 for the spectral index of proton and helium nuclei
as determined from our data and normalize the flux at I0 TeV to the JACEE
data. The spectral index for CNO and Mg groups is chosen slighty flatter
as suggested by direct measurements to which we refer for relative
normalization. The iron spectrum is normalized to a flux of 2.42 10 .5
nuclei/(m2"sr's'GeV/nucleon) at i00 GeV/nucleon, while its spectral index
° is considered as a free parameter.
159 OG 5.1-5 
The angular enhancement functions have been calculated in Ref. 3. The 
intensity of prompt muons is found < 4% on the considered range of 
depths, so that the second ter  in (1) has b en neglected. The muon 
intensity is reported in Fig. 1. together with the intensity points 
measured with the spark chamber a p ratus located in the Mt. Blanc tu nel, 
garage 27. The agr ement is excellent, so giving a unique intensity-depth 
set of measurements from 3900 to 10000 hg/cm 2 s.r. very well represented 
by the relation 
rTT,K(h) = (7.63 ±.48) 010 -'exp [-h/(8l0. 4±. 84)] cm - 2S -lsr - 1 
~ 
Following the procedure of Ref. 2 we derive the primary all-nucleon 
spectrum in the relevant energy range 10 13 t 20l01~ eV 
dN 
dE 0 
= (4 8+ 2)E-2 •79 ±.03 -2 -1 -lG V-I 
• -. 0 '. cm s sr e 
The rates of events with exacty n muons have b en calculated following 
the procedure described in Ref. 4. 
where P (Eo,A) is the pro ability to sample n muons of a shower 
n 
resulting fr  the interaction of a primary with energy Eo, and mass 
A, and the primary spectrum is described as a superposition of single 
power spectra 
dN -y.(A) 
d - ~. k. (A) Eo 1. o 1. 1. (i=p,a,CNO,Mg,Fe) 
Inputs to P
n 
(EO,A) come fro  the energy and radial muon distributions 
calculated by aisser and Stanev (Ref. 5) for our experimental site. We 
assume a value of -2.79 for the spectral index of proton and helium nuclei 
as determined from our data and normalize the flux at 10 TeV to the JACEE 
data. The spectral i dex for CNO and Mg groups is chosen slighty fla ter 
as su gested by direct easur ments to which we refer for relative 
normalization. The ir n spectrum is normalized to a fl x of 2.42 10- 5 
nuclei/(m 2 °sr"soGeV/nucleon) at 100 eV/nucleon, while its spectral index 
is considered as a free param ter. 
160
OG 5.1-5
Beyond a rigidity Rc 2 106 GeV/c, all spectra steepen to y 3.0.
The breaks for nuclei different from protons are at a total energy
(A/2)R .
c
Fig. 2 shows that the measured rates are well described by an iron
spectral index in the range 2.6 - 2.7.
This model describes very well both the all-nucleon flux in the range
10 13 - I0 l_ eV and the all-particle flux between I0 Is - I0 le eV
(see for exemple the compilation of Hillas in Ref. 6). Normalization
coefficients, slopes and breaking points or all components are summarized
in table 2.
CONCLUSION
We have determined a primary cosmic ray spectrum fitting both our
experimental multiple muon rates and the all-nucleon flux derived from
the single muon intensities underground.
In the frame of the interaction model developped by Gaisser, Elbert and
Stanev, we are able to reproduce NUSEX muon data with a primary
composition in which the iron spectrum is only slightly flatter than the
proton one.
This result rules out the popular idea that the primary composition
varies drastically with increasing energy, leading to the dominance of
heavier nuclei at energies i0 Is - i016 eV.
References
[I] G. Battistoni et al., Phys. Lett. 133B (1983) 454 and paper to be
submitted to Nucl. Instr. and Meth.
[2] L. Bergamasco et al., Nuovo Cimento C6 (1983) 569.
[3] H. Bilokon et al., Nuovo Cimento C8 (_985) 93.
[4] G. Bologna et al., Nuovo Cimento C8 (1985) 76.
[5] T.K. Gaisser and T. Starter : private communication.
[6] A.M. Hillas : Proceedings of the Cosmic Ray Workshop, edited by T.K.
Gaisser (University of Utah, 1983), p.16.
Figure Captions
Fig. i - Muon intensity underground at Mt. Blanc.
Fig. 2 - Comparison between experimental rates and the predictions of
our model of primary composition for different values of the
iron group spectral i,ldex.
o
60 
 .1-5 
Beyond a rigidity R = 2 10 6 GeV/c, all spectra steepen to y = 3.0. 
 
he reaks f r uclei ifferent fr  rotons re t a t tal e ergy 
( /2)R • 
 
Fig. 2 sho s that the easured rates are ell described by an iron 
spectral index in the range 2.6 - 2.7. 
his odel escribes ery ell oth t e ll- ucleon fl  i  t e ra ge 
10 13 - 101~ e  and the ll-particle fl  bet een 101S - 10 16 e  
(see for exemple the compilation of illas in ef. 6). ormalization 
coefficients, slopes and breaking points or all co ponents are su marized 
 le . 
NCLUSION 
e ave eter ined a ri ary cos ic ra  s ectrum fitti g oth ur 
experimental ultiple muon rates and the all-nucleon flux derived from 
the single uon intensities underground. 
I  t  fra e f t  i t raction odel evelo ped  aisser, lbert a d 
Stanev, we are able to reproduce NUSEX uon data ith a pri ary 
co position in hich the iron spectru  is only slightly flatter than the 
proton one. 
his r sult r l s ut t  opular i ea t at t  ri ary mposition 
varies drastically ith increasing energy, leading to the do inance of 
heavier nuclei at energies 10 15 - 10 16 eVe 
eferences 
[1] . attistoni et l., Phys. ett. l33  (1983) 454 and paper t  be 
bmitted  ucl. str.  eth. 
[2] L. Bergamasco et al., uovo Ci ento C6 (1983) 569. 
[3] . ilokon et l., uovo i ento 8 (1985) 93. 
[4] G. Bologna et a1., uovo Ci ento C~ (1985) 76. 
[5] T. . aisser and T. Stanev : private co munication. 
[6] . . illas : roceedings f t e osmic ay orkshop, e ited by . . 
aisser ( niversity of tah, 1983), p.16. 
Figure Captions 
Fig. 1 -
Fig. 2 -
Muon intensity underground at Mt. Blanc. 
Comparison between experimental rates and the predictions of 
our odel of pri ary co position for different values of the 
iron group spectral i~dex. 
• 
161
OG 5.1-5
Table I
Rate of multiple muons
Multiplicity # events Time
i 20429
2 211
3 29 18946 hours
4 4
5 2
6 I
Table 2
Group K (m'2s'Zsr'SGeV "s) y Points of
i i change of slope_ E(GeV)
p 3.28 I0 _ 2.79 2 I0 e
He 1.75 I0 _ 2.79 4 l0 s
CNO 6.20 l0 s 2.71 1.4 l0 T
Mg 9.20 l0 s 2.71 2.6 I0 ?
Fe 2.6"2.7 5.2 l0 T
.. 
ultiplicity 
p 
e 
1 
 
 
 
 
 
e  
g 
 
-8 
10 
10-9 
,. 
~ 
VI 
'VI 
-10 
"i 10 ~ 
:s 
H 
10-11 
10-12 
3900 
61 
able 1 
ate f ultiple uons 
ifF events 
0429 
11 
 
 
 
1 
able  
K (m- 2 s- 1sr- 1GeV- 1 ) 
i 
3.28 10" 
. 75 1 " 
.  1 3 
. 0 1 3 
y 
2.79 
. 9 
. 1 
. 1 
i 
. +2.7 
• NUSEX 
o GARAGE 27 
5500 7100 8700 10300 
h !hg cni2) 
Time 
946 ours 
chan~e 
2 
 
.  
.  
.  
10-4 
10
5 
u 
OJ 
VI 
" > ~ 
c: 
10
6 
$ 
-1 
10 
10-8 
10
9 
 .  
Points of 
of sloEe z E(GeV) 
10 6 
1 6 
1 7 
1 7 
1 7 
~F. =2.5 
=2.6 
=2.7 
4 


Primary cosmic ray spectrum in the 10 to the 12th power - 10 to the 16th power eV energy range from the NUSEX experiment

Primary cosmic ray spectrum in the 10 to the 12th power - 10 to the 16th power eV energy range from the NUSEX experiment

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