The extensive air showers (EAS) cascade curves from the Cerenkov light lateral distribution measurements are recovered and the maximum depth fluctuations of the shower development theta x sub m both on the Cerenkov and charged EAS components are defined. At E sub 0 approximates 10 to the 18th power eV the mean content of protons is greater than 85%, and p-air cross section theta sub 0 p-air  750mb

Dyakonov, M. N.

Ivanov, A. A.

Knurenko, S. P.

Kolosov, V. A.

Krasilnikov, D. D.

Pavlov, V. N.

Sleptsov, I. Y.

Struchkov, G. G.

English

NASA Technical Reports Server

182 OG5.1-13
FLUCTUATIONS OF DEVELOPMENT Nh_LI_ DEPTH AND
NUCLEAR C0_°OSITION OF PRIMARY COSMIC RADIATION
M.N.Dyakonov, A.A.Ivanov, S.P.Knuremko, ID.D.Krasilnikov_
V.A.Kolosov, I.Ye.Sleptsov, G.G.Struchkov, V.N.Pavlov
Institute of Cosmophysical Research & Aeronomy,
Lenin Ave., 31 677891 Yakutsk, USSR
ABSTRACT
The EAS cascade curves from the Cerenkov
light lateral distribution measurements
are recovered and the maximum depth
fluctuations of the shower development
6X both on the Cerenkov and charged EAS
componentsm are defined. At Eo_--10_8e¥ the
mean content of protons is greater than
85%, and p-air cross section _g_-air_-750mb.
1. Method. The lateral distributions of the EAS Cerenkov
iight Q(R) in the interval of the core distances R = 20 76
1500 m_ud in a wide range of primary energies E_ - 8.10
1,5.10"_eV on the EAS Cerenkov light observation_ at the
Yakutsk array for 1970-1983 are analyzed. In Fig.1 the ave-
rage cascade curves of the EAS electrons N^(X) recovered
from Q(R) by the method [I] are presented _.Errors of Ne(X)
due to the measurement errors of Q(R) , the uncertainty of
the angular distribution function of the electrons in part-
ial showers E2J and aerosol distribution in atmosphere [3]
are shown by dashes.
2. Results. Dependence of the average depth of maximum Xmax
on E "is as follows:
o Xm = (720+16) + (73±l_).lg(Eo/lO 18) (1) "
It is the main not only for a choiceof the EAS development
model (here and further we shall mean by it a choice of the
multiplicity law and the energy spectrum of secondary par-
ticles) but also for the determination of the energy depen-
dence of hadron-air cross section and of nuclear composition
of primaries.
The cascade curves presented in Fig.1 and described by
the gamma distribution allow to obtain the total energy E_
of the EAS electron-photon component on the energy dissipa-
ted by electrons over the observation level X o.
Er:.- _t--o_ 1 + 3.5 (Xm/Xo) 6" _°Ne(X')dX , (2) "
where _ is critical energy and tois a unit of radiation
lengt_in the air.
From analysis of relations EeM/E o and Ne(Xm)/Ne(Xm-300)
we find out that the Landau hydrod_nmmic model_N_th the
multiplicity law of secondary particles ns_Z EO'Z_ and with
82 
TUATI NS F EL P ENT MAXIMUM EPr   
CLEAR OMPOSITI N   S I  DI TI N 
G -13 
.N.Dyakonov, . .Ivanov, S.P. nurenko, In.n. rasilnikovJ 
. oKolosov, I. e. leptsov, . .Str chkov, . .Pavlov 
I stit te f Oosmopbysical esearch  er y, 
enin ve., 31 1 akutsk, S  
S CT 
e  e r es o   erenkov 
li t l t r l istri ti n easurements 
r  r vered  t  axi  t  
l t ati ns f t  er l ent 
m ot    Oer kov  ~ed  
components are defined. At Eo ~10 8eV the 
ean ntent f r t ns i  r ater t  
85%, and p-air cross section 6'p-air ~ 750mb. 
. ethod.  r l i t ti ns   S er ov 
light QCR) in the interval of the core distances R = 20 16 
1500 m ~d in a wide range of pri ary energies E = 8.10 + 01~eV  t   ere kov li t ser ati g t t  
akutsk rr  f r - 83 r  a al zed. I  i .  t  a e-
r e s e r s f t   l tr s  ( ) r ered 
from Q(R) by the method (1) are presented; Errors of Ne(X) 
 t  t  easure ent rs f ( ) , t  certainty  
t e a gular istri ti n f cti  f t e electr s i  art-
l ers [   sol i t i ti n .in t osphere [ ] 
r  sho n by ashes. 
2. Results. Dependence of the average depth of maximum ~ax 
  i  as f ll s, 1 
o ~ = (720±16) + (73:14).lg(Eo/10 8) (1) 
t i  t  ain t l  f r a c iceof t  S e el ent 
odel r   rt er e all ean    i    
ultiplicity la  and the energy spectru  of secondary ar-) t l  r t  t ination  t  r  en-
e ce f dron-air r ss s ti  a  f clear positi n 
f ri aries. 
  r s r nted i  i .   scri ed  
t  a a i tri ti n llo  t  t i  t  t t l r  EEM 
f t   l tr - oton ponent  t  r  i i a-
ted by electrons over the observation level Xo. 
j3 " • SXO EEM = to 1 + 3.5 (Xm /Xo )6. 0 Ne(X)dX , (2) 
where fo is critical energy and tois a unit of radiation 
le tn in t e ir. 
From analysis of rel\tions EEM/Eo and Ne(Xm)/Ne(Xm-300) 
we find out that the Landau hydrodynamic odel w:1th the 
multiplicity law of secondary particles nsoc E01/Jand with 
https://ntrs.nasa.gov/search.jsp?R=19850025741 2020-03-20T18:01:48+00:00Z
18S
0G 5.1-13
normal law of their rapidities corresponds the most to the
experiment. This model also better agrees with experimental
energy-dependent fluctuations in X :
m Eo/I018)6X m = (66±4) - (12+2) • lg( (3)
The dependence (3) is obtained by data of 980 shower events
on a slope of the lateral distribution function (LDF) of
charged particles (black triangles in Fig.2)and by q50
events on the recovery methods N(X) on Q(R)(open squares).
This dependence slightly differs_from our earlier results
[@] owing to more correct account of measurement errors and
increase of the EAS statistics. For the comparison in Fig.2
the expected dependences g Xm on Eo are presented for the
models HDM and N/_. The latter one has nsOClnE o and almost
constant energy spectrum of secondary particles in units of
rapidities. Nuclear composition of primaries was taken in
the calculation as consisting of protons and nuclei of the
group VH(A = 5q) in different ratios determined by the mean
mass number <A>. Such mass composition at fixed <A) gives
the largest values of the depth of maximum and its fluctua-
tions in comparison with any other composition of primaries.
Therefore at fixed E^ and the EAS development model the low
boundaries of errorsUof _ and 6Xm give the upper estimation
<A> and alp-air" An alternative possibility is monochromatic
nuclear composition of primaries which leads to the smallest
meanings of Xm and dXm at fixed <A).
_. Discussion. In Fig.2 a different character of the depen-
dence dXm on Eo for HDM and _ at the same meaning
_m/dlgEo = ER is explained by the fact_that both models
preliminarily were reduced to the same Xm = 720 g.cm-2 at E_
" = qOq8eV by the variation (A). Therefore the composition
on N[PMwith the increase of Eo changes from the enriched he-
av_jnuclei (<A)_-gO) to more mixed one and the fluctuations
increase. And on HDM the composition from more mixed (<A)_-6)
becomes a purely proton one and (_X_ decreases. The opposite
character of the dependence (_Xm on Eo according to the _PM
model at various meanings of ER is caused by the fact that
at (ER)calc.< (ER)exp. one should enrich the nuclear compo-
sition by heavy nuclei and otherwise - by protons. And only
at absolute equality (ER)calc" = (ER)exp. the composition
" must not change with energy. Obtained dXm on (3) is in fa-
vour of the increase of the interaction cross section with
energy and high values of ER /d_x /dlgEol evidence the en-
richment of the nuclear composition by protons with the in-
crease of Eo, i.e. d(A)/dlgEo_ O.
3 
O  1-13 
r al la  f t ir r idities c rres nds t e ost t  t  
experi ent. his odel also etter agrees ith experi ental 
r - ependent l t ati ns i   : 
6X  = (66±4) - (12±2) • ~g(Eo/1018)  
he dependence ( ) i  tai ed by ata f 980 sho er e ents 
on a sl e f t e l t r l istri ti n f cti  (L ) f 
r ed articles ( l  tria les i  i . ) d  1  
events on the recovery ethods e(X) on ( )(open squares). 
his e e dence li tl  iff rs fr  r rli r r lts 4  O ing  or  rr ct nt f easure ent rs  
i crease f t  S st tisti s. r t e co parison i  i .  
the expected dependences (5 Xm on Eo are presented for the 
models HDM and MPM. The latter one has nsoc IDEo and almost 
nstant r  t  f dary arti les  its  
r 1dities. uclear c position f ri aries as ta e  i  
t e calculati n as c nsisti g f r t ns and clei f t e 
group (   51) i  iffere t r ti s deter ined by t e ean 
ass ber ( ). ch ass c position t fi   ) i s 
t  l r est l es f t  t  f axi   it  fl t a-
ti s i  co parison it  any t er co position f ri aries. 
herefore t fi  o  t   l ent odel t  l  
boundaries of errors of ~ and 6  give the upper estimation 
(A) and 6p- air• An alternative possibility is monochromatic 
clear c position f ri aries hich lea s t  t e s allest 
meanings of Xm and 6Xm at fixed (A). 
• iscussion. I  i .   iff r t aracter f t  en-
dence Xm. on Eo for HDM and MPM at the same meaning 
~dlgEo = ER is explained by the fact_that both models 
preliminarily were reduced to the same ~ = 720 g.cm-2 at Eo 
 101 e   t  ari ti n ( ). herefore t  position 
on MPM with the increase of Eo changes from the enriched he-
avy clei «A) ~40  t  ore ixed one and t e fl ct ati ns 
i r ase. n    t  position fro  ore ixed «A) ~ ) 
becomes a purely proton one and 6:xm. decreases. The opposite 
character of the dependence 6:xm. on Eo according to the MPM 
odel t ri s eanings f  i  s   t  f t t t 
at (ER)calc.< (ER)exp. one should enrich the nuclear compo-
iti   ea y clei a  t er ise -  r t ns. nd l  
at absolute equality (ER)calc. = (ER)exp. the composition 
must not change with energy. Obtained 6Xm. on (3) is in fa-
ur   se f  ti n ss t  it  
energy and high values of ER /d6Xm,/dlgEo I evidence the en-
ric ent f t e clear c position by r t s it  t e i -
crease of Eo' i.e. d(A)/dlgEo.c:: o. 
184
OG 5.1-13
In Fig.3 the dependences _ and 6Xm on (A) for various
meanings of p-air cross sections are presented--Here by se-
lection of the scale the experimental data on _ and gXm
are combined into the dashed region which allows 9o localize
those meanings (_p-air and (A) which satisfy the measu_e-
merits (choice of meanings of these parameters is shown in
the bottom in Fig.3)
Thus, if the Landau hydrodynamical model is realized
then according to our measurements the mean content of pro-
tons in the primary cosmic rays is greater than_5 % and
p-air cross section gp-air _-750 mb at Eo = 10"QeV.
Fig.1. Cascade curves of development
of the EAS electrons. Points indicate
locations of the maximum depth of the
EAS development.
4 
 1-13 
In Fig.) the dependences ~ and 0Xm. on (A) for various 
eanings of -air cross secti s are presented~ Here by se-
lection of the scale the experimental data on ~ and6Xm 
r  bined i t  t  s  r i  hich llo s t  l ali e 
those meanings 6p- ir and (A) which satisfy the measure-
ents (c ice f eanings f t s  ara eters i  s  i  
t  t't o  i  i .)) 
hus, if t e andau hydrodynamical odel i  realize  
t  acc r i g t  r easure ents t  ea  t nt f r -
t s i  t  ri ary c s ic r s i  r ater 1~5  a  
p-air cross section 6 p- air ~ 750 mb at Eo = 10 eVe 
I I 
600 SOD 1000 1200 
i . . ascade r s f e el ent 
f   t s. oints i ate 
l cati s f t e aJd, u  depth f t e 
E S develop ent. 
185 On 5.!-13
_p.a|# 663 mb
---" 80
value dX_ of the shower
_ development maximum depth
,_o on the primary particle
energy. Triangles and
/ ---HDM "60 squares are experimentaldata, lines - calculated-- MPM
_0 I I I
1017 I0m i01g values. Figures near the
curves are __dXm/dlgEo.eV
10o
/ \ Boo
" HtlIlIIUnHUII  II
,oo_ E:lO'_V, HDM _0o5o °
600 _ 56o
2o
_oo'_ 520
I t0 20 30 '_0 50
- Fig.3. Dependence of the mean value Xm and dXm
on the mean atomic weight of the primary ensemble.
Dashed region is the region of measured values
,,. Xm and OX_ w_th e_rors. Dashed, dottedand dash-
dotted li_s show the calculation for (_p-air =
= 460, 660 and 840 mb, respectively. Values (A)
and (_p-air which satisfy the experiment are de-
term&ned by a solid line.
Reference s.
I. Dyakonov, M.N., et al., (1981), Proc.17-th ICRC, Paris,
. _6,q06.
2. Dyakonov, _.N., i dr., (1975), Izv.AN SSSR, ser.fiz.,
t.39, _ 6, 1249.
(1983), Proc.18-th ICRC, Ba_galore_6, 210.
3. Dyakonov, M.N., (1983), Proc.qS-th ICRC, Bangalore,6, q_q." 4
90 
60 
... TO 
Ie 
~fiO 
85 or, .1-13 
Fig.2. 
Dependence of fluctuation 
al ue 6 Xm f t e sho er 
development axi um epth 
on the pri ary particle 
ergy. riangles d 
squares are experimental 
ata, li es - lculated 
values. Fig~es near the 
curves are dXm/dlgE • 
'  40  
Fig.3.Dependence of the mean value lSn and d Xm 
 t  ean at ic eight f t  ri ary e se ble. 
Dashed region is the region of measured values 
Xm and 6x with errors. Dashed, dotted and dash-
dotted linis show the calculation for 6 p-air = 
 0,  a   b, r spectively. alues ( ) 
and 6p- ir which satisfy the experiment are de-
ter ined by a s li  li e. 
eference  
1. yakonov, .N., 
6, 106. 
. yakonov, M.N., 
t. , m , 49. 
3. Dyakonov, M.N., 
4. yakonov, .N., 
et l., (1981), roc.17-th rO O, aris, 
i r., ( 75), l .  , r.fiz., 
(1983), roc.18-th rO O, angalore,§, 210. ( 83), roc.18-th lO O, angalore,§, 111. 


Fluctuations of development maximum depth and nuclear composition of primary cosmic radiation

Fluctuations of development maximum depth and nuclear composition of primary cosmic radiation

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