The extensive air showers spectrum on scintillation desity Rko in primary energy region E sub approx. 10 to the 15th power - 10 to the 20th power eV on the Yakutsk array data and recent results of the Akeno is given

Knurenko, S. P.

Krasilnikov, A. D.

Krasilnikov, D. D.

Pavlov, V. N.

Sleptsov, I. Y.

Yegorova, V. P.

English

NASA Technical Reports Server

194 OG5,1-16
EAS SPECTRU_I IN THE PRI_dLRY ENERGY REGION ABOVE 1015 eV
BY THE AKEN0 AND THE YAKUTSK ARRAY DATA
ID .D.Krasilnikov _,S .P.Knurenko, A.D .Krasilnikov,
V .N.Pavlov, I.Ye.S1eptsov, V.P.Yegorova
Institute of Cosmoph_sical Research & Aeronomy,
Lenin Ave., 31, 677891 Yakutsk, USSR
ABSTRACT
The EAS spectrum on scintillation density
results of the Akeno is given.
1. Introduction
At present the EAB observations at sea-level take the
widest energy range of primaries. The obse_ed EAS spectra
on particle number N in a shower at E <_10'°eV and on par-
ticle density j%oe at a distance R=600 m from axis at Eo>
3.1017eV are obtained. Either for the recovery of the spec-
trum on E or for the comparison it is reasonable to obtain
these results in aform of "corrected"spectra where effects
of the development fluctuations (different for N and p6oe )
and N and peoo measurement dispersions (different for vari-
ous arrays) are taken into account. To consider the EAS
spectrum on the whole it is required also to use in the
analysis a common basic unit of measurement of the shower
particle number (density) and a common parameter of the
shower size. Yet it is reasonable and possible only on the
basis of _6o0 : there is the experimental estimation ofp6oo
and E relationship and only in the Akeno array data there
is th_ possibility of transition from N to p6oo •
2. Results
a) Yakutsk. In the central part of the array [41 the regis-
tration of showers was triggered by a small master (SM) and
on the whole array - by a big master (B:). For the analysis
the shower events were selected with an axis within fixed
receiving areas (different for various ranges of _oo ) andfor those periods of the array operation T, when 100 % -
efficiency of registration and levels of _]%oe summary re- •
lative deviations of fluctuations of the shower development
a_d their measurement dispersions obtained from a total mea-
surement simulation [5] and accepted for the analysis [1,2] .
were provided. Each shower was individually treated as fo-
llows: 1) from approximation of measured particle densities
4 G . 16 
 M   MARY  I  E 15 v 
  O   OTS    
I .n. rasilnikov!,S.P.Knurenko, . . rasilnikov, 
V.N~Pavlov, I.Ye.Sleptsov, .P. egorova 
I stit te f os opAysical esearch  er y, 
enin ve., 31, 677891 akutsk, SS  
S CT 
he E S spectru  on sci tillati n densit~ 
9600 in primary energy region Eo'!'! 1015_1020 
eV on the Yakutsk array data ana recent 
res lts f the keno is given. 
. ucti n 
t present the E S observations t sea-le el take the 
idest energ~ range of pri aries. The obse~~ed EAS spectra 
on particle nu ber  in a sho er at E ~ 10 e  and on par-
ticle densit~ psoo at a distance R=600 m from axis at Eo> 
. 17e  r  t i ed. it er r t  r~ f t  c-
tru  on  r f r t e co parison it is reas able t  tai  
t  r Hlts i  f r  f rrected"spectra here ff cts 
of the development fluctuations (different for N and psoo ) 
and N and P600 measurement dispersions (different for vari-
s ~  r  t  i t  unt.  nsider t   
spectru  on the hole it is required also to use i  the 
alysis a c on asi  nit f easure ent f t  s er 
article nu ber (densi~) and a co on para eter of the 
s er i . et it i  r s nable a  ssi le l   t  
basis of psoo : there is the experimental estimation ofpsoo 
a  o r l ti ship a  l  i  t e keno arra  at  t r  
is the possibility of transition from N to psoo • 
. esults 
a) akutsk. In the central part of the array (4] the regis-
tr ti  f sho ers as trig ere  b~ a s all aster ( ) and 
on the hole arra~ - b~ a big aster ( M). or the a al sis 
t  er ents ere l t  it   is it i  i  
receiving areas (different for various ranges of P600) and 
for those periods of th  array operation T, when "-'100  -
efficiency of registration and levels of 8psoo su ary re-
lative deviations of fluctuations of the shower develop ent 
and their easure ent dispersions obtained fro  a total ea-
sure ent si ulation [5J and accepted for the anal~sis [1,2] 
ere provided. ach sho er as individually ,treated as fo-
llo s: 1) fro  approxi ation of easured particle densities 
• 
• 
https://ntrs.nasa.gov/search.jsp?R=19850025744 2020-03-20T18:01:57+00:00Z
195 • o_ 5.1-16
by _ (R)ic_ R-ni [5 ] ni and 2Goo,_ were determined; 2) _6oo,t
was reduced to the zenith angle @ =0°, atmospheric tempera-
ture 240 K and pressure 100_ mb ( 26oo and E o relationship at
the atmospheric depth X=I025 g.cm"2 at these parameters was
found) using the absorption length measured in the experi-
ment• _(_6oo ) = (218 +-15) + (172 ± 15).sec@, g.cm -2, 0<
60°, a barometric coefficient O(p = -0,25 ±0.03 % per mb and
temperature coefficient _(T(P6oo ) = 0.30 • 0.11% per K.
For -0.35 <lgp6o 0 _ 0.6 as an intermediate parameter of sho-
wer size the _3oo i having the absorption length X (p3oo) =
251 _ 21 g.cm 2j e4#o ° and Qsoo= (0.14 • 0.01) •
" Ps0o 0"89_0"02 were used. --
- Data used in spectrum construction on the whole have
following common characteristics:
lg [p6oo ,m'2 ] _6oo ST_ ,m2s.sr Numberof events
SM -0._5 _ 1 0._0@0.17 (0,16@@.3_).1013 53#
I 1.5o.22 o.21(1.88 4:4o)-Io  5" lo9B_ >. 1..5 , O. 21 - 69 • 10_ ,-_ 79
Introducing into the observed intensities the correc-
tions for the summary effect of the development fluctuations
and measurement dispersions with the correction factor [2] K=
= 0.98 [1 . _2_oo ] -0.5_(_-1) the differential fo(_oo )
and the integral Fo( _6oo ) corrected EAS spectra (see Figu-
re) were obtained.
. The differential spectrum for -0.341gp6oo < S.7 displays
significant irregularities and at the description by fo(_eoo)
. = A( _60o/10)-_ -1 has the following parameters:
Ig P6oo -0.3_0.5 0.5_1.2 1.2_1.7 1.7e2.3
Ig A -13.37_0.0_ -13.6_@0.02 -13.92_0.05 -13.20_0. 09
_+1 2.95_0.O_ _.58_O.O5 2.#5_0.10 _._e0.11
The spectrum on _6eo obtained by the relationship _6oo=
= (2.05 +-0.11) • ( Q_oo /107) 0"99_0"02 from the transforma =
• tion of the density spectrum of the shower atmospheric Ce-
renkov light Q4oo [I ] and having the form of the spectrum of
_o_;,:Lui.,atmosphe_e,;__.:_the change _or -0.3_ lgp6oe c. 1.
r " _: ....
" In the Figure a dashed line corresponds to the observed
spectrum on Have_ah Park data[6] reduced by us to the scin-
tillation deyslty jD_oe due to [7]. In this case according
195 Ub 5. -  
, by PCR)iOCR-ni (5] ni and 1'600,\ were determined; 2)'p600,i 
was reduced to the zenith angle 6 0°, at ospheric tempera-
ture 240 K and pressure 1 09 mb ( £600 and Eo relati nship at 
the at ospheric depth X=1025 g.c -2 at these param ters was 
found) using the absorption length measured in the experi-
ment A (psoo ) = (218 ± 15) + (172 ± 15)·S6C(9, g.c -2 , e~ 
600 t a barometric coefficient cX. p = -0,25 to.03 % per mb and 
te perature coefficient do. T( P600 ) = 0.30 i: 0.11 % per K. 
For -0.35 ~ Ig P600 <:: 0.6 as an i ter ediate parameter of sho-
wer size the P300 i having the absorption length A. ( P300 ) = 
* -2' 0 251 21 g.c  , e ~ 40 and P600= (0.14 i: 0.01) • 
• P30Cl 0.89*0.02 were used. 
Data used in spectr  construction on the whole have 
foll ing co mon characteristics: 
8M 
BM 
EM 
19 [P600 , -2 ] , 0P600 ' Q , ?s· sr 
-0.35 • 1 0.40.0.17 (0.16.4.33).1013 
1 .1.5 0.22.0.21 (1.88.4.40)·10~§ 
'> 1.5 ' 0. 1 5.69 .10' 
Number 
of events 
534 
109 
79 
Intr ducing into the observed i tensities t e co rec-
ti ns for t e su mary effect of t e' el pment fl ctuations 
and measurement dispersions with the correction factor [2] K= 
= 0.98 [1 + op~ooJ -0.5ae(~-1) the differential f
o
(p6oo ) 
and t e i tegral F oC::> P600) corrected EAS spectra (see Figu-
re) were obtained. 
The di ferential spectrum for -0.3",lgp6oo <:: 1.7 displays 
significant irregularities and at t e description by f oCp6oo  
= A( P600 /10) -~ -1 has t e foll ing param ters: 
19 P600 -0.3.0.5 0.5.1.2 1.2.1.7 1.7.2·3 
19 A -13.37.0.04 -13.63.0.02 -13.92.0.05 -13.20.0. 9 
2.45.0.10 
The spectru  on 1'600 obtained by t e relati nship 9600 = 
= C 2.05 ± 0.11) • C Q"o  / 07) 0.9g.0.02 fr  the tr sfor a ~ 
ti n of t e density spectr  of the shower at ospheriC Ce-
renkov li ht Q400 [1] and having the for ,of t e spectrum of 
l:01J&:1n;.tmospb er ;~~irms,the challge for -0.3 <: IgP600 <:. 1. 
In t e Figure a dashed li e co responds t  the observed 
spectr  on Have~ah Park data(6) reduced by us t  the scin-
till ti n density P600 due to [7]. In t is case according 
196 OG 5.1-16
to [8] the effect of 6"pso at ig96oo _ I is small (%10_
on intensities) and at ig P600 >--_ 1 somewhat increases. Ta-
king into account this fact we find a satisfactory agree-
ment of the results of both arrays. It is remarkable that
the Haverah Park spectrum reveals also the steepening ten-
dency for 1.8 _ lgpsoo _ 2.3.
log' Ib_ _b3 Ib2 Ib" lb° I_' t_2
' ! ,o'°
+++++ +++++ + "-
ld,O + + ++,+ ",._'_
+ +_fc4p _ .
L,,_. + @'@" @
} ":® BM YAKUTSK ._i 1012• %oCl_m
...... FIAVERAHPARK IT
1(j12
•_6oo" m-2
I,o_ 10' 1,o° lO' 1,o2 1,03 I/ I0,_
b) Akeno. The observed EAS spectrum at sec @ = 1.1 (at the
depth 10qq g.cm-2) is given by f(N=)dNe= A(Ne/q06)-_N -I
with A = (1.2 • 0.2).q0-q3m--2s--Isr=.Ipart.-q,_CN= 1.49 _0.17 '
for 5 _lgN e < 6 and 8_N = 1.80 • 0.12 for 6 < lgNe<8.
Some corrections were made: the spectrum is reduced to the
Yakutsk level 1025 g.cm-2 with absorption length 54 (Ne) =
235 g.cm-2; the effect of the shower development fluctuati-
ons was taken in?o account on [9] with average correction
factor K_ = 0.89 ['1 + gNe2]-0"598N(9_N 1) = 0.77 where
the deviations were taken according to [q0] to be 0.7 for
5 < lgN e _ 6 and 0._u+for 6 _ lgNe< 8.
From [qq,q2] we find igp6oo = Ig [ _oo, e + psoo,y_] = "
= o.961 igNe- 7.46 at the depth 966 g.cm-= at T = 279 K.
96 Oil 5.1-16 
to [81 the effect of 6'P6oo at 19 psoo:ES 1 is s all ( ~ 1~ 
on intensities) and at 19 P600 ~ 1 somewhat increases. Ta-
king i t  account t is f ct e fi  a satisfact ry a ree-
ent f t  r sults f t  rr s. t i  re arkable t at 
t e averah ark spectru  re eals als  t e stee ening te -
dency for 1.8 ~ 19 P600 ~ 2.3. 
'L 
VJ 
-10 
10 
) keno. he observed E S spectru  t sec G  .  ( t t e 
depth 1011 g.cm-2) is given by f(Ne)dNe= A(Ne/106)-re N-1 
with A = (1.2" 0.2).10-13m-?s-:tsr-~part.-1, ~N= 1.49 *0.17 
for 5 .tt:. IgN e .tt:. 6 and re N = 1.80 i: 0.12 :f' or 6 c::. IgN e c::. 8. 
e rr cti s ere ade: t  tr  i  r ed t  t  
Yakutsk level 1025 g.cm-2 with absorption length A (N ) = 
235 g.cm-2; the effect of the shower development fluctuati-
ons was taken into account on [91 with average correction 
factor Ko = 0.89- [1 + ONe2 1 -0.5~N(~N-1) = 0.77 where 
the deviations ere taken according to [10] to be 0.7 for 
5 c:::: 19Ne .tt:. 6 and 0.44 for 6 c:::: 19Ne.tt:. 8. 
From [11,12) we find Ig P:oo = Ig [ .r:ioo, e + P:oo ,}-l'1 1 = 
= 0.961 19Ne- 7.46 at the depth 966 g.cm at T = 279 K. 
" 
• 
197 OG 5.1-16
Recounting p6oo to depth 1025 g.cm-2 with 5[(_soo) = 390
g.cm -2 at T = 240 K with o(T = 0.3 % per K and to the Yakutsk
bas_ unit of muon equivalent having the relationship u_/Ue=
= 1.15 with the electron equivalent unit _3J the relation-
ship lgp6oo = 0.96-1gN e -_.5S_ is obtained.
In the Figure the differential and integral corrected
EAS spectra on P6oo from the Akeno data are given. For^l_ @600
0.12 we obtain: f,,(Q60n )dp6oo = A_(p6oo /10 -i'_U)_'IdPsoo
with Ao = (1.2 • 0.2").l-O-5"297m-2s-._sr-l(part./m2)'l, "-
9e = 1.55 +-0.18 for -2.76<1gp6oo< -1.80 and 8e=1.88±0.13
for lgP6oo> -1.80.
_. Conclusion
In the considered 5-decade energy range the EAS spect-
rum on P6oo reveals significant irregularities. For lgp6oo<l.2
the steepening(rather consecutive)of inclination of _P6oo )
with increase of P6oo occurs: -_-1=-2.55e0.18; -2.88±0.12;
-2.95±0.z(_.and -°3.58±0.05 for _ lgp6oo = -2.76±-1.8;
-fl.8_-0.3, -0.3_0.5 and 0.5_1.2, respectively. At lgp6oo>1.2
the irregularity is observed: -_e-1 = -2._5±0.1 at 1.2
lgp6oo<l.7 and -_e-1 _-3 at 1.7_lg_soo < 2.3. We assume
that four shower e_ents with lg]06o0 >2.5 from the spectrum
of [6] if to eliminate the effe6_s of methodical character
could indicate the possible existence of the other irregula-
rity in the range out of the control of the Yakutsk array.
References
1. Krasilnikov, D.D. i dr., (1983),Kosmicheskie luchi
s energiei vyshe 1017eV, Yakutsk, 117.
" 2. Krasilnikov, D.D. i dr.,(1985), Izv.AN SSSR, ser.fiz.
49, No.1.
3. Nagano, M. et al.,(1984_,J.Phys.G, 10, 1295.
4. Kerschenholz,I.M. etal. _1973),Proc.13-th ICRC, Den-
ver, __, 2507.
5. Dyakonov, M.N. etal., (1981),Proc .17-th ICRC, Paris,
9, 166.
6. Bower, A.J. et al.,(1981),Proc.17-th ICRC, Paris,
, q66.
7. Bower, A.J. et al.,(d983),J.Ph_s.G,9, L.53.
8. Brooke, G. et al.,(1979),Proc.16-th ICRC, Kyoto,
_8,13.
9. Kalmykov, N.N ,(1969),Yadernaya fizika, 10, 121.
• 10. Kulikov, G.V._(1973),Thesis, _GU.
11. Hara, T. et al.,(1983),Proc.18-th ICRC, Bangalore,
11, 272.
. 12. _'ags.uo,M. et al.,(1984)_J.Phys.Soc.Japan, 55, 1667.
97  1-16 
Recounting P600 to depth 1025 g.cm-2 with A ('psoo ) = 390 
g.cm-2 at T = 240 K with c(T = 0.3 % per K and to the Yakutsk 
basic unit of muon equivalent having the relationship u~/ue= 
 .  ith t e electr  e uivalent nit [ ] t e r l ti -
ship 19psoo = 0.96 •l gNe - 11 .534 is obtained. 
In the igure the ifferential and i te ral corrected 
EAS spectra on psoo fro  the Akeno data are given. For li Oqpo 
<:::. .  e tai : foe 9600 )dP600  r/P600 / -1 •80r ·'1d}'6oo 
with Ao = (1.2 z 0.2)·10-5.297m-?s-.sr-1(part./m2)-1, 
~ = 1.55 ± 0.18 for -2.76.c.lgP600.c. -1.80 and re=1.88:t0.13 
for 19P600> -1.80. 
i, 3. Conclusion 
I  t e c nsi ered 5-decade energy ra e t e E S s ect-
rum on Psoo reveals significant irregularities. For 19P6oo<'1. 2 
the steepening(rather consecutive)of inclination of ~P600) 
ith increase of e.soo occurs: -re-1=-2.55't0.18; -2.88t;0.12; 
-2.95't0.04 and -3.58±0.05 for A 19P600 = -2.76z-1.8; 
-1.8 .. -0.3; - .  .. 0.5 and . . . , res ectively. t 19'p6oo>1.2 
t e irr larit  is ser e : -00.-   - .4 't .  t .  < 
19P600 <1.7 and -ge-1 ~ -3 t . < 19psoo <:::. . . e assu e 
that four shower events ith 19P600 >2.3 fro  the spectru  
f ( )   i ate  ct  f ethodical aracter 
could indicate the possible existence of the other irre la-
ri tr.Y i  the range out of the control of the akutsk array. 
eferences 
. rasil i ov, . . i1 r.,(1983),K s icheskie l i 
s ergiei s e  'le , akutsk, . 
2. rasil i ov, . . i r.,(1 ), Izv.A  , s r.fi . 
!t-9, o.1. 
3. agano, . et ale ,(1984),J .Ph;ys.G, 10, 1295. 
. erschenholz,I. . t ale .(1973),Proc:13-th I e, en-
ver, 4, 2507. 
5. yakonov, . . et al.,(1981),Proc.17-th ICRC, Paris, 
.2, 166. 
6. Bower, A.J. et al.,(1981},Proc.17-th ICRC, Paris, 
,2, 166. 
7. Bower, .J. et al.,(1983),J.Phys.G,j, L.53. 
8. Brooke, G. at al.,(1979),Proc.16-th lCRe, Kyoto, 
8, 13. 
. Eal ykov, . .,(1969),Yadernaya fi i , , 121. 
10. Kulikov, G.V.,(1973),Thesis, MGU. 
11. ara, T. et al.,(1983},Proc.18-th rCRC, Bangalore, 
11, 272. . 
12. Nagano, M. at al.,(1984),J.Ph;ys.Soc.Japan, 22, 1667. 


EAS spectrum in the primary energy region above 10 to the 15th power eV by the Akeno and Yakutsk array data

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