Average estimations of the shower energy components are presented and their sum gives E sub 0 (Rho sub 600) - an average function of the relation of E sub 0 with the shower size parameter Rho sub 600 measured at the Yakutsk extensive air showers (EAS) array. Using this relation to the EAS spectrum obtained at the Akeno and Yakutsk arrays the energy spectrum of the cosmic ray total flux within 15  lg (E sub 0,eV)  20 by the EAS methods is recovered

Dyakonov, M. N.

Ivanov, A. A.

Kolosov, V. A.

Krasilnikov, D. D.

Lischenyuk, F. F.

Sleptsov, I. Y.

English

NASA Technical Reports Server

190 OG 5.1-15
ALL PARTICLE ENERGY SPECTRUM OF COS_IC RAYS
IN 1015 to 1020eV Region
• 4
LD.D.Krasllnikov,l M.N.Dyakonov, A.A.Ivanov,
V.A.Kolosov, F.F.Lischez_Tuk, I.Ye.Sleptsov
Institute of Cosmophysical Research & Aeronomy,
Lenin Ave., 31 677891 Yakutsk, USSR
ABSTRACT
Average estimations of the shower energy compo-
nents are presented and their sum gives (E o
(P6oo))- an average function of the relation
of E o with the shower size parameter p6eo measu-
red at the Yakutsk EAS array. Using this rela-
tion to the EAS spectrum obtained at the Akeno
and Yakutsk arrays the energy spectrum of the
cosmic ray total flux within 15_lg(Eo,[eVJ) _20
by the EAS methods is recovered.
1. Introduction. Earlier beginning from 1971 we esti-
mated the primary energy E o on the atmospheric Cerenkov
light flux density on the core distance 400 m at the Yakutsk
EAS array [1] . Last years the experimental data on a maximum
depth, muon energy spectrum and other average characteristics
of the EAS development are obtained which are important to
estimate the shower energy components. By a balance of the
latters one can determine the E o.
2. Estimation of E o b_ Energy Balance Method. The sho-
wer primary energy consists of the next components: E o = Eei+
E_i+ EhA+ Ee_ Eh+ E_+ E_= Ei+ E, where the first three terms
show the energy loss into the atmosphere ionization (E i) by
electrons, muons and by splitting the nuclei and the last
four ones - the energy dissipated in the earth in the form
of electron-photon, nuclear-active, muon and neutrino compo-
nents (E). Our estimation [2]differs from one [_] by account-
ing of the atmospheric Cerenkov li@ht losses [5]on which E -
a main component of the E o is estimated and by use of the _w
measurement results of the muon energy spectrum for Ej_.
Eel. For 1017_ Eo_1019eV the relation of Eei with
the atm-_pheric Cerenkov light total flux q_,(in number of
photons) and from the depth of maximum of showers Xma x 1
(g.cm -2) is given by Eel = 2.07.104(1.04+5.8.10-_'Xmax )- •
. _-1. _, ,eV where _= _m "_a L1 is a light transmittance
190 
L PARTIOLE ENERGY S OTRUM F OOSMIO AYS 
I  015 t  020eV egion 
[D.D.Krasilnikov;1 .N.Dyakonov, A.A. Ivanov, 
.A.Kolosov, F.F.Lischenyuk, I. e.Sleptsov 
O  5.1-15 
Institute f Oosmophysical esearch  eronomy, 
enin ve ° ,  77891 akutsk, SR 
BSTRAOT 
verage esti ations of the shower energy co po-
ents are resented and t eir su  i es <. E 
 
(P600 ) > - an average function of the relation 
of Eo with the shower size parameter P600measu-
r  t t e akutsk S rray. sing t is la-
ti n t  t e B S spectrum obtained at t e keno 
a d akutsk rr ys t e e ergy s ectrum f t e 
cosmic ray total flux within 15 ~lg(E ,[eV]) ~ 20 
o 
by the EAS ethods is recovered. 
. I tr duction. arlier beginning fro  1971 e sti-
mated the primary energy Eo on the atmospheric Oerenkov 
light flux density on the core distance 400 m at the Yakutsk 
E S array (1] • ast years the experimental data on a ~  
depth, uon energy spectrum and other average characteristics 
of the EAS development are obtained hich are i portant to 
sti ate t e s er ergy c ponents.  a alance f t e 
latters one can determine the Eo. 
2. Estima~ion of Eo by Energy Balance Method. The sho-
wer primary ene~gy consists of the next components: Eo : Eei+ 
E~i+ Ebi+ Eei ~+ E~+ Ev: Ei+ E, where the first three terms 
show the energy loss into the atmosphere ionization (E ) by 
electrons, uons and by splitting the nuclei and the last 
f r ones - t  e ergy issipated i  t e rth i  t e for  
of electron-photon, clear-active, uon and neutrino co po-
ents ( ). ur esti ation [2] iffers fro  one [4]  account-
ing of the at ospheric erenkov lig t losses [5]on hich E .-
a main component of the Eo is estimated and by use of the H~w 
measurement results of the muon energy spectrum for E JA. • 
E i • For 10
17 ~ Eo~101gev the relation of Eei with 
the at ospheric erenkov light t tal flux~H(in nu ber of 
photons) and from the depth of maximum of showers Xmax 
-2 1 4( -4 )-1 (g.cm ) is given by Eei = 2.07· 0 1.04+5.8.10 .Xmax • 
• .1'-1. 'PH ,eV where !f = fm .:fa L.1 is a light transmittance 
• 
https://ntrs.nasa.gov/search.jsp?R=19850025743 2020-03-20T18:02:03+00:00Z
191 0(_5.1-15
Coefficient by atmosphere due to molecular (Rayleigh _m )
and aerosol (_a) scatterings. According to [6 et all a
main aerosol part is i_ a ground layer of _1 km thickness.
If to asst_ae that the aerosol is concentrated at depth
900 g.cm -2 and 3= 0.6 at Eo = 1016eV them 3= 0.62 at Eo
1018eV. According to these estimations we took J = 0.60 ±
0.04. Then due to the experimental dependeuce Xmax from _600
and the observed correlation of qoH with• _6o0 [7_we found
the average value lg(_L,{eV_ = (0.98±0.05).1gp6oo +
+0.079
+ q7.620.0.09 7.
_" Its value is small and is observed to be equal
to the average meaning expected from calcttlations by diffe-
rent EAS development models, E_i = (0.12 + 0.09).E_.
E_. If to suppose that the average part of h_drons
on the-'atmosphere Ph(X) = 0.02+0.01 from Ne(X) , average
energy of the nuclear splitting 8 nd = 0.5 GeV [8] and add-
ing the usual ionization losses of hadrons we found Ehi =
(5.6±2.2).I0-2.Eei . If Ph(X) and $ nd are somewhat over-
estimated then it is probably quite compensated in estima-
tion of Ehi by not accounted here the effect of photonucle-
ar reactions [9].
E_ . When the muo_ component registration threshold
_,t_'-----I GeV, as it is at the Yakutsk array, then E_ =
_'N)_ (> I GeV) where the much component energy _ =
= (>IGev)]-I.
•(1 + a-1 )_for the energy spectrum of the shower muons
in form N_ (>_,GeV)oc( 8_+ a)-_. which refers to one mu-
ch wi_a _a _ _ev. uaAcu_awions snow that when the muons
generated-ouly due to decay of pio_s and kaons then the
much energy spectrum does not almost depemd on the EAS de-
velopment model and the _ very poorl_ depends on Eo. From
umique measurement resplts of the much energy spectrum in
showers with Ne = 2.10_at sea level [10] we find that a =
= 10 GeV, _ = 1.64 and 8_ = 18.2 Ge¥. At 8_,th r = 1.1
GeV _11_ , 5 GeV _12_ and in the case Ne = 10° [13] the re-
sults confirm the mentioned approximation (Fig.l). Using
_ = (16 _ 3)GeV and the observed relation lgN_ (> 1 GeV)=
= (0.8_ + 0.08).lg_soo + 6.@9I+0"0_2• - . 6 _3_ we obtain
191 OG 5.1-15 
coefficient by atmosphere due to molecular (Rayleigh a'm) 
and aerosol ( $a) scatterings. According to (6 et all a 
main aerosol part is in a ground layer of -1 km thickness. 
If to assume that the aerosol is concentrated at depth > 
900 g.cm-2 and [f = 0.6 at Eo = 1016eV then [J = 0.62 at Eo 
1018eV. According to these estimations we t ok ~ = 0.60 ± 
0.04. Then due to the experimental dependence ~ax from ~600 
and the observed correlation of ~H with f600 (7)we found 
the average value Ig(\L,[evJ) = (0.98;;1:0.05)·lg P600 + 
+ 17.620:g:g~~. 
E".i· Its value is small and is observed to be equal 
to the average mea ing expected from calculations by diffe-
rent EAS development models, E}li = (0.12 ± 0.09)·E J-l • 
~ • If to su ~ose that the average part of hadrons 
on the at osphere Ph(X) = 0.02;;1:0.01 from Ne(X), average 
energy of the nuclear splitting f, nd = 0.5 GeV [8) and a d-
ing the usual ionization losses of hadrons we found Ehi = 
(5.6z2.2).10-2.Eei. If Ph(X) and g nd are somewhat over-
estimated then it is pro ably quite compensated in estima-
tion of ~ by not accounted here the effect of photonucle-
ar reactions [9]. 
E J! • When the muon compo ent registration threshold 
€ thr = 1 GeV, as it is at the Yakutsk array, then E fL = 
-~, -
€")l ·N}l (;> 1 GeV) where the muon component energy &}ol = 
= [N}l (>1 Gev)]-1. SE.fL ,maxf.fL.dN}l(>£fl)~a.(~ _1)-1. 
-1 ~ 0 
·(1 + a ) for the energy spectrum of the shower muons 
in form Nfl (>t:",,- ,GeV)OC( cJA: + a)-~ which refers to one mu-
on with Eft :> 1 GeV. Calculations show that when the muons 
generated only due to decay of pions and kaons then the 
muon energy spectrum doe§ not almost depend on the BAS de-
velopment model and the e~ very poorly depends on Eo. From 
unique measurement results of the muon energy spectrum in 
showers with Ne = 2.105 at sea level [10] we find that a = 
= 10 GeV, Y = 1.64 and E}L = 18.2 GeV. At £J!,thr = 1.1 
GeV (11) , 5 GeV [121 and in the case Ne = 106 [13] the re-
sults confirm the mentioned a proximation (Fig.1). Using 
E;}L = (16 :I: 3) GeV and the observed relation IgN)A. ( > 1 GeV)= 
= (0.84 ;;I: 0.08) ·lg P600 + 6.491 :g:~ [3] we obtain 
192 UG 5.1-15
_= _aa+O.086
ls(_,#,[eV])- ( o.8_o.o8).iS9_oo+ "_'_-o.Io7
EO_" Assuming that the neutrino carries away 27, 90 and 67%
the much energy due to decay of pions, kaons and muoms,
respectively, and the ratio of kaons to pions is 0.22±0.09
[8] we obtain E_ = (0.6@ + 0.18).E_.
Adding all the above _omponent_ of E^ based consider-
ably on the experiment the average estimation is as follows:
_ _mh+0.066
lg(E o, [eV] ) = (0.98 + o.03)'lgp6o0 + ""'J_-0.077"
_. Euergy Spectrum of the primaries. Using the above estima-
tion of E o for the EAS spectrum obtained ca the Akeno and
Yakutsk array data in a corrected.form [31the energy spect-
rum of all the particles at energzes 15_<lg(E_, [eV])_20 is_recovered. It is show_ in Fig.2 where the daaSed lines corre
spored to the results at E n + A E n. As it is seen this spectrum
reveals sigaificaut irregularities and being approximated by
a form J(Eo)dEoOC Eo_-ldEo it has the following exponents:
algE o 15.*16. 16.*17.5 17.5e18.2 18.2_18.9 18.9_19.4 19.@-20.
+I 2.59+.18 2.91+.13 2.99_+.04 3.63+.05 2._7±.09 3.48±.11
Integral intensities with account of accuracy of the determi-
nation of E o are as follows:
lg(Eo, [ e'V'J) 15 16 17 19
I(>Eo),m.s.sr (2.3±0.6)10 -6 (5±1.6)10 -8 (6+2)10 -12 (3±1)I0 -I_
_-%!05 u O '_.. Po,eV
4Qk x -2 \
•10 "_ O-:) ".. \ ',... '.q
2'+
• .,, ++. ,_.+
+'+ _ Ix • \ ........ _ E..
_3 -- _ +++ .... "\'', ", "
:_ '_ ++ .+. -, ',
; \, - ++++,++"-') "%_,, ". _ _p',{,+'_' ". Xl_-,0 'd+_ '.t + " , _ "
\, _ .s, ..........
X ; .",. ......i , £_., +,0.,eV _uJ° @BM Y_I , Tli ....
..,,._.
11.oe/
.... E_ t,Eo o_ [3] IZ'ig.1. 1- [_o], 2- [1_], .........,,,,
,o'' ,p,, _.,,v ,,o" *_ ,@_-ha],_ [_],
5- N_ (>8_)o_(_,_ . 10) -1"6+ Fig,2, !-Yak_tsk.a_d 2 -
Akeno [31, 3- [1¢J, ¢-
[15] , 5- at Eo + aE o
(upper) and En-- aE_-
(lower), 6 - _16]. _
2 OG 5.1-15 
19(E}{, [eV)) = ( 0.84%0.08) .lg pGOO + 16.699:g:~g~ 
k. ssuming t t t  utrino rries a ay ,  a  67  
of t e uon energy due t  decay of pions, kaons and uons, 
r pectively,  t  r ti  f ns t  i ns i  . ±0.09 
[8) e obtain  ~ = (0.64 :t 0.18).Ejt • 
dding ll t e above co ponents of  based c nsider-
l   t  eri ent t  erage 1ma~ion i  s f ll s: 
19(Eo,[eV]) = (0.98 ± 0.03)·lgP600 + 17.754:g:~~. 
3. nergy s ectr  f t  Pri aries. sing t  a ve sti a-
ti n of Eo for the EAS spectru  obtained on the keno and 
Yakutsk array data in a corrected form [31 the energy spect-
rum of all the particles at energies 1,5 ~ 19(E , [eV])!:: 20 is 
r overed. t i  s n i  i .2 here t  Sfted li s rre-
spond t  the results at o ± o• s it is seen t is spectru  
reveals significant irregUlarit~es and being approximated by 
a form J(Eo)dEoCX: E~4' -1dEo it has the following exponents: 
AlgEo 1,5.+16. 16.+17.,5 17.,5+18.2 18.2+18.9 18.9+19.4 19.4+20. 
~ +1 2.59±.18 2.91±.13 2.99±.04 3.63±.05 2~47±.09 3.48±.11 
I tegral i t nsities ith count f curacy f t  ter i-
ation f Eo are as f ll s: 
19(Eo ' [ l)     I(~Eo),m.s.sr (2.3±0.6)10-6 (5±1.6)10-S (6±2)10-12 (3±1)10-14 
Fig.1. 1- [10], 2- [131, 
3- [ 12 ] t 4- [11] t 
,5- N}i (> E}l )oc ( E}t + 10) -1 • 64 ig.2. 1'""!'Yakutsk and 2 -
keno [ 1, - [14], 4 -
[15] , ,5- at Eo + AEo ( per) and  - l!.E ( l er),  - ~ . 0 
193 OG5.1-15
4. Discussion. A good agreement with results of energ_
balance of small EAS [14] and of a direct calorimetry [15J
testifies a correctness of Eo-p_oo obtained by us. The latter
one is lgEo=(0.94+ 0.03)(lgNe-8.042) + 17.754+0]0_ for mea-
surements at Akeno (920 g.cm-2).
For lg(E_, [eV])_19 the spectrum reveals a consistent
steepening w_th energy Eo which considerably differs from
its earlier accepted form [16 et al]. It more c_rresponds to
a picture expected at the diffusion of the mixture of the
alactic originnuclei [17]. The irregularity (rather "bump"-
ype) at 19_<lg(E, [eV])_20 is difficult to interpret by
evidence of an e_ragalactic component: the particles of
these energies also arrive from low galactic latitudes main-
ly and their anisotropy phase changes with E o [18 et all.
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4. Discussion. A good agreement with results of energy 
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All particle energy spectrum of cosmic rays in 10 to the 15th power - 10 to the 20th power eV region

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