Pr~.mana, Vol. 12, NO. I, January 1979, pp. 33-44, ~)Printed in India.
Characteristics of high energy interactions I. High energy gamma-ray spectra near the top of the atmosphere
R H A S A N , A K A G R A W A L and M S S W A M I
Department of Physics, Aligarh Muslim University, Aligarh 202 001 MS received 30 May 1978; revised 4 November 1978
Abstract. An emulsion chamber was used to study the characteristics of high energy nuclear interactions from the production spectra of 3,-rays. The emulsion chamber, which comprised of two parts, namely the detector and the graphite producer unit, was exposed to cosmic rays for about 7 hr at an atmospheric depth of 10 g cm --° at Hyderabad (geomagnetic latitude 7"6°N). 720 electromagnetic cascades due to ),-rays were recorded in the detector. These cascades were classified into three groups; (a) ),-rays from nuclear interactions in the detector (b)),-rays from nuclear interactions in the producer unit and (c))'-rays of atmospheric origin. The energies of the cascades were determined using photometric method. The spectra of )'-rays from groups (a) and (c) were determined and compared with similar spectra obtained at greater atmos- pheric depths. The spectra were found to obey a power law. The spectrum of )'-rays of atmospheric origin was found to steepen at high energies, Ey > 2200 GeV.
Keywotds. Emulsion chamber; atmospheric )'-rays; collecting powers; production rates; steepening of the ),-ray spectrum.
1. Introduction
Useful information on the characteristics o f high energy interactions can be inferred from the studies o f energy spectra o f )'-rays incident on and produced in an appro- priately designed emulsion chamber. F o r this purpose, an emulsion chamber, which comprised o f alternate layers o f emulsions and heavy and light materials, was exposed to cosmic rays for 6 hr 47 min at an atmospheric depth o f 10 g c m -~. Using this chamber the energy spectra o f atmospheric )'-rays and ),-rays produced in interactions occurring in heavy metals and graphite were studied. The procedure and approach followed in this study are similar to those o f Malhotra et al (1965).
In this paper, we present the design and exposure o f the emulsion chamber. The classification o f electromagnetic cascades and their selection criteria and methods o f energy estimation are discussed. The energy spectra o f atmospheric ),-rays and ),-rays produced in heavy metals are obtained and compared with each other as well as with those obtained at greater atmospheric depths.
In part 2 (Agrawal et al 1979), we present the analysis o f nuclear interactions in graphite, Results on the multiplicity, the transverse m o m e n t u m distribution and the fractional energy distribution o f ),-rays will be discussed.
P.--3
33
2. Experimental details
2.1. Design and exposure of the emulsion chamber
The most important consideration in the design of the emulsion chamber was to visually detect high energy electromagnetic cascades. For this purpose, heavy metal sheets were inserted between the emulsion plates so as to develop the electromagnetic cascades to their maximum within short distances of their travel without much lateral
spread.
The emulsion chamber, shown in figure 1, consisted of two parts--the detector and the producer unit. The detector consisted of 21 vertical layers of 200/~m thick Ilford G-5 emulsions sandwiched with 20 sheets of lead and tungsten. Each vertical layer of emulsion comprised of three rows and three columnsof emulsions each of area 30'5 × 28.0 cm 2. The emulsions were coated on thin plastic sheets. The detector was symmetrical about its central plane. The inner three metal sheets, on either side of the central plane, were of 5 mm thick lead, the next four sheets were of 1.6 mm thick tungsten and the outer three sheets were of I mm thick lead. The emulsions and the metal sheets were separated by 50 /zm thick polythene sheets. These layers were tightly packed and were held together by an iron frame which overlapped the faces of the detector by 1.6 cm on each side. The properties o f t h e composite detector were:
density--12.5 g cm -3, radiation length =0"532 cm and geometrical interaction length
=12.5 cm.
The producer unit, which had the same face area as that of the detector, consisted of six layers of 200/zm thick Ilford G-5 emulsions arranged alternatively with five sheets of 5 mm thick graphite. Emulsions and graphite sheets were also separated by 50/zm thick sheets of polythene. One such tightly packed producer unit was placed on either side of the detector. Each producer unit was separated from the face of the detector by 10-1 cm thick styrofoam and was 4 cm higher at the top as shown in figure i. The whole chamber was surrounded by 1.27 cm thick tufnol.
The emulsion chamber was exposed to cosmic rays by means of a large balloon at a vertical depth of 10 g c m -~ for 6 hr 47 min over Hyderabad (geomagnetic latitude 7.6°N). The flight curve is shown in figure 2. The balloon flight was organised by the Tata Institute of Fundamental Research, Bombay and the University of Bristol, England. The emulsion plates were also developed at TIFR.
,o,T I/
:' ,tom. i/
o.,.o,or 5.cm
11/
Styrofoorn I0.I 1 16 c~i~H , , cm I 4 c n ~
pro~.~ u~i, / ~.~Tcm II
Figure 1. Vertical s~tton of the emulsion chamber perl~ndicular to the plane of the emulsion. (not to scale)
High energy interactions 1 35 2.2. Scanning of emulsions
The composition o f detector was such that it facilitated quick longitudinal develop- ment o f electromagnetic cascades without much lateral spread. The cascades were visible to the naked eye as black streaks when the emulsions were viewed against an illuminated ground glass plate. The black streaks were examined under a microscope to pick up genuine cascades. In all 720 cascades were detected. Each o f these cas- cades was followed through successive emulsions towards its origin using the illu- minated ground glass plate. When it became too thin to be seen by the naked eye, it was followed under the microscope to its origin or to its p o i n t o f entry in the detec- tor.
2.3. Classification of events
Detailed examination o f the origin and development o f cascades led to the following classification.
2.3.1. Atmospheric y-ray events: The cascades which were, caused by individual y-rays from the atmosphere were classified as atmospheric y-ray events, in this type o f events, each cascade was followed either to an electron pair or to a few tracks with no neighbouring tracks converging to a point in the adjacent metal sheet. In some cases, the cascade was followed to a few tracks entering the detector,
2.3.2. Detector events." The cascades which were caused by y-rays from nuclear interactions in the detector itself were classified as detector events. Since radiation length in the detector was small (0"532 cm), y-rays from nuclear interactions in the detector materialised rapidly without much lateral spread. This led to an overlap o f
4O
. . O
E
== 100
2 0 0
4OO 1000
6 1
10 -
@(3 -
m
w
I
w
I 6 0 0
Figure 2.
Beacon signal
unreadable 1430 I.S.T,
1 I I I
8 0 0 1 0 0 0 1 2 0 0 i 4 0 0
Time ( I . S . ' T . )
"lqlne-altitude curve for the balloon flight.
Termination by radio command
[mpoct area 17~-30'N
~ 73 °- 57' E
% % 1600
cascades due to different ~,-rays from a single interaction. Therefore, the detector events revealed a core structure when viewed under the microscope. Each of these cascades was followed either to a small number of tracks with some neighbouring tracks converging to a point in the adjacent metal sheet or, in a few cases, to a nuclear interaction in an emulsion. Further, secondary nuclear interactions were observed frequently in the course of following the detector events.
2.3.3. Graphite events: Since the detector and the producer unit were separated by 10.1 cm thick styrofoam, y-rays from a nuclear interaction in the producer unit were laterally well separated when they entered the detector. This type of events which looked like a single cascade to the naked eye actually comprised of a number of sepa- rate near parallel cascades spread over a distance of a few hundred microns. Careful tests were performed on the cascades in each of these events to examine whether these cascades converged to a point in or outside the producer unit. We had 20 graphite events and all these events converged to various points well inside the producer unit.
We attempted to locate these events in the emulsions of the producer unit but did not succeed. So for further analysis we assumed that the interactions occurred in the central plane of the producer unit.
2.4. Energy measurements
The energy of each cascade was determined by measuring its central density of electron tracks by the photometric method (Duthie et al 1961). The central density is defined as D=ln(Jo/J), where J i s the intensity of light transmitted through a slit of 10/~m width centred on the cascade axis and J0 is the average intensity of light transmitted through adjacent regions away from the cascade axis. Values of the central density were computed at various radiation lengths and for different energies of y-rays using the tables prepared by Kidd and Nishimura (1960).
At any given stage of cascade development, the central density of a cascade was found to be a function of its energy E 0 and its dip angle 8 in the emulsion. For our chamber we computed the maximum value of the central density Dma x as a function of energy E 0 for fiat (8 =0) cascades. The relation between E 0 and D,,,x (figure 3) was of the type
eo = ,i. ( l )
where the values of A and n were 3000 and 1.08 respectively. In practice the cascades were not flat, their dip angles were in the range 0.15 ~< sin 8 ~< 0.92. Further, the maximum cascade development, in most of the cases, could occur in a metal plate rather than in an emulsion. These two factors were taken into account in the energy estimation of cascades using (1). The central track density was measured in three successive emulsions around the cascade maximum and the average value Day was computed for each cascade. The factor f(8) to convert Day to Draax was found to be (1 +0"01 cosec ~ 8). The dip angle corrections to Day were also computed and the final relations between D~v and Dma x were
D,~ax ----f(~) (0.17+0.83 cos ,~) for ~ values in the range 0 . 1 5 ~ sin ~ ~<0.76,
High energy interactions I 37 10.0
mQx
10
0.1
10 2
I I
10 3 10 4
Energy ( GeV )
Figure 3. C0rve showing the maximum central density Dma x vs the energy of the cascade Eo. The points shown are for those events whose energy was estimated by the track counting method.
Dma x = f ( 8 ) (0"10+0"90 cos 6) for 6 values in the range 0'76 < sin 8 ~< 0.92.
To check the validity o f (1), it was desirable to have independent estimates o f the energies o f the cascades for which Dma x values were already available. In some o f these cases, the n u m b e r o f electron tracks within circles o f radii 20 to 100/zm around the cascade axis at various initial stages o f the cascade development was determined.
The energies were obtained by comparing these numbers with those given in Kidd and Nishimura (1960) tables. The independent estimates o f the energies as a function o f the corresponding Dma x values were also plotted and shown in figure 3.
The agreement between the two estimates o f energy was good, at least for cascades o f energy less than 1250 GeV. It was assumed that (I) was also valid for higher energy cascades.
Although (1) was obtained and justified for cascades initiated by individual y- rays, it was also used to measure the energy o f the composite cascades initiated by several y-rays (detector events). The justification for this p r o c e d u r e stemmed from the work o f Ohta (1971) and Duthie et al (1961).
F o r five o f the very high energy detector events, the central density o f the cascades at the maximum development was so high that no meaningful signals could be recorded by the photometric method. In these cases the energy was estimated by measuring the track density at various points 50 to 200/zm away from the cascade axis.
2.5. Selection criteria
The iron frame supporting the detector shielded its faces by 1.6 cm on each side.
Events were accepted for analysis only if they entered via the unshielded parts o f the detector.
The efficiency for visual detection o f a cascade was f o u n d to be a function o f its maximum central density D~,ax and its dip angle 8. T o ensure 100% detection efficiency o f cascades, selection criteria were necessary. F o r this purpose, the inte- gral number distribution o f Dma x was plotted for all cascades. The distribution was found to obey a power law o f the type: .N(>~D~x ) : c o n s t . D~a x for cascades with Dma x ~ 0"36 and dip angles in the'range 0" 15 ~ sin 8 ~0.92. At lower values o f Dma x the distribution flattened on account o f p o o r detection efficiency. Thus the detection efficiency was 100 K for cascades with Dma~>~ 0"36 (energy >~ 1000 GeV) and dip angles in the range 0.15 ~< sin 8 ~<0.92. T o determine the detection efficiency for low energy ( < 1000 GeV) cascades, the steep cascades were removed from the sample and the integral n u m b e r distribution o f Dm~ x was again plotted. After a few trials it was found that the detection efficiency was also 100% for cascades with Dma x ~ 0"18 (energy >7 470 GeV) and dip angles in the range 0-15 ~~ sin 8 ~< 0-60.
The photometric method o f energy estimation was possible only for cascades which developed to their maximum in the detector. F o r atmospheric y-rays, the selection criteria described above ensured a minimum path length o f 9 radiation lengths in the detector. This was sufficient to develop the cascades to their maximum. However, the origins o f detector events were distributed fairly uniformly in the detector.
Therefore, an additional criterion was imposed for these events so that a minimum o f 6 radiation lengths was available for cascade development. The producer events also satisfied the selection criteria described above.
2.6. Numbers of events detected
The numbers o f events o f the three types which satisfied our selection criteria discussed in the last section are summarised in table 1. Out o f the 272 detector events 31 were caused by a-particles, 8 by heavy nuclei and the rest were attributed to the singly- charged particles. The energy spectrum o f primary cosmic rays will be presented elsewhere.
Table 1. Numbers of events of different types detected.
Type of event
Atmospheric y-rays Detector events Graphite events
Effective Range of Number
Energy (GeV) depth dip angle of
(gcm -~) sin 8 events
E~ ;~ 1000 1 7 " 0 0.15--0.92 43 470 ~ E~, < 1000 1 1 " 3 0.15--0"60 36 ,~E~ ;B 1000 1 7 " 0 0.15--0"92 122 470 ~ -~E~ < 1000 1 1 " 3 0"15--0"60 150
~E ;D 470 1 1 . 3 0.15--0.60 20
High energy interactions I 39 2.7. Collecting powers
The selection criteria for the acceptance o f different types o f events were discussed in § 2.5. The number N~ o f each type of events recorded depends on the a m o u n t o f matter traversed by their primaries, their interaction mean free path at and the geometry o f the primaries in the detector. In order to correlate the number o f events N~ in each category with their production rates Rt (number/g sterad see) at the top o f the atmosphere, a knowledge o f the collecting power S~ (cm 2 sterad sec) o f the chamber for each type o f events was essential. T h e collecting power S~ was defined by the expression
s , = N,/(a,Rt). (2)
The collecting power St for each type o f events was computed using the m e t h o d o f Malhotra et al (1965). In our calculations, a value o f 125 g cm-2 for the attenuation length o f nuclear active particles in the atmosphere was used; the interaction lengths o f nuclear active particles in air, producer unit and detector were 80 g c m -z, 75 g cm -~
and 12-5 em respectively. The calculated values o f the collecting powers for each type o f events are given in table 2.
3. E x p e r i m e n t a l results
3.1. Energy spectrum of atmospheric ~,-rays
The numbers o f atmospheric y-rays detected in different ranges o f dip angle are given in table 1. T o obtain the integral energy spectrum, proper weighting factors were given to events in different ranges o f dip angle. These factors were calculated from the collecting powers given in table 2. Thus events with energy Ey >~ 1000 GeV were given a weight o f 1.0 axtd events in the energy range 470<~E~,<1000 GeV were given a weight o f 2.9. T h e integral energy spectrum o f atmospheric ~,-rays is shown in figure 4. The overall spectrum is best fitted by a power law
N ( ~ Ev)
= const. E -~ ywhere the value o f f l is 1.88+0.10. It can, however, be seen from the figure that the spectrum Of atmospheric y-rays steepens in the high energy region. Therefore, the Table 2. Collecting powers (cm I sterad see) for various types of events computed
for different ranges of dip angles.
Type of events sin 8
0.15 -- 0 . 6 0 0.60--0-92 Nuclear events 9.47 × 107 6"81 × 107 Graphite events 5.61 × 107 4.60 × 107 Atmospheric y-rays 5.68 x 107 10.93 × l0 T
UJ A I
e,, E Z
10 -
-1.88 ± 0.10 E~.
I I
10 2 10 3 10 4
Energy (GeV)
-j - 16r
¢7
^ 1
E _ _ l d a Z
Figure 4. Integral energy spectrum of the atmospheric ~.rays.
spectrum was divided into two energy ranges. In the energy range 470 <~E r ~2200 GeV, the spectrum is best fitted by a power law of index/3x=1.64~0.07 and in the energy range 2200<Er~<4500 GeV the spectrum is represented by a power law of index flz=3"0q-0"3. The steepening of the ~,-ray spectrum at high energies was also observed by Kidd (1962), Malhotra et al (1965), Bowler et al (1962) and Takahashi et al (1977). Table 3 lists the values offl as obtained by several authors.
3.2. Energy spectrum o f detector events
The numbers of detector events detected in different ranges of energy are given in table 1. The energy of a detector event represents the total energy Z'E~, radiated in the form of ~,-rays in an interaction. As in the case of atmospheric y-rays, detector events were also given appropriate weights. The events in the energy ranges 27E~
>~ 1000 GeV and 470 ~<Z'Ey< 1000 GeV were given weights of 1.0 and 1.7 respectively.
The integral energy spectrum of detector events is shown in figure 5. In the energy range 470 ~<Z'E~, ~2.2 x 104 GeV, the spectrum is best fitted by a power law
N(/> Z'E~,)=const. (Z'Ey) -~
where the value of a is 1.55:~.0.06. The spectrum of detector events, hereafter re- ferred to as SEy spectrum, unlike the spectrum of y-rays, does not steepen at high
41
Depth (g cm -~)
8
9 (26) 10 22 (37)
20O 220 260 540 650 720 735
Exponent o f
Energy range (GeV) the power Reference
law (8)
Values in brackets represent the effective
500 - - 5000 2.0 4- 0"5 70 - - 2000 1-9 + 0"3
- - 0"2 4 7 0 - 2200 1.64 4- 0-07 2 2 0 0 - - 4500 3"0 4- 0"3
370 - - 2650 1.57 4- 0.08 2650 - - 10000 3'0 =J= 0.8
100 - - 20000 1 "7 -- 1.9 2 5 0 - - 2000 2"3 =J= 0'2 2 0 0 0 - - 10000 2"8 =E 0"2
50 - - 2000 1 "85 200O - - 40O0O 1 "95
200 - - 20000 2.07 ± 0"10 2000 - - 20000 2.3 4- 0"2 100O - - 100O0 1 "85 __+. 0.30
3 5 0 - - 100O 2"0 4- 0'2 100O-- 1000O 2"3 4- 0.2
depth.
10 3
Bowler et al (1961) A b r a h a m et al (1963) Present experiment
Malhotra et ai (1965)
Apanasenko et at (1968) Bowler et al (1962) Takahashi et al (1977) Lattes et al (1971) Shibata et ai (1977)
Heidbreder and Pinkau (1968) Akashi et al (1963)
A I
..O t~
E D Z
10 ~
10 2
I I
10 3 10 4 I
Energy ('GeV) H i g h e n e r g y i n t e r a c t i o n s 1
Table 3. Observations on y-ray spectrum at various depths.
Figure 5. Integral energy spectrum of the total energy (gET) radiated in the form of y-rays in interactions occurring in the detector.
Table 4. Observations on ~VE, spectrum at various depths, Depth (g cm -~) Energy range (GeVI Exponent of the Reference
power law (a)
10(17) 4 7 0 - - 22000 1.55 _4 0.06 Present experiment
22 (37) 370 - - 40000 1.44 :!: 0-05 Mathot-ra et al (19651
220 300 - - 20000. 2-1 -4: 0. I Bowler et at (1962)
540 2000-- 10000 2.1 ± 0.1 Lattes el al (1971)
650 2000 - - 30000 1.76 ± 0.07 Shibata et al (1977)
735 2000--20000 2-1 ± 0,1 Ake, shi et~11(1963)
Values in brackets represent the effective depth.
Table 5. Rates of production of y-rays in air at the top of the atmosphere (the units are events per g sterad sec).
Production rate Reference
(E, ~ 470 GeV) (13"5 -~ 1-0) x 10 -~
(12"6-2: 0.8) :< 10 u (16"0 :L 2.0) × 10-"
Present experiment Malhotra et al (1965) Duthie et al (1962)
energies. I n t a b l e 4 we s u m m a r i s e t h e results o n Z'Ey s p e c t r u m as o b t a i n e d by v a r i o u s a u t h o r s .
3.3. Production rates
T h e p r o d u c t i o n rates o f a t m o s p h e r i c y - r a y s a n d d e t e c t o r e v e n t s at the t o p o f the a t m o s p h e r e were o b t a i n e d f r o m e x p r e s s i o n 2. S u b s t i t u t i n g p r o p e r values for e a c h class o f events, t h e p r o d u c t i o n r a t e o f d e t e c t o r e v e n t s per g r a m o f t h e d e t e c t o r c o n s i d e r e d to b e a t t h e t o p o f t h e a t m o s p h e r e is
Rl(>/ZrEy) = 1.90 x 10 -4 (~rEy)-l"5~ for 470 ~ ~rE r -~2-2 x 104 G e V .
S i m i l a r l y , t h e p r o d u c t i o n r a t e o f y - r a y s in a i r at t h e t o p o f t h e a t m o s p h e r e is given b y t h e e x p r e s s i o n
R e ( > / E y ) = l . 4 2 × 10 -a E), -1"88 for 470~<Ey ~ 4 " 5 x 10 s G e V
T a b l e 5 s u n u n a r i e s t h e p r o d u c t i o n rates o f y - r a y s as o b t a i n e d by different a u t h o r s .
4. Discussion
4.1. Multiplicity o f y-rays
F i g u r e s 4 a n d 5 r e s p e c t i v e l y s h o w t h e y - r a y s p e c t r u m a n d Z'Ey s p e c t r u m o b t a i n e d in t h e p r e s e n t e x p e r i m e n t . T h e v a l u e s o f t h e e x p o n e n t s a a n d / 3 n o w o b t a i n e d as well as t h o s e b y o t h e r a u t h o r s a r e s u m m a r i s e d in t a b l e s 3 a n d 4. I n o r d e r to m i n i m i s e t h e influence o f p o s s i b l e s y s t e m a t i c e r r o r s in a a n d / 3 , it is b e t t e r to discuss t h e difference
High energy interactions 1 43 in the exponents ~ and ft. F r o m the values of ~ and fl listed in tables 3 and 4, it is seen that the difference (fl--a) is always positive. Thus it is clear that the effective multiplicity M(i.e., the average number of y-rays in interactions) increases as a func- tion o f energy. The exact form o f this function is model dependent.* In our experi- ment as well as in those o f Malhotra et al (1965) and Bowler et al (1962), the value offl abruptly increases in the high energy region while the value o f c~ remains the same for the whole energy range. This change in the value offl occurs at energy (2-3).103 GeV.
Thus it follows that as pointed out by Malhotra et al (1965), the effective multiplicity increases more rapidly with energy in the high energy region. This suggests a possi- ble change in the mechanism of multiple particle production at high energies. This conclusion is supported by the work o f Wdowczyk and Wolfendale (1973) who found that in the energy region (105--10 s) GeV, the multiplicity varies as E ~/~ while in the low energy region it varies as E J/~ or log E.
4.2. Steepening o f the y-ray spectrum
The spectrum o f y-rays observed in the present experiment steepens at e n e r g y , ~ 2 . 2
× los GeV. The steepening o f tl~e spectrum could be explained in terms o f an in- crease o f the exponent o f the primary cosmic ray spectrum or a change in the mecha- nism o f multiparticle production at high energies. If the steepening is attributed to the corresponding steepening o f the primary cosmic ray spectrum then a similar steepening should also have been observed in the XE~, spectrum. N o such steepening was observed in the present experiment as well as in other experiments. The spectrum can be represented by a single power law for the whole energy range considered.
Moreover, the breakpoint, the point at which the spectrum steepens, should shift to lower energies with increasing atmospheric depths. Allhough a shift in the break- point towards lower energies was observed, its magnitude is not sutficient to justify the above model. The steepening o f the y-ray spectrum could also be accounted for in terms o f a change in multiparticle production at high energies. In the last section it was seen that the multiplicity o f y-rays increases rapidly in the high energy region.
This coupled with the fact that the pion inelasticity remains constant over a wide range o f energies, could account for the observed steepening o f the -/-ray spectrum.
5. Conclusions
F r o m the analysis o f atmospheric y-rays and nuclear events, we conclude as follows.
(i) The integral energy .spectrum o f y-rays in the energy range (470--4.5 × los) GeV can be represented by a power law with exponent f l = 1-88=k0-10. However, the spectrum is best fitted by a power law with exponent fl1:1.644-0.07 in tile energy range (470--2.2× l0 s) GeV and with exponent fla---3.0q-0-3 in the energy range (2.2 x 10a--4-5 × l0 s) GeV. The increase in the exponent value (steepening) is probably due to the rapid increase in the multiplicity o f particle production in the high energy region.
*For instance, Bowler el al (1962) on the basis of the statistical model had shown that M=a E m, where m = (fl-- tt) / (fl-- 1). Using the values of/~ = 1-64 ~ 0-07 and a = 1.55 _--Iv. 0.05 we found m == 0.16 d= 0"15.
(ii)
(iii) (iv)
T h e i n t e g r a l e n e r g y s p e c t r u m o f the n u c l e a r e v e n t s c a n b e r e p r e s e n t e d b y a p o w e r law w i t h e x p o n e n t - = 1 . 5 5 ~ = 0 . 0 6 in t h e e n e r g y r a n g e ( 4 7 0 - - 2 . 2 × 104) G e V .
T h e p r o d u c t i o n r a t e o f a t m o s p h e r i c ~,-rays o f e n e r g y g r e a t e r t h a n 470 G e V at t h e t o p o f t h e a t m o s p h e r e is (13-5d:1-0)-10 -9 p e r (g s t e r a d sec).
T h e p r o d u c t i o n r a t e o f n u c l e a r e v e n t s in t h e d e t e c t o r , c o n s i d e r e d t o b e a t t h e t o p o f t h e a t m o s p h e r e , o f e n e r g y g r e a t e r t h a n 470 G e V is ( 1 3 . 7 + 0 . 7 ) . 1 0 -9 p e r (g s t e r a d see).
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