2 M. KAZUNO

of the angular distribution of secondary particles, such energetic mesons might be produced via an isobar process. Meanwhile, since PETERS (~) proposed a model for the propagation process of air showers by means of successive decay of baryon isobars (,,4) the Russian group presented some experimental evidence which is favourable (5,~) to Peters' model. However, to date there is not much experimental work published which would be useful for discussing the reality and the role of energetic secondary mesons in cosmic-ray jets.

The present work aims to show further information concerning the produc- tion mechanism of energetic mesons in cosmic-ray interactions. The following Sections will deal with: a) anomalies appearing in the characteristics of jets; b) production probability of energetic secondary mesons; c) properties of ener- getic mesons expected by the isobar process and the Landau process and d) interpretation of the production mechanism of energetic mesons.

2. - Anomal ies appearing in the characteristics of Jets.

The term anomaly or large fluctuation is often brought forward as an ex- planation of the event whose characteristic features of multiple particle pro- duction do not agree with those of commonly observed jets. Main aspects of so-called anomalies appearing in the characteristics of jets may be as follows.

2'1. Inelasticity o] collision. - The inelasticity of collision, in cosmic-ray interaction, can be roughly estimated from the total energy liberated into the electromagnetic cascades, by assuming the charge independence in produc- tion of pions. That is, the inelasticity K~ ~ (3ZEv).E~ -~. This K~ should be smaller than the inelasticity estimated from all the secondary particles since the energy transfer to nonpionic particles is not taken into account. ~Tever- theless, the value of K= estimated by the above relation often turned out to be larger than unity.

For example, 7 out of 33 ICEF primary jets (7) exhibit a value of K~ larger than unity, which contradicts the conservation of energy. Although there may be some inaccuracy in the estimate of the cascade energy, the values K . ~ 1.0 imply that K= is approximately equal to unity. By adjusting these values (K=~ 1.0) to K~----1, the differential distribution of the values of Ku

(2) B. PETERS: Journ. Phys. Soc. JaTan, 17, Suppl. A-III, 522 (1962). (a) B. PETERS: CERN, 66-22. (4) y. PAL and B. PETERS: Mat. ~ys. ~fedd. Dan. Vid. Selsk., 33, No. 15 (1964). (5) N. G~r and V. S~ESTOPER0V: Proc. Int. Con]. Cosmic Rays, Jaipur,

vol. 5 (1963), p. 268. (6) N. DOBROTIN, N. ZELEVINSKAYA, K. KOTELINIKOV, V. ~{AXIMENKO, V. PUCtIKOV,

S. SLXVATINSKu and I. FETISOV: Proc. Int. Con]. Cosmic t~ays, Jaipur, vol. 5 (1963), p. 79. (7) K. IMAEDA and 3i. KAZUNO: Suppl. ~Vuovo Cimento, 1, 1197 (1963).

2 M. KAZUNO

of the angular distribution of secondary particles, such energetic mesons might be produced via an isobar process. Meanwhile, since PETERS (~) proposed a model for the propagation process of air showers by means of successive decay of baryon isobars (,,4) the Russian group presented some experimental evidence which is favourable (5,~) to Peters' model. However, to date there is not much experimental work published which would be useful for discussing the reality and the role of energetic secondary mesons in cosmic-ray jets.

The present work aims to show further information concerning the produc- tion mechanism of energetic mesons in cosmic-ray interactions. The following Sections will deal with: a) anomalies appearing in the characteristics of jets; b) production probability of energetic secondary mesons; c) properties of ener- getic mesons expected by the isobar process and the Landau process and d) interpretation of the production mechanism of energetic mesons.

2. - Anomal ies appearing in the characteristics of Jets.

The term anomaly or large fluctuation is often brought forward as an ex- planation of the event whose characteristic features of multiple particle pro- duction do not agree with those of commonly observed jets. Main aspects of so-called anomalies appearing in the characteristics of jets may be as follows.

2'1. Inelasticity o] collision. - The inelasticity of collision, in cosmic-ray interaction, can be roughly estimated from the total energy liberated into the electromagnetic cascades, by assuming the charge independence in produc- tion of pions. That is, the inelasticity K~ ~ (3ZEv).E~ -~. This K~ should be smaller than the inelasticity estimated from all the secondary particles since the energy transfer to nonpionic particles is not taken into account. ~Tever- theless, the value of K= estimated by the above relation often turned out to be larger than unity.

For example, 7 out of 33 ICEF primary jets (7) exhibit a value of K~ larger than unity, which contradicts the conservation of energy. Although there may be some inaccuracy in the estimate of the cascade energy, the values K . ~ 1.0 imply that K= is approximately equal to unity. By adjusting these values (K=~ 1.0) to K~----1, the differential distribution of the values of Ku

(2) B. PETERS: Journ. Phys. Soc. JaTan, 17, Suppl. A-III, 522 (1962). (a) B. PETERS: CERN, 66-22. (4) y. PAL and B. PETERS: Mat. ~ys. ~fedd. Dan. Vid. Selsk., 33, No. 15 (1964). (5) N. G~r and V. S~ESTOPER0V: Proc. Int. Con]. Cosmic Rays, Jaipur,

vol. 5 (1963), p. 268. (6) N. DOBROTIN, N. ZELEVINSKAYA, K. KOTELINIKOV, V. ~{AXIMENKO, V. PUCtIKOV,

S. SLXVATINSKu and I. FETISOV: Proc. Int. Con]. Cosmic t~ays, Jaipur, vol. 5 (1963), p. 79. (7) K. IMAEDA and 3i. KAZUNO: Suppl. ~Vuovo Cimento, 1, 1197 (1963).

I S O B A R P R O C E S S A N D L A N D A U P R O C E S S I N C O S M I C - R A Y JILTS 3

-o

for the 33 jets was obtained, and is shown in Fig. 1. As seen in Fig. 1, the dis tr ibut ion of the values of K= is roughly divided into two groups. One group

consists of ~ of the events with an average ( K = ) = 0.]7, while the other group

consists of the events with <K=> =

lo = 0 . 9 7 . I f the events having a

- - larg'e K= are a t t r i bu ted to eentral collision s, the f requency of occurrence

of such collisions is too large com-

pared with t ha t expeeted from their ,deome~rieal cross-section.

0 0.5 1.0 K

Fig. 1. - Fract ion of the pr imary energy transferred to secondary pions (K=) in

the ICEF pr imary jets.

Similar evidence to the above

h a s bee]] presented b y GRIGOROV

el, al. if), who employed a large ionization chamber in a nmunta in

exposure (3200 m above sea level). The experime]l t has shown tha t the e~ler~'y t ransfer into secondary ~o

mesons, in the bursts produced by sfllgle char~ed nuclear act ive par~i-

cles of the )',7> 1.3.1(P -~ eV, is of two types as show:a in Fi F. 2. Ea l f of

F I0~

-t

r

r-

o 0.5

L i__ i

1.0

Fig. 2. - Fraction of the primary energy transferred to secondary ~o mesons (K=o) in the bm'sts of Ep> 1.3-101-~ eV, (see

ref. (s)).

the ( v e n t s fell into a group which has a m a x i m u m at K~0~0 . ] , and the rest fell into a~H)ther group with a m a x i n m m

at K,o,-~0.8, where K=o is the fraetion of the p r i m a r y enerRT l iberated into oifly secondary 7~ ~ mesons a t an intvraetim).

2"2. M e a n energy of secondary part ic les . - F r o m the numerous exper iments

in the accelerator e~lel~y region, it. is k, mwn tha t the l)imm p1 oduer by nucleon-

(8) H. BABAYAN, No BE3"ADJAN, YA. B.4.BECIII, Z. BUJA, N. GRIGOROV, J. LSKIEWICZ, J. MASSALSKI~ A. OLES, C. TRETYAKOVA and V. SCHESTOPEROV: Journ. Phys. Soc. Japan, 17, ,.quppL A-III , 383 (1962).

4 M, KAZUN0

nucleon interact ions have an energy, on the average, of 0.4 GeV in the c.nl.s.

On the other hand, for cosmic-ray interact ions, the mean energy of secondary

pions in the e.m.s, is ( 0 . 5 ~ 1 . 0 ) G e V , and a t mos t .4bout a few GeV (9) for in teract ions of ~ 10 ~5 eV.

However in some interact ions, a few pions of ve ry high c.m.s, energy are produc<~d (e .g . )25 GeV (~o)) and the energy of such a pion is somet imes com-

parable with the p r i m a r y energy. The occurence of such high-energy secondary

pions m a y also be seen in the I C E F jets. F igure 3 (~) shows the dis t r ibut ion

of the energies of secondary part icles in units of the fract ion of p r i m a r y energy.

The events in Fig. 3 involve 78 secondary jets f rom the 21 p r i m a r y jets of

3O

2O u)

0 0.1 0.2 0.3 0.4 0.5 0.6

Fig. 3. - Distribution of the fractional energy carried by individual secondary particles in the 1.s. Data obtained from the singly charged primary jets with hrh~< 5 and 7c >~ 19

in the ICEF stack.

2gh< 5 in the I C E F stack. These p r i m a r y jets have been scanned for secondary

part icles for more thun one in te rac t ion m.f.p. Thus the energies of the second-

a ry part icles could be es t imated b y the i r interact ions. As seen f rom Fig. 3

the grea t ma jo r i ty of the secondary part icles received an e n e r g y < 2 % of the

p r i m a r y energy (similar results have been repor ted b y others (~.6)). There-

fore, i t seems unlikely t ha t tile part icles which received an energy more than

(9) p. FOWLER and D. PERKINS: Proc. Roy. Soc. Zondon, A 278, 401 (1964). (lo) l~I. TEVCI~ER, E. LOHRMANN, D. ttASKI~ and M. ScHEIN: Phys. Rev. Lett., 2,

313 (1959). (11) M. KAZUNO: Nuovo Cimento, 47 A, 73 (1967).

ISOBAR PROCESS AND LANDAU PROCESS IN COSMIC-RAY J E T S 5

2 0 % of the p r i m a r y energy are due to the pionizat ion process. These high-

energy secondary particles m a y be ei ther persis t ing p r i m a r y particles or par-

ticles produced by a different process than the pionizat ion process.

To examine the l a t t e r possibility, i t is be t t e r to consider the energies of

~~ since the r~ ~ mesons are obviously not pers is t ing p r i m a r y particles.

Table I depicts the events in each of which a r:~ carries ~ 2 0 % of the

p r i m a r y energy.

TABLE I. - The ]faction el primary energy carried by a secondary rz~ in the ICEF primary lets (1~).

No.

2 32 50

313 347

Type

5 + 3@ 1 + 23p 1 -~ 14p O+ 13p O+ 7p

E, (TeV) E~.(TeV)

13.6 4.8 4.8 1.7 0.69 0.6 2.9 ] .4 2.7 0.7

Fraction

0.35 0.35 0.87 0.48 0.26

As seen in Table I , each rc~ c~rries, on tile average,--~ 40 % of the p r i m a r y energy. The events in Table I were selected f rom the I C E F p r i m a r y

jets in which the p r i m a r y energies were reliably determined. The r~o-meson

with the highest energy in each jet was obtained by assuming tha t the r:~

carries an energy equivalent to t ha t the highest energy single cascade in a

jet in which the energies of individual cascades have been es t imated (see the

/ C E F data book ('3)). A single ~0-meson which carries ~ 40 % of the p r i m a r y energy cannot be a t t r ibu ted to the pionization process.

3. - Production probability of energetic secondary mesons.

I t is not ye t known whe ther such energetic mesons as described above are

produced via isobars and fu r the r whether an isobar is formed in every inter-

action in the cosmic-ray energy region. Therefore in this Section, the experi-

menta l product ion f requency of energetic mesons is t en ta t ive ly compared to

the product ion probabi l i ty of the decay mesons f rom a specific isobaric s ta te

which is formed f requent ly in the accelerator energy region.

(12) I.C.E.F. COLLAI~ORATION PAPER: Suppl. Nuovo Cimento, i , 1039 (1953). (1~) I.C.E.F. data, book: Published by Chicago University (1963) and available

from the University.

6 ~. KAZUNO

In cosmic-ray interaction, it is reasonable to assume tha t a major i ty of

isobars may be nucleonic since the product ion of hyperonic isobars from

nucleonic pr imary particles seems less frequent (< 0.2 (~)).

3"1. I n the case of incident isobars. - By an incident isobar, we mean tha t

the isobar which is formed by an incoming particle in the 1.s. a t a collision.

Therefore a target isobar refers to an isobar which is formed by a target par-

ticIe in the same system.

I f the energetic ~0 mesons involved in the events appearing in Fig. 1 should

be considered to be the decay 7:0 mesons of incident isobars, then at least 20 %

of the e~ents involved the formation of incident isobars. Similar evidence to

the above has been reported by GRmonov et al., i.e. the interactions in which

the major port ion of the p r imary energy is transferred into a few 7:0 mesons

occurred with ~ frequency of ( 1 0 ~ 2 0 ) % in an experiment on bursts (5).

These frequencies of occurence of energetic 7:0 mesons are roughly compa-

rable to the probabil i ty of yielding 7:0 mesons from the nucleonic isobars of

the I = ~, J = ~ state. Theft is, if one assumes tha t an incident particle

(usually ,~ proton in cosmic-ray p r imary jets) collides with ~ proton or neutron

with equal probabi l i ty and fur ther tha t the incident particle goes to an isobar

of various possible charge states (considering here only the ~, ~ state) while

~ssuming ~ 30 % (~4) as the frequency of single charge exchange (i.e. exchange *+ *o f l~,*++ of one charge) between colliding nucleons then the isobars W33, W~3 and ~.~3

TABLE II. - Probabilities of various decay pions from the incident isobars.

Interaction Incident isobar Target

I

p + p A n*+ + (p o r J~(~*+)

Dcc~y of incident isobar

p + n ~ (1/6) x 0.7 n +n(5/6) XO.7

Probability

0.117 0.583

p + n

Vi~ charge exchange

A ~*o +

A ~*++ +

O'~ *+ +

(p or A ~*++

(It or ~ * o )

(n or A ~*~

Via charge exchange

A ~*~ + (p or A "*+) A r'*~ + + (p or JC*-)

p+n-(1/5) x 0.3 x 0.5 n+T: ~ (4/5) X 0.3 X 0.5 p +n+(6/6) X 0.3 X 0.5

s a m e a s a b o v e

0.030 0.120 0.150

?

(14) R. DANIEL, N. DtraG~rRXS~D, P. ~ALHOTRA and B. VIJAYALA.KSt[MI: Suppl, •uoVO Cimento, l, 1169 (1963).

I S O B A R P R O C E S S A N D L A N D A U P R O C E S S I N C O S M I C R A Y J E T S 7

will occur in t h e p r o b a b i l i t i e s of 0.70, 0.15 a n d 0.15 r e s p e c t i v e l y . T h e n if each

of those i soba r s d e c a y t h r o u g h v a r i o u s d e c a y m o d e s w i th t h e b r a n c h i n g r a t i o s

g iven b y STER~HEIMER ct al. (~5), ~--24 o//o of t he deeav~ p a r t i c l e s a re e x p e c t e d

to be ~" mesons , as m a y be seen in Tab le I I .

3"2. I n the case oJ target isobars. - Tile d e c a y p a r t i c h ' s of t a r g e t i s o b a r a r e

n o t e n e r g e t i c a l l y consp icuous in t he 1.s., Mthough t h e y a r e of high e n e r g y in

t h e c .m.s . As shown in t h e p r e v i o u s ana lys i s (1.7), t h e d e c a y p a r t M e s of t a r g e t

i soba r s m a y be d e t e c t e d by m e a n s of t he cut-off m e t h o d (7). I n t he r ( f . (7),

i t is seen t h a t t h e ] C E F j e t s of Nh~<5 a n d 7, ~,5, in which p a r t i c l e s in the reg ion

of l a r s emiss ion a~lgle ~re s e p a r a t e d f rom t h e p i o n i z a t i o n p a r t i c l e s w i th a

c e r t a i n a s s u m p t i o n (7), occm ' red wi th a r a t i o of 39/151 - - 0.26 in t h e case of

one charged p a r t i c l e cut-off a n d ]3/151 = 0.09 in t h e case of a two c h a r g e d

p a r t M e cut-off. H e r e t h e s e cut-off p a r t M e s have been a s s u m e d to be d e c a y

par t i ( . les of t a r g e t i sobars .

The exl)(~cted p r o b a b i l i t i e s for t h e d e c a y of a t a r g e t i s o b a r i n to one or two

c h a r g e d p a r t i c l e s (a p r o t o n or a c h a r g e d p ion or bo th ) in t h e case of t he reso- _ kP*++ n a n t s t a t e (~, ~) a r e 0.50 a n d 0.16, p r o v i d e d t h a t t h e i soba r s . r *+, OV*~, ~'a3

a n d . ~ - occur w i t h t h e proba .h i l i t i es of 0.425, 0.425, 0.075 a n d 0.075 respec-

t i v e l y as show~l in T a b l e I I I . These p r o b a b i l i t i e s of va r i ous charge s t a t e s were

ob t ' f i ned b y a s s u m i n g t h e same cond i t i ons as in t he case of i n c i d e n t i sobars ,

r]'ABI.E l l I . -- Probabilities o/ various decay pious Jrom target isobars.

IBtt~r- action

p -f- p

p + n

Incident

(p or ,tg '*E )

Vi~ charge exchange

(p or ~ ' *~+)+ i

/ i

! (n or ~ * o ) 5 , I

(p or A "*~)

Via charge exchange

(p or A~*~+)+ (n or &-,o) +

Target isobar

2g'*o

Decay of target isobar

p + ~ ~ (1/6) • 0.7 • 0.5 n+n+(5/6) • 0.7 X 0.5

p@n-(1/5) • 0.3 x 0.5 • 0.5 n +re ~ (4/5) • 0.3 • 0.5 • 0.5 p + ,'z+(6/6) • 0.3 • 0.5 • 0.5

i . . . . .

p@~z-(1/5) x 0.7 X 0.5 nTr : ~ X 0.7 • 0.5

n § ~-(6/6) X 0.3 X 0.5 • 0.5 p + n ~ (1/6) x 0.3 • 0.5 • 0.5 n+n+(5/6) • 0.3 • 0.5 x 0.5

Proba- bi l i ty

0.058 0.292

0.015 0.060 0.075

0.070 0.280

0.075 0.013 0.062

(15) R. STERSrHEIMER and S. LINDENBAUM: Phys. Rev., 123, 333 (1961).

8 3[. KAZUNO

except for the additional assumption tha t 50 ~o of the target particles are originally neutrons. The actual f requency of occurrence of the particles sepa- ra ted by the cut-off method was about a half of the expected probabi l i ty for

the ta rge t isobar of ~, ~ states. One of the reasons for the small f requency in the exper iment is that , al-

though many different isobaric states may contr ibute, the exclusion (due to the exper imental criteria) of some of the decay particles which appeared to be slow in the 1.s., f rom the aI~gular distr ibution led to some loss in the detect ion

of the decay particles.

4. - Properties of energetic mesons expected in isobar process.

4"1. Energy o/ decay mesons. - The energy carried by a decay pion from a nucleonic isobar with the process A ~ 2 4 7 can be es t imated by the fol-

lowing relation. That is,

(1) \ ~ - / ~ , )/~v* = 2 t11.2~* '

where/~'~, and E'=, are the energies of the decay pion in the 1.s. and the isobar rest system. Therefore, for Mao.= 1236 MeV, the decay pion will carny, on tile average ~ 20 ~o of the p r imary energy and for M x . = 2360 MeV, ~ 42 %.

P]~TE~s (~6) has es t imated the proport ion of an average and a max imum energy of decay pions in the two-body process for various isobar states. I t is possible tha t even a single pion may carry more than a half of the p r imary energ3~ if the pion is emi t ted in the forwardmost direction of the 1.s.

4"2. Angular distribution oJ the decay mesons. - As shown in the previous investigation (1), the emission aI~gle of decay pions from the isobar process 2~ '* -+p '+r : ' will be dis t r ibuted around the position; logtg0jv.L = - - X • with the average angular dispersion a = 0.28 (in logarithmic units) in the 1.s., where - - X + and - - X _ are the expected positions of the incident and target

isobars on the log tg0 scale, and are expressed (~) as

(2) X+ = logTov$ = - - log t g 0 x $ ~ 2 log7~ -k log2(1 - -Kb) -k log (M/Mov.) ,

(3) X_ = logT~v, - = - - log t.gOx, - =

= log �89 {[(1 - - Ub)(M/Mx,)] -t- [(1 - - Kb)(M/Mx,) ] - ' } .

In eqs. (2) and (3), K~ is the inelast ici ty coefficient for the pionization process.

(16) B. PETERS: Proc. Int. Con]. High Energy Phys. CERN (1962), p. 623.

I S O B A R P R O C E S S A N D L A N D A U P R O C E S S I N C O S M I C - R A Y J E T S 9

Therefore, the angular distr ibution of the decay pious f rom a t a rge t isobar of

M x . = 1688 MeV will be at: - - X _ = l o g t g 0 x . - -- logtg<0=,> = - - -0 .169 if the

aver,qge inelast ic i ty for the fireball sys tem (K~} = 0.3, and a t ]og t g ( 0 ~ } = = - - 0 . 2 8 5 if <Kb> = 0.5.

In the c.m.s. , the emission angle of the decay pious m a y be es t imated direct ly b y the following relat ions:

(4)

(5)

7~.Mov. = (i - - K ~ y, M ,

. , sin 0~, 0 f=, yx* tg O,v = (fi~,./fl~,) + cos 0~, ~ tg -:~ ,

where ' refers to the isobar rest sys tem and * refers to the e.m.s.

I f one assumes the isotropic angular dis t r ibut ion of the decay pious in the isobar rest system, the average angle of the decay pious f rom all the known

nucleonic isobars (say between 2840 MeV and ]236 MeV) which decay into

the ground state, will be a t (0",> = 10.0 ~ for tile interact ion of Ep = ]0 ~ eV with K ~ = 0.5. The value of (0",> is obta ined f rom eqs. (4) and (5) 1 0 . - - v ~ \ . . . . . . L \x\ by inser t ing the average values of i ~ ~! ~ - . . . . a~

(M/Mov,> = 0.560 and <0~,} = 90~ ! \ \ ~ , ~ ~:~ .~ c) When one considers the transi t ions of i ~ x~_~ ~ isobars into various in te rmedia te , \\~\ states, then the value ( M / M v . } = 1o F ' , \ \ \\\x

= 0.675 m a y be applied. The relation ~ ~ "' \ ~:\~\ ' , \ o \ x~x (0",> VS. E, for various types of in- ~ ~7 \ \ ~ x~ teract ion are shown in Fig. 4. ~ ~ \ , ~ o \ \

10 c _. \ \ xx \ \ \ \ \ \ \

\ \ \ \ \ \ Fig. 4 . - Emission angle, <0",> in the \ X 6 ' \ c.m.s., of energetic pions from the isobar 0.2 . . . . . . ~. \ \\\\\ \ \ \ \ \ \

X \ \ \ \ k p r o c e s s and t h e L a n d a u p r o c e s s , eal- \ ~ ~ x x x X ' euhted from eqs. (5) and (7). o Prc- 10-" . . . . . . . . . . . . % ~ ~ sent experiment. - - Landau process. 10 lO ]o lO

- - - - - - Isobar process. E (eV) a) Kb=0.5 , <M/Mx. > =0.56, <0~,> =90~ b) Kb=0.5, <M/Mx.> =0.68, <0~,>=90~ c) Kb=0.1 , <M/M\.> =0.56, <0~',> =90~ b) Kb=0.1 , <M/M\.> =0.68, <0~,>=90~

e) K b = 0.5, <M/Mov,>= 0.68, <0~, : 10~

5 . - P r o p e r t i e s o f e n e r g e t i c m e s o n s e x p e c t e d in t h e L a n d a u p r o c e s s .

By tlfis, the proper t ies and the product ion mechanism of energetic secondary mesons were inves t igated main ly in comparison with the isobar process. In

10 ~f. KAZUNO

this Section, the propert ies of energetic mesons will be studied by comparing to those expected in the Landau theory for the multiple particle format ion ( ' ) .

5"1. Energy o/ mesons. - R~cently, GEtCASIMOVA (is} repor ted the possi-

bil i ty of the product ion of ve ry energetic secondary mesons, which will fly away in the backward hemisphere o~ the

0.6

0.4

0.2

0 1010 1012 1014 10 m I0 m 1020

E(eV)

Fig. 5. - Fraction (F) of the primary energy (Ep, in the 1.s.) carried by a pion from the progressive wave, cal-

culated by eq. (6).

of the p r imary energy. t ion is expressed as (~9)

1.s., on the basis of the Landau theory. In Landau~s theory, energetic mesons m a y be produced as a result of the format ion

of a progressive wave (~9) (i.e. a shock wave), the role of which was not dis-

cussed in the original theory of Landau. The propert ies of the progressive w:tve have been investigated separately b y GERASIMOVA et a~. (19) (hereaft(r , the phe- nomenon concerning the progressive wave will be called the Landau process).

According to the investigation made by GERASIMOVA et al., the progressive wave

c,~rries a large fract ion F (e.g. ~ 4 0 % ) In the c~se of a nucleon-nucleon collision, the frac-

(6) F = 0.79(Ep/#c2) - ln5 ,

where E , is the p r imary energy in the 1.s. and #c 2 is a pion mass. Equa t ion (6) gives F - - 0 . 4 4 at E~- -1012eV and F = 0 . 2 0 at E ~ 1 0 l~eV. The relat ion between F and E , is shown in Fig. 5. F rom the en t ropy and the t empera tu re of the progressive wave, one part icle (probably a pion) is expected (19) in the

wave, irrespective of the pr imary energy. ]f this is the case, one pion m ay carry :~way ,~ 44 ~() of the p r imary energy at E , ---- 10 ~ eV. This indeed agrees with the exper imental results shown in Subsect. 2"2. The fractional energy F

carried by the pions which are emi t ted in the backward hemisphere of the 1.s.

(assuming them as the decay pions from target isobars) in 5 jets (:o) is also

compared with tha t expected in eq. (6) and displayed in Table IV.

(17) L. LANDAU: IZV. Akad, Nauk, SSSR, 17, 51 (1953). (is) N. GERASIMOVA: Proc. Int . Con]. Cosmic Rays, vol. 2 (London, 1965),

p. 914. (19) N. GERASIMOVA and D. CHERNAVSKY: ~,urn. ~ksp. Teor. Fiz., 29, 372

(1955).

I S O B A R P R O C E S S A N D L A N D A U P R O C E S S I N C O S M I C - R A Y J E T S I I

TABLE IV. - The compariso~t o] the energy and the emission angle o] the backward pions with the predictio~s oJ the Landau process.

Type

0+1+22/) 0 + l + I 2 p 1 + 0 + 12~t l + l + 2 1 p 0 + l + 1 7 p

y~ M (GeV)

6.65 8.35

16.3 19.1 49.0

Charge of ~'

Fraction F Emission * angle 0", (degrees)

E r : ,

(GeV)

I !

+ , 1.48 + o r - I 2.74 + e r - - ! 4.69

, I 7- 4.40 + 1 15.8

Experi- Lund,~u men~

0.22 O.52 0.33 0.50 0.29 0.47 0.23 0.45 0.32 0.40

Experi- Landau ment

4.3 6.4 3.2 4.3 2.0 3.4 2.0 2.6 0.4 1.3

5"2. Emiss ion angle o/ energetic mesons. - The emission angle 0", in the e.m.s, of the pion f rom the progressive wave is

(7) < 0 ~ , > - p' - ~'~ p*l Fy~ M '

since the pion carries a fract ion F of the p r i m a r y energy. Assuming * \

Pt = 0.4 GeV/c, the theoret ical values of (0~,2 for the pions f rom the wave,

for various E~, was calculated and is shown in Fig. 4. The expected values

of (0",> of pions f rom the progressive wave were also compared with those

of the backward pions (~o) as shown in Table IV. The exper imenta l values of F and <0",> of the backward pions are not inconsis tent with those of the

Landau process a l though the exper imenta l values are sys temat ica l ly smaller than those expected f rom the Landau process. The reasons will be discussed in Subsect. 6"3.

5"3. Charge ratios o] energetic mesons. - In tile L'~ndau process in te rpre ted by GERASIMOVA et al. (19), it is not l ikely tha t the product ion of two or three

energetic p a r t M e s f rom tile progressive wave take place, as the critical tem-

pera tm'e ( k T c ~ t t c 2) and the en t ropy (S = ~(E~/ttc2) -~') of the wave allow the

product ion of only about one part icle of pion mass. I f it is so, then the neutra l

pions would appea r with ~ 3 3 ~ of the probabil i ty . This gives ~ slightly

higher f requency than tha t obtained in the present exper iment (i.e. ~ 2 0 % ) .

(20) K. IMAED~t, M. KAZUNO, L. PEAK and R. WOOLCOTT: NUOVO Cimento, 43, 206 (1966).

12 M. KAZUNO

6 . - D i s c u s s i o n .

In the present work, the na ture and the cause of the large variat ions on the propert ies of multiple-meson product ion process were invest igated with a viewpoint tha t an additional product ion process (other than the pionization process) which creates very-high-energy mesons, plays a competi t ive role with the pionization process at a certain type and a certain p r imary energy of interaction.

The general knowledge from the previous experiments, the average prop- erties of multiple-particle product ion mechanism are characterized in the

phenomena of ra ther low-energy hydrodynamic thermal equilibrium system, from which mesons are emi t ted isotropically with a moderate energy. This feature seems correct for many events and is well in terpre ted by the two- fireball model. However, the fact tha t a product ion of ve ry energetic pions, or emission of such pions in the backward hemisphere of the 1.s. are out of the concepts of this fireball model.

Therefore the na ture and the product ion mechanism of such energetic pions were investigated by comparing them with the isobar process and the L a n d a u process which allow the product ion of energetic pions.

6"1. Energy trans/er to energetic pions. - As shown in Subsect. 2"2 and 5"],

the exper iment showed tha t the energy carried by a single pion often exceeds the p r imary energy by more than 20 ~o whereas the average secondary pions carry only an order of ~ 1 ~o of the p r imary energy. Via the isobar process, a decay pion is expected to carry, on average, (20--40)~o or more of the pri- mary energy, according to the mass of isobar produced (see Subsect. 4"1). Also in the Landau process, a pion produced through the progressive wave is expected to carry about 40% of the p r imary energy at E~ ~ 1012 eV and

20~o at E~ = 1016 eV regions (see cq. (6)). An expected difference between the two processes is tha t the Landau pro-

cess predicts a decrease of the energy-transfer to the pions produced via the wave (see Fig. 5) with increase of p r imary energy, whereas the isobar process

seems to give an increase (is) of the energy-transfer to decay pions as the pri-

mary energy increases if the product ion of heavie risobars becomes more

f requent in the higher-energy region. However this m ay not occur since a

heavy isobar tends to decay into many particles.

6"2. Charge ratios o] energetic pions. - In the Landau process, the charge ratios of pions produced via the progressive wave is simply assumed to be a ma t t e r of statistical process. Tha t is, the product ion of ~+:~:-:~o would be 1 :1 :1 . On the other hand, the isobar process gives various proport ions of charge

ISOBAI~ PROCESS AND LANDAU PROCESS IN COSMIC-RAY J E T S l ~

rat ios for de~.ay pious according to the kind and the decay mode of isobars.

As shown in Sect. 3, ~+:~- :~0 would appear with the rat ios of 0.73:0.03:0.24

in the ease of incident isobar (see Table I I ) and 0.43:0.16:0.41 in the case of t a rge t isobar (see Table I I I ) . These ratios have been ob[ained for the isobar

s ta te I = ~, J = ~- with the assumpt ions given in Subseet. 3"1 and 3"2. As men- t ioned in Subsect. 3"1, the energetic neutral st, condary pions have been ob- served with a f requency of ~ 2 0 % . Fur the rmore , in the exper iment on the

backward pious (see Table IV) three in five jets exhibi ted the posi t ively charged energetic secondary pious, while the charges of the energetic pious in the

remaining two jets are e i ther posit ive or negative. These eharge ratios are

ra ther eonsistent with those expected in the isobar process.

6"3. Angular distribution o] energetic pious. - In the Landau process, the

emission angle of energetie pious f rom the progressive wave is given only as

a function of the p r i m a r y energy (see eq. (7)). However , the angular distribu-

t ion of pious produced through the isobar process cannot be given uniquely since it depends on various factors such as the inelast ici ty of the interaction, the mass of the isobar and its decay mode (see Subsect. 4"2).

The curves for the isobar process shown in Fig. 4 are obta ined by eqs. (4)

and (5) with the assumpt ions (M/M~+.} = 0.56 and 0.68, (Kb} = 0.1 and 0.5

and (0'=,} = 90 ~ The emission angles of pio~ls f rom the isobar process are, as a whole, larger than those expected in the Landau process.

The emission angles of the energetic pions in the exper iment (~o) seen in

Fig. ~ appear in d isagreement with those expected in the isobar process. How-

ever, these exper imenta l points c'in still be explained by the isobar process, because the observat ion of pious in the exper iment has been confined to only the ex t reme backward angular region of the isobar rest system. I f the emission a.ng'les of pious a t the isobar rest sys tem are confined to within 160 ~ 0'=, < 180 ~ then the e.m.s, ano'les of these decay pious will be smaller than those for the

Landau process (e.g. (0",} = 2 ~ at E~ = ]0 u eV), as can be seen in Fig. 4. Oil the other hand, the curve for the Landau process m a y be shifted

toward a smaller angle if the values of pt of the backward pious obtained in the exper iment (i.e. <0.2 GeV/e (:0)) are applied instead of the value

pt = 0.4 GeV/c. When pt = 0.2 GeV/c is taken, the curve for the Landau pro- cess comes to the r ight across the exper imenta l points.

7 . - C o n c l u s i o n s .

Owing to the small sample in the present exper imenta l data , the produc-

t ion mechanism of energetic pious ill cosmic-ray interact ions can be inter-

pre ted by ei ther the Landau process or the isobar process. However , it is obvious tha t the fireball process cannot explain this product ion mechanism.

14 ~I. KAZUNO

The conclusions which are d r awn f rom the p resen t inves t iga t ion , are t h a t :

i) The f rac t iona l ene rgy of the p r i m a r y t r ans fe r red in to energet ic pions

in the e x p e r i m e n t is, on average, 40 ~o at ( E , ) = 5-:10 ~ eV, while the L a n d a u

process gives 38 ~o (see Subsect . 5"1) for the same p r i m a r y energy. The isobar

process gives the f rac t ion as 22 ~o if the average isobar mass is ( M j ~ . ) =

= 1236 MeV and 4 4 % if (Mo~o.)= 2360 MeV (see Subseet . 4"1).

ii) The charge rat ios of such energe t ic secondary pions seem in agree-

m e n t wi th those expec ted in the isobar process (see Subsect . 6"2).

iii) The angu la r d i s t r ibu t ion of these pions, observed in the p resen t

exper imen t , can be i n t e rp re t ed b y e i ther the isobar process or the L a n d a u

process.

F r o m the above evidence, t he isobar process is r a the r favourab le to ex-

pla in the p roduc t ion of energet ic secondary pions in cosmic- ray jets. A fur-

t he r a ccumula t i on of da t a will ~llow a more deta i led a rgumen t .

The au tho r wishes to t h a n k Prof . C. O~CEALLAIGH for m u c h e n c o u r a g e m e n t

and Prof . K. I3IAEDA for useful discussions.

R I A S S U N T O (*)

Si studiano le proprieth ed il mecc~nismo di produzione dei pioni secondari molto energetici, osservati nei getti di raggi cosmici, confrontandoli con quelli previsti nel processo isobarico e nel processo di Landau. La frequenza di produzione nell'esperi- mento dei mesoni n o energetiei secondari ~ in accordo con quella prevista nel processo isobarico. Si potrebbero spiegare con entrambi i processi precedenti le energie di questi pioni energetiei e la loro distribuzione angolare. I rapporti di carica di tall pioni nel- l'esperimento sono piuttosto favorevoli ~1 processo isobarico.

(*) T r a d u z i o n e a cura del la Redaz ione .

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