Fortschritte der Physik / Progress of Physics: Band 14, Heft 6 1966 [Reprint 2021 ed.] 9783112500323, 9783112500316

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FORTSCHRITTE DER PHYSIK H E R A U S G E G E B E N IM AUFTRAGE D E R PHYSIKALISCHEN GESELLSCHAFT IN D E R DEUTSCHEN DEMOKRATISCHEN R E P U B L I K VON F. KASCHLUHN, A. LÖSCHE, R. RITSCHL UND R. ROMPE

A K A D E M I E

-

V E R

L A G

•

B E R L I N

I N H A L T

Y. S. BARASHENKOV, V. M. MALTSEY, I. PATERA, V. D. TONEEV: Inelastic Interactions of Particles at H i g h Energies

357

H A N S \Y. W I T T E R N : Disintegration leichter Atomkerne im CoulombfeUl

401

Die „ F O R T S C H R I T T E D E R P H Y S I K " sind durch den Buchhandel zu beziehen. Falls keine Bezugsmöglichkeit durch eine B u c h h a n d l u n g vorhanden ist, wenden Sie sich b i t t e in der Deutschen Demokratischen Republik an den A K A D E M I E - Y E R L A G ,

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Fortschritte der Physik 14, 357-399 (1966)

Inelastic Interactions of Particles at High Energies I. (The Composition and Multiplicity of Secondary Particles) Y . S . BABASHENKOV, V . M . MALTSEV, I . P A T E R A * ) , V . D . T O N E E V

Joint Institute for Nuclear Research, Laboratory of Theoretical

Physics

I. Introduction At present there are already many experimental data on the inelastic interactions of elementary particles. An analysis of the data allows one to draw some important and quite definite conclusions about the character of high-energy inelastic processes or, in other words, about the properties of interactions occuring in small space-time regions. This is important especially as at present we have no consistent theory of strong interactions and all theoretical assumptions a t high energies are of a model semiphenomenological character. At the same time there is, as yet, not a paper where the available experimental information would be collected and reviewed. The aim of the present paper is to collect and analyse not using any preconceived theoretical models the results of many experiments in high-energy region T S: GeV 1 ) when the de Broglie wave lenght becomes smaller t h a n the geometrical size of colliding particles and effects related to the intrinsic structure of elementary particles are essential 2 ). A special case is the antinucleon annihilation. Many fast secondary particles can be produced in this case even at very low energy, of an incident antinucleon. The antinucleon annihilation is therefore very similar to high energy inelasticinteractions. The corresponding experimental data will be further considered for all energies starting with the lowest ones T ~ 0. Of a large experimental material we choose merely some main characteristics of inelastic interactions. Such are, first, I. The distribution of inelastic interactions over the multiplicity of particles produced; the composition of secondary particles. Of great significance, in this case, are the probabilities of three particle reactions (for example, p + p *) Permanent address: Institute of Physics, Prague. Here and in what follows T is the kinetic energy of an incident particle in the laboratory system. 2 ) The preliminary version of the present review was published as a JINR preprint [J]. However, for the last one year and a half the situation in several points has been markedly changed due to more exact experimental data. We are extremely grateful to all physicists who sent us their remarks and new experimental results. 27

Zeitschrift „Fortschritte der Physlk", Heft 6

358

V . S . BARASHENKOV, V . M . MALTSEV, I . PATERA, V . D . T O N E E V

p + n + 7T+ or it + p n + 7t+ + which are the simplest tool of testing different theoretical schemes and models 3 ). I I . The energy and momentum distributions of the particles produced, in particular the value of their transverse factor. I I I . The angular distributions of secondary particles in the center-of-mass system. In the present review we discuss only the first part of these characteristics. The other characteristics will be discussed in two further reviews. The experimental total cross sections (Tln for inelastic processes and their theoretical analysis are given in our other paper [4]. A particular case of inelastic reaction is the charge exchange and spin flip elastic scattering and also "elastic scattering via an inelastic channel" (for definition and detailed discussion of the corresponding cross sections 28 20.8 ± 2.5 PF-BC [41] 12.3 ± 1.9 P-BC [42] -4.8 - 2.4 C [30]

H - B C [43] H - B C [43] H - B C [44] H - B C [43] H - B C [44] H - B C [44] C [30] H-BC [45] 4) P F - B C [41]

95

+

91 ± 1 1 . 4 91 ± 1 1 . 8 90.9 ± 7.2 81 ± 1 2 . 1 77 ± 6.5 70.5 ± 6 74 ± 6 1 ) 1 5 . 6 ± 2.4 20.4 ± 4.7

1.6 ±

0.2

2.8 ±

2

22.0 ±

>22.6 ± 17.2 ±

2.6

3.0 4.3

The value W3 was determined from W3 = (trin — j n ; the cross section 3 must behaves as a curve with a peak. The decrease of values of fF4 at T > 5 GeV is also due to this fact. It is that shape that the curve W^T) has in the case of •k — N interactions, though the position of its maximum determined by the condition W^T) ^ [100 - Wa(T) - W6{T)] is not very exact. The larger n, the higher energies at which the peak should be occured in W„ (T). If with T > 1 GeV partial channels have no resonances, the energy dependence Wn(T) should be determined in general by the relation of the relevant phase volumes. In fact, this is just the main content of the Fermi statistical theory [46, 47]. Table 3 p — p Interaction

T

[GeV]

Numb er of charge particles n

Method

2

4

6

10

8

0.81 0.925 0.97 0.97 1.5 1.5 2

H-DC [IS] 100 Em [14] 100 H-DC [JS] 100 H-BC [19] 2:99.9 ^0.1 H-DC [20] 96.7 ± 1.8 3.3 ± 1 . 8 1 H-BC [21] ) 93 ± 1.1 7 ± 1 . 1 H-BC 88.9 ± 1.7 11.1 ± 0 . 6

2.7 2.75 2.85 3 3.5 4.15 5.3 6.2 6.2 8.7 9 9 9 9 9

Em [25] H-DC [20] H-BC [26] Em [27] Em [48] Em [49] H-DC [50] Em [5/] Em [52] Em[S] Em [7, 53] Em [54] Em [55] Em [56] Em [57]

79 ± 4.1 82.3 ± 3.1 82.1 ± 3.4 8 1 . 3 ± 4.1 74 ± 8.9 58 ± 8.5 45.4 ± 8.7 32.2 ± 2 0 . 3 63.6 ± 10.5 45.3 ± 5.2 35.1 ± 7.7 44.7 ± 6.1 44.8 ± 4.2 46.6 ± 5.4 43.3 ± 1.1

21 ± 4 . 1 17.7 ± 3 . 1 17.8 ± 0 . 9 18.7 ± 4 . 1 24.2 ± 4 . 3 41 ± 6.4 48.5 ± 8.7 53.8 ± 1 0 . 6 33.4 ± 1 4 . 2 44.7 ± 5.1 46 ± 8.1 48 ± 6.2 42.2 ± 4.1 44.7 ± 5.3 46.7 ± 1:0

1.8 ± 0 . 9 0.7 ± 0 . 4 6.1 ± 4 . 1 11.8±2.7 ~3 8.8 ± 2 . 3 13.5 ± 5 . 6 7.3 ± 2 . 4 10.6 ± 2 . 1 8.1 ± 2 . 2 9.6 ± 4 . 3

2.4 ± 0 . 6 0.62 ± 0 . 6 2 ~0.4

14 14 18.9 18.9 22.6 24 25 25.8 27

Em [5S] Em [59] Em [60] Em [61] Em [62] H-BC [63] Em [64] Em [65] Em [66]

33.3 38.5 46.6 29 37.8 28.5 23.6 33 19.8

42.8 ± 5.2 38,5 ± 9.5 32.9 ± 1 7 41 ± 3 33 ± 6.5 42.4 ± 2.9 30 ± 8 28 ± 12.3 33.9 ± 3.4

20.8 ± 3 . 6 19.2 ± 7 . 7 12.3 ± 7 . 2 19 ± 2 19.8 ± 5 . 5 21.9 ± 2 . 4 29.1 ± 8 27 ± 12.3 28.1 ± 3.2

2.5 ± 1 . 3 0 5.4 ± 3 . 7 ±1 8 7.5 ± 3 . 8 6.2 ± 1 . 4 8.2 ± 9 . 0 10 ± 1 3 13 ± 2.4

12

[22-24]

See footnote

± 4.6 ± 9.5 ±24 ± 2 ± 6.7 ± 2.7 ± 8.2 ±11.9 ± 2.9

to Table 1.

go.i 0.3

±0.3

1.3 ± 1 . 3

0.9 ± 0 . 9

1.2 ± 0 . 8 5.4 ± 3 . 6

0.6 3.8 1.4 2 1.9 1.0 6.4 ~2 4

±0.6 ±3.8 ±1.4 ±1 ±1.9 ±0.6 ±9.3

~2.7

±2.0

1.0 ± 0 . 7

1.4 ± 1 . 4 1 ±1

364

V . S . BABASHENKOV, V . M . MALTSEV, I . PATERA, V . D . TONEEV

From the considerations of the isotopic invariance and the invariance with respect to the charge conjugation all the above data of the Tables and Figures remain constant, if P

n,

71+

7T~

(2)

are simultaneously exchanged places or p

are replaced.

p,

n - > n,

7t+

7t~

(3)

Table 4 n—n Interaction T[GeV]

Number of charge particles n

Method1) 2

H-DC [16] ) H-DC [18] H-BC {Iff] H-BC [21]2) H-BC [22-24]

0.81 0.97 0.97 1.5 2

2

4

83.9 ± 3.4 74.3 ±15.1 83.3 ± 3.5 > 7 5 ± 2.3 79.8 ± 1.7

11 16.4

±3.4 ±7.2 ±1.5 ±1.3 ±0.7

!) All the values If* given in this Table were obtained from the experimental data on p—p interactions with the aid of the isotopic invariance condition. 2) The given values are only the estimate since the considerable part of stars 30%) is not separated by partial channels.

Table 5 p—n Interaction T [GeV]

Method

8.7

Em[S]

9 9 9 14 14 18.9 18.9 25 25.8 27

Number of charge particles n 1

3

33.6 ± 5 . 5 52.7 ± 7.9 79.7 ± 1 1 . 9 Em [57] 30.6 ± 5 . 1 53.8 ± 5.0 77.5 ± 3.5 Em [55] 29.9 ± 4 . 2 46 ± 5.1 65.5 ± 7.3 74.1 ± 5.6 Em [67] Em [59] 44.5 ±11.7 Em [5S] 49.0 ± 6.2 Em [61] 15 ± 2 42 ± 3 50 ± 3 Em [60] 81 ± 1 6 Em [64] 40 ± 1 0 Em [65] 29 ± 1 4 31 ± 1 4 43.6 ± 1 2 . 8 Em [66] 33.9 ± 4.5

5

7

12.7 ± 3.3 19.1 ± 5 13 ± 5 . 7 18.8 ± 6.6 16.1 ± 3.1 22.9 ± 4.3 18.2 ± 2.8 34.5 ±11.1 27.5 ± 4.7 27 ± 2 32 ± 3 7 ± 4 23.3 ± 1 1 . 3 17 ±15.3 24 ± 15.1 41.1 ± 4.7

0.9 ± 0.9 1.2 ± 1.2 2.2 ± 6.0 3.2 ± 7.2 7.5 ± 2.1 10.7 ± 3 6.4 ± 1.6 22 ± 9.7 17.3 ± 3.7 11 ± 1 13 ± 2 9 ± 5 26.7 ± 1 1 . 1 20 ± 1 5 . 2 28.2 ± 1 4 . 2 15.2 ± 3.4

9

11

~0.4 ~0.5 0.6 ± 0 . 6 0.9 ± 0 . 9 1.3 ± 0 . 7 3.9 4 4 3 ~6.7 ~3 ~4.2 5.3

±1,8 ±1 ±1 ±3

±2.0

2.3 ± 1 . 4 1 ±1 1 ±1 ~3.3 4.5 ± 2

365

Inelastic Interactions of Particles at High Energies I. 2.2. D i s t r i b u t i o n o v e r t h e n u m b e r of s t a r - p r o n g s

The detection of neutral particles faces great experimental difficulties, so the distribution over the total number of charged and neutral particles is known in comparatively rare cases. Usually, only the distribution over the number of charged particles is measured experimentally N 1 w± = " = _ y o-«»^? (4> " n v A7 ~± ^ ") )n»n W m Table 6 p—p Interaction T [GeVl —0 0.05 (0-50.05 (0-r0.08 (0-f0.15 (00.47

0.1) 0.1) 0.23) 0.23)

Number of charge particles n

Method

0

2

4

6

Em [6S] H-BC [69]

4.0 ± 2 . 8 2.5 ± 1 . 7

64 ± 6.8 40.7 ± 5.5

30 ± 6 . 5 50.6 ± 5 . 6

2 ±2 6.2 ± 2 . 6

H-BC, D-DC [69]

3.0 ± 1 . 7

38.5 ± 4.9

53.5 ± 5

5

P-BC [70]

5.9 ± 2

40

± 4.2

49.7 ± 4 . 3

4.4 ± 1 . 7

21.7 ± 8 . 7

56.6 ± 10.4

21.7 ± 8 . 7

2.4 ± 0 . 5

36.7 ± 1.6

56.2 ± 1 . 7

4.7 ± 0 . 7

± 5.2

54.6 ± 1 . 3

8.4 ± 0 . 3

50.9 ± 1

9.1 ± 0 . 5

41.6 ± 1 . 4 10.2 ± 1 . 0

7.6 ± 4 . 1

Em [(?«] P-BC [71]

0.92

H-BC [72]

1.27 2.2 2.45 2.76

H-BC [73] H-BC [74] H-BC [75] H-BC [257]

10Î0.6 7.3 ± 0 . 5

32.4 ± 3 . 6

36

32.2 ± 0.9 37.4 ± 2.3 49.8 ± 1.8

±2.2

Table 7 p—n Interaction T[GeV]

Method

~0 0.05 (0 H- 0.1) 0.08 (0 + 0.23) 0.15 (0 -H 0.23) 0.47 0.9 0.9 (0.8 -r- 1)

Number of charge particles n 7

1

3

5

Em [6S] D-DC [69]

11.1± 5.7 7.1 ± 6.8

77.8 ± 8 71.5 ±12.1

11.1 ± 5.7 21.4 ± 1 1

P-BC [70]

22.4 ± 6.5

45 ±

7.9

30.1 ±

Em [68]

25

± 10.8

68.7 ± 1 1 . 6

6.3 ±

P-BC [72] H-BC [76]

17.6 ± 3.8 14.1

64.8 ± 4.8 54.4 ± 5.6

H-BC [77] !)

12

6 4 5

-10

7.3 6

17.6 ± 3.8 30.4 ± 4.9 2 3 5

2.5 ± 2 . 5

1.1

Î10

The given values Wf and W^1 were obtained under the assumption that W^ = 12%. The latter value follows from the statistical theory of multiple production.

366

V . S . BAKASHENKOV, V . M . MALTSEV, I . PATERA, V . D .

TONEEV

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fi «4H .2 ° SS .-a s 3 o ,n ° 1.78 >1.93 3.06 < 9 . 9 !)

4

±1

6.3

±1.51)

5.7

±0.6

8.8

±0.91)

1) Calculated under the assumption that Tip ~ ~ 0.5 and n, t ± — 2 ( s e e Table 17). In this case ri ~ 1.5 n± + 0.25. 2 ) With account of the corrections given in paper [96]. 3 ) Obtained under the assumption that the number of the produced nucleons is n N = 1 and % ± ~ 2n n ". 4 ) The given value concerns the interactions for which the inelasticity coefficient is K* > 0.5 ("the mirror coordinate system"). 5 ) Obtained, by using the isotopic invariance condition, from the experimental data on TZ~—71 interactions. At T > 3.3 GeV the values of w± are unknown, whereas for N the conditions »(ir+p) = »(7t - n) are fulfilled. 8 ) All the given values of and n are obtained by using the isotopic invariance conditions from the experimental data on n~—p interactions. Obviously, at all energies n(-K+n) = n(rc"p). 7 ) The average number of fast shower particles produced by the pion interaction with the emulsions is shown. 8 ) Strictly speaking, the given data concern the 7t~—C12 interactions. Since the main contribution to these data is given by fast shower particles one can expect that the difference from the case of -K—N interactions will not be very great.

380

Y . S . B A R A S H E N K O V , V . M . MALTSEV, I . P A T E R A , V . D . T O N E E V

approximated by the function n(T) ~

£

^(T)

+ c ~ «2"/« + b.

(6)

The values of the parameters, a, b and c are shown in Table 15. Table 15 The values of the parameters in formulae (6) and (7) Interaction

a

b

c

a'

b'

N -N N -N •k - N

3.2 4.7 3.2

0 0.55 -0.2

0.5 0 0.25

1 4.7 1

0.45 2.2

2

Formula (6) well agrees with the results of the calculations on the statistical theory of multiple particle production [13S\. The departures from this formula (both experimental and theoretical ones) are observed only in the case of N — N and n — N interactions with T < 1 GeV, where the number of newly born particles is small 1) and more detailed isotopic relations are necessary. At the same time, it should be noted that the accuracy of modern measurements is still low and the acceleration experimental data in Figs. 5—8 can be approximated also by more rapidly increasing functions, for example, + c ~ a'T 1 /,

n{T)

b'

(7)

(see Table 15). At energies T > 30 GeV, where all the experimental information has been obtained from cosmic-ray experiments, the situation is considerably less clear. In addition to great errors in the values n and w*, here the energy T is determined very inaccurately. Experimental errors are especially great in the region T > 103 GeV, in fact, here one may speak only about the order of values. From Fig. 6 it is seen that up to the energies T ~ 100 GeV the experimental data can be well approximated both by curve (6) and curve (7). At higher energies the multiplicity is increased noticeably slower, than T1!'. In a recent paper [134] from a new analysis of photoemulsion cosmic ray data by various authors the following "average world" values of the multiplicity of charged particles have been obtained: 17.1 ± 3.1 at 16.2 ± 2.1 at 15.4 ± 2.8 at

T ~ 2.8 • 103 GeV T ~ 104 GeV T ~ 1.8 • 104 GeV

for N — N interaction and 10.1 10.2 10.3 10.4 for 71 — N interactions.

± ± ± ±

2.3 1.6 2 2.4

at at at at

T T T T

~ ~ ~ ~

1.6 • 6.4 • 10* GeV 8.1 • 102 GeV 1.15

Inelastic Interactions of Particles at High Energies I.

381

On the basis of these data an extremely important conclusion on the saturation of the multiple production of particles at T ~ 2 • 103 ^ 104 GeV in N — N interactions and a t T ~ 2 • 102 -r- 103 GeV in 71 — N interactions has been obtained. However, this conclusion does not appear to be convincing enough. As has been stated above, a t 10s 104 GeV one may speak only about the order of the magnitude of the average numbers n and n ± . Besides, the data on N — N and tt — N interactions cannot be considered separately from nucleon-nuclear interactions. Since the cross section of the inelastic interactions (Tin depends upon energy very weakly (or, perhaps, remains constant up to ultrahigh energies T ~ 1010 GeV [4]) then "multiplicity saturation" should be observed _ +

h~

n

r

3 o nh > 3 o

xfS

+ UH &3in Al27ozC12, 3in emulsion.

10

* I'' 10

¿ y

1

10

102

*

103

10U

10S T

Fig. 9. The average number of charged particles produced by interactions of protons and pions with nuclei (according to the data of paper [6]) n h — is the number of black tracks in the star (slow particles are, in the main, protons). The sign TT indicates the data obtained in the analysis of interactions with the nuclei of shower particles produced in the preceding nuclear interaction. The majority of these particles are pions. (about 80%, see [I]). The dashes show the interpolation curves.

also in particle interactions with nuclei. As is seen from Fig. 9, nothing of the kind has been observed experimentally. Available experimental data on the whole energy range T > 1 GeV do not contradict relation (6). As has been discussed above (see 2.2) the average numbers n and n* are invariant with respect to transformations (2) and (3). In conclusion of this section, consider the reactions for strange particle production to the investigation of which a large number of experimental and theoretical papers has been dedicated. At energies T 1 GeV the average number of particles produced in such reactions is approximately the same as in reactions without strange particles. For example, in n ~ — p interactions at T = 16 GeV [135] n* = 4.4 ± 0.2 in reactions with strange particles n* = 4.3 ± 0.1 over all the reaction channels on the average.

382

V. S. Barashenkov, V. M. Maltsev, I. Patera, V. D. Toneev

A t smaller energies, when energy, consumed by new particle production does not differ greatly from the sum of the masses of strange particle produced, multiplicity in reactions for strange particle production is smaller than average. For instance, in u - — p interactions at T = 6.65 GeV [136\. In,± = 2.5 ± 0.1 in reactions with strange particles n* = 3.2 ;£ 0.2 on the average. A t the same time K-meson pair production is accompanied by the production of a larger number of pions than hyperon production. I n antinucleon annihilation with the energy T 5S 1 GeV the average number of particles in reactions of .strange particle production appears to be also somewhat smaller than the average number (at T = 0.47 GeV, 4.4 ± 0.5 and 4.95 ± 0.2, respectively [71]). 2.4. M u l t i p l i c i t y of p r o d u c e d p r o t o n s , n e u t r o n s a n d p i o n s From statistical considerations based on isotopic spin invariance one may expect t h a t in the channels with sufficiently large number of produced particles the multiplicity of charged pions is on the average two times larger t h a n the average multiplicity of neutral pions: nu± ~ 2nn°. If the number of produced particles n 1, then the numbers of and -nr meson also become approximately equal: 8 n n + ~ n„- ~ ). At 1 GeV when the main contribution to the cross section (Tin is given by channels with large number of produced particles all these relations are valid for the average numbers as well. From experimental data presented at Tables 16 and 17 it is seen that in the case of 7t~ — p interactions the above relations are valid a t relatively lower energies than for p — p interactions. This is due to the fact t h a t the system tt — p is, from the very beginning, symmetrical in the electric charge. I n the antinucleon annihilation the equality of the average numbers n n + ~ n n ~ n n " is well fulfilled for all energies (see Table 18). If the number of produced particles n 1, then the average numbers of produced protons and neutrons are also approximative to each others n v ~ n n I n the case of N — N interactions this relation is fulfilled much better than in the case of 7i — N interactions. From Tables 16 and 17 it is seen t h a t in the accelerating energy region a relative fraction of heavy particles produced in inelastic N — N interactions decreases more than two times: up nT\n ~ 0.7 at T ~ 1 GeV down nTjn ~ 0.3 at T ~ 25 GeV. For a further energy increase the ratio wt/w changes very slowly and at giant energies T ~ 105 106 GeV is about 0.2 [151, 152], I n the case of 7t — N interactions in the accelerating energy region the relative fraction of produced heavy particles is about two times smaller than in N — N interactions at T ~ 1 GeV this fraction is about 0.3 at T ~ 16 GeV about 0.2. For higher energies there are no experimental data at present. 8

) In the general case, obviously

%1+ + nT+ = tin- + nT- + Q where Q the summary electric charge of colliding particles, is the number of charged heavy particles (K* mesons, protons and so on). With increasing energy the relative portion of heavy particles decreases (see below).

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385

Table 18 Antinucleon annihilation at an energy T — 0.08 (0 -j- 0.23) GeV [70] (P-BC)

p-p P-n1)

1.53 ± 0 . 0 8 1.13±0.18

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The given values were calculated from the experimental data on antiproton interaction with protons and carbon : % ( ï n ) = 2i„(pC 12 ) — rârt(pp). (Errors — root-mean-square). Table 19 Cross section for the reaction p + p - > p + p + 7r° T + oo gesetzt werden. Man kann sich diese Situation auch anschaulich klar machen. Wegen der Bedingung (36) gilt Er