Mechanism of interaction of fast nucleons with nuclei

North-Holland Publishing Co., Amsterdam Nuclear Physics 24 (1961) 642--656; © without written permission from the publisher Not to be reproduced by photoprint or microfilm

MECHANISM OF INTERACTION OF FAST NUCLEONS WITH NUCLEI V. S. BARASHENKOV, V. M. MALTSEV and E. K. MIKHUL

Joint Institute for Nuclear Research, Dubna, USSR Received 1 October 1960

Abstract : The paper presents the results of the calculations of intranuclear cascades generated by a 9 GeV proton in photoemulsion nuclei . From comparing these results with the available experimental data it follows that an intranuclear cascade mechanism is operating in nucleon. nucleus collisions at E = 9 GeV just as at lower energies . What the nucleon-nucleus interaction mechanism is like at very high energies (E >> 10 GeV) - whether it is a nucleon-tube mechanism or an intranuclear cascade mechanism - is still an open question . The presentpaper is a direct continuation of ref. 1) .

l . Introduction Quite a few papers have recently been concerned with the investigation of different aspects of the interaction between 9 GeV protons and nuclei This keen interest is largely due to the two following facts: 1) From the investigation of nucleon-nucleus interactions it is possible to obtain interesting information on the elementary NN-interaction event. For example, it is possible to determine the total cross section of NN-interaction at by experimental data on the length of the fast nucleon mean free path in photoemulsion ; the investigation of the energy spectra of particles produced in nucleon-nucleus interactions furnishes information on the spectra of particles produced in NN-collisions and makes it possible to evaluate the average energy lost by the nucleon in one NN-collision event, etc . Some related questions will be considered in the next section. 2) Several authors (see for example refs. 21,22)) expressed the supposition that already at 9 or 10 GeV the "intranuclear cascade mechanism" occurring at lower energies (see ref. 23)) must be replaced by the "tube mechanism" when the primary nucleon interacts with several nucleons of the nucleus at once. At present there is no unanimous opinion on this question among physicists. Ref. 1) offers arguments against the tube model and points out that the basic experimental data do not contradict the intranuclear cascade mechanism . Yet no results of the numerical calculations of these cascades were presented t. In ref. s) it is also pointed out that the tube mechanism cannot explain all

t Lukin et al. noted 10) that the inferences of ref . 1) on the mechanism of interaction between 9 GeV protons with a nucleus are in agreement with the results of experiments on cosmic rays with an average energy E _ 100 GeV (for detail see ref. sa)) . 642

MECHANISM OF INTERACTION OF FAST NUCLEONS WITH NUCLEI

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experimental data. The authors of this investigation hold that the interaction of a 9 GeV nucleon with a nucleus has a character intermediary between the tube model and the intranuclear cascade model. Friedlander 11 ), on the contrary, holds that the tube mechanism is the basic one at E = 9 to 10 GeV. To discriminate between the two nucleon-nucleus interaction mechanisms under discussion, we performed numerical calculations for the intranuclear cascade and compared the results with experimental data. As will be shown below, the results of the calculations explain the experiments, quite well . Taking account of the objections raised in ref. 1) against the tube mechanism, we yet think it possible to claim that the intranuclear cascade mechanism occurs in the interaction of 9 GeV protons vith photoemulsion nuclei just as at lower energies . It stands to reason that we mean the interpretation of merely the chief experimental facts, such as averages of particles of different types, their energy and angular distributions . In details, of course, there may be deviations from the intranuclear cascade mechanism or at any rate from that approximate model which we considered t. 2. Gross Sections of Interaction of Fast Particles with Nucleons of Nuclei To calculate intranuclear cascades it is necessary above all to know the cross sections of interaction of 9 GeV nucleons with the nucleons of the nuclei. To determine these cross sections we shall make use of the experimental value of a mean free path in photoemulsion. Usually the cases of elastic scattering of fast particles on nuclei are not detected in the track scanning of fast particles in photoemulsion. At high energies elastic scattering is almost entirely diffractional and occurs at very small angles which are the smaller the larger the nuclei. A special technique is necessary to 15)) . detect a small curvature of tracks in elastic nuclear scattering (cf. ref. As a rule, elastic scattering on hydrogen tt occurring at comparatively large angles is only detected apart from inelastic interactions .

whole group of D . I . Blokhintsev noted that in the interaction of fast particles with nuclei a matter 24 ) . density of nuclear fluctuation in the result of a nucleus as a nucleons may leave the nucleus splinters out of the V . I . Veksler drew our attention to the fact that the expulsion of large . wave in a dense substance of a shock can also occur due to a mechanism similar to the propagation nucleon-nucleus interthese possible into account In our approximate calculations we do not take

t

action mechanisms .

very small those cases of elastic scattering on hydrogen when the particles scatter at of GeV the contribution angles are not detected either. Estimates showed that at energies E S 10 the mean free path . At the length of such undetected interactions does not change appreciably the region of small higher energies the bulk of particles elastically scattered on hydrogen gets into case in eq . (1) should be calculations (in this in at angles and this should be taken into account replaced by aria ; see below) .

tt Of course,

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AND E . K. MIKHÜL V . S . HARASHENKOV, V . M . MALTSEV

The mean free path in these cases is equal to 1 L= 1 Ni Qi, +Nx ut where NH is the number of hydrogen nuclei in 1 cm3 of photoemulsion, N{ the number of nuclei of other elements in 1 cm 3 of photoemulsion, in is the total cross section of interaction of the primary particles (pion, nucleon, K-meson, etc.) with hydrogen and aâ is the cross section of inelastic interaction of this particle with other nuclei. At high energies when the wave length of the particles interacting with photoemulsion is much less than the size of the nuclei an optical model can be applied quite well. If the elastic non-diffractional scattering is neglected, which is justified at high energies, the cross sections a;â are expressed in this case through the parameters of the nuclei (which can be taken, for example, from experiments on the scattering of fast electrons on nuclei) and through the total cross section of the interaction of a primary particle with the nucleons of a nucleus at .

Fig. 1. Dependence of the mean free path of particles in photoemulsion L on the total cross-section of the interaction of these particles with nucleons ar g . Values of L in cm are marked off on the axis of the ordinates and values of art in units 10-27 cma on the axis of the abscissa .

Fig. l lists the calculated values L = L (at) . As was shown by calculations, the difference of the paths L (at) in Inford G-5 and NIKFI-R photoemulsions is insignificant . The curve in fig. 1 is applicable to both types of emulsion - not only for nucleons but also for particles of other kinds. The applicability of the curve improves with the growth of energy.

MECHANISM OF INTERACTION OF FAST NUCLEONS WITH NUCLEI

645

In a number of cases the use of the dependence L = L (at) is the only method of determining the quantity at (cf. ref. 18 )) . The cross sections thus obtained are cross sections, averaged with respect to isobaric spin, of interaction with nucleons bound in nuclei. Yet at high energies E » EF -,v 30 MeV the binding energies in nuclei can be neglected and these cross sections prove to be very close to those for the interactions with free nucleons (cf. ref. 18 )) . In ref. 9 ) the value L < 35 .7±0.7 cm was obtained for the mean free path of a 9 GeV proton. The corresponding cross section of the NN-interaction is crt ~: (32-'. 35) x 10 -27 cm2 (see fig. 1). If the value ße1 = 8.6 x10-27 cm2 is assumed for the elastic scattering cross section in accordance with ref . 25), then crin ? (23 to 26) x10-27 cm2 . We shall select at = 35 x10-27 ß:m 2 and crin = 26 x10-27 cm2. 3. Nuclear Model and Experimental Data Used in Calculat' ~n of Intranuclear Cascade In the calculations we assumed that the nuclear properties can be described by the Fermi-Gas model. It was also assumed that the nucleons are distributed uniformly within a sphere with a radius R = r0A* (A is the atomic weight of the nucleus) t. The value ro = 1 .35 x 10 -13 cm was used for determining the value of the contant ro . In ref. 23) it was shown that the results of the calculation of the intranuclear cascade obtained within the framework of tnis model for energies E +G 2 GeV are in sufficiently good agreement with experiment. It can well be expected that the applicability of this model will improve with the growth of energy. It will be noted that at energies E > 1 GeV the concrete selection of a nuclear model has an essential effect only on the characteristics of low-energy b-particles tt and, to a certain extent, g-particles . Now, the characteristics of fast particles change little when the nuclear parameters vary widely. To simplify the problem all characteristics of nN- and NN-interactions within the nuclei are regarded as averaged over the isobaric spins of mesons and t Neglecting the diffuseness of the nuclear boundary is an approximation better suitable for

heavy than :for light nuclei . It does not introduce essential errors within the) imits of the accuracy of the photoemulsion data available at present with which the results of the calculations will be compared . Yet in other cases there may arise appreciable deviations from. experiments . We are indebted to D . I . Blikhintsev, M . G. Mesheheryakov and A . A . Tyapkin who, while discussing the results of the calculations drew our attention to the phenomena in which these deviations are observed. This problem is being studied in detail .

tt just as it was done in ref. 1 ) all particles observed after nucleon-nucleus collisions will be

divided into three types : s-, g- and b-particles . This division is justified by the fact that in photoemulsion each of these types has a characteristic type of tracks (for detail see ref. 1 )) . Table I lists the values of the energy of pious and nucleons, necessary for further discussion, for each of these three types.

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AND B . K . MIKHÜL V . S . BARASIIENKOV, V. M . MALT5EV

nucleons . As was shown by estimates, this averaging yields a satisfactory approximation . Besides, all characteristics of inelastic collisions of nucleons and mesons with the nucleons of the nucleus are regarded as averaged with respect to the events in which different numbers of particles are produced. Since we shall regard the characteristics of nucleon-nucleus collisions as also averaged with respect to the events with different numbers of particles produced, this approximation cannot introduce any appreciable distortions into the results of the calculations. TABLE 1

Pion and nucleon energy values Kinetic energy (GeV) Nucleons

(

s-particles (shower particles)

0.5 =9

g- particles (cascade particles)

0.03- 0.5

b-particles (particles with black tracks)

a-mesons 0.08 :-Tirmaz ; Tvmax rzte 8

<0 .03

0.015 =0.08 <0 .15

In the case of NN-collisions the entire region of energies was divided into five intervals ; in the case of nN-collisions four energy intervals were considered. The characteristics of elastic and inelastic NN- and xN-collisions, with the exception of the total cross sections ßt, were regarded as constant for each of these intervals and were taken from experimental investigations 26 ), both energy and angular distributions of secondary particles being taken into account The values of the total cross sections at(E) determining the path and the point of the collision of a nucleon and a pion in the nucleus were assigned with a considerably smaller pitch AE, which practically did not differ from assigning a continuous curve . Table 2 liststs the energy intervals under consideration . TABLE

Energy intervals AE (GeV) NN 9 -;-4.5 4.5-' 1 .5 1.5-1 1 .0 .5 <0.5

XN 8-, 3 3 -; 1 1 -0.5 <0 .5

MECHANISM OF INTERACTION OF FAST NUCLEONS WITH NUCLEI

647

The division of the energy interval E > 1 GeV into smaller intervals is not feasible owing to the lack of detailed experimental data. However, the contribution of particles with very high energies must be fairly small since the average energy of pions and nucleons after the first (NN)-collision En o--_ 1 GeV and En ow 3.5 GeV 19, 20 ), which is considerably less than the maximum energy E = 9 GeV. On the other hand, the division of the lower-energy region into smaller intervals can essentially affect only the results of the calculations for b-particles, since the energy of the primary proton is sufficiently high, and sparticles and a larger part of the g-particles are produced in the collisions of high-energy nucleons and pions with a nucleon of the nucleus. Yet in the most essential region E ~w 1 GeV the true characteristics of NN- and 2VN-collisions do not change considerably as compared with their averages used in the calculations. The characteristics of the first inelastic NN-collision (E = 9 GeV) were calculated by the statistical theory cif the multiple particle production with allowances for the peripheral NN-interactions on the strength of experimental . The data on the elastic investigations 19,20) and theoretical papers 17,27,28) scattering of nucleons are taken from ref. 25) . The cross sections at and Crin are determined in sect. 2. 4. Calculation Method The calculations of the intranuclear cascades were performed by the MonteCarlo method for the case of relativistic three-dimensional kinematics with allowances for multiple particle production .

Fig. 2. Scheme of calculation of intra-nuclear cascades . The meaning of individual blocks is clear from the text.

The following calculating procedure was used (see the scheme in fig. 2) 1) The coordinates of the point of the entry of the primary proton into the nucleus were randomly selected .

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V. S . BARASMENKQV, V. M . MALTSEV AND E. K . MKEUL

2) Using the value of the total cross section of the interaction of nucleons at the value of the nucleon free path in nuclear substance LN = LN(at) was randomly selected . 3) If the value LN was such that no NN-collision inside the nucleus was possible, the calculation stopped . The number of the protons Nni which have not interacted with the nucleus determines the cross section of the reaction ar .-_ xro2 AI 1-

Nni N

where Nt is the total number of the protons colliding with the nucleus. 4) If the value LN was such that NN-collision occurs inside the nucleus, the three-dimensional coordinates of the point of collision were determined and the type of NN-interaction was randomly selected as either elastic or inelastic. 5) If NN-interaction was elastic, one passed to point 2) . The number of nucleons Nel which have experienced one or several elastic collisions inside the nucleus and come out determines the cross section of the quasi-elastic interaction with the nucleus asel = .r02A*

NeI N-

(elastic scattering on the bound nucleon in the nucleus) . 6) If NN-interaction was inelastic the number of the particles produced, their energy and emission angles were randomly selected t. Then one passed to point 2) or to point 7) depending on whether the particle produced was a nucleon of a pion. 7) Using the values of the total cross section of pion-nucleon interaction at (E) the value of the pion free path in nuclear matter L,, = L (art) was randomly selected. 8) If the value L. is such that no ;rN-collision inside the nucleus was possible the calculation stopped and the piori was recorded as having left the nucleus . 9) If the value L, was such that a nN-collision inside the nucleus was possible, the three-dimensional coordinates of the points of collision were determined and the type of nN-interaction was randomly selected as elastic or inelastic. 10) If aN-interaction was elastic, one passed to point 2) or 7) depending on whether the particle was a nucleon or a pion . 11) If the .;RX-interaction was inelastic the number of particles produced, their energy and emission angles were randomly selected . Then one passed

The angular and energy distribution of the particles produced in the first NN-collision were awigned directly in the laboratory system of coordinates. For the subsequent NN- and .7cNcollisions the angular and energy distributions were taken from ref. :e) in which they are given only for the centre-of-mass system. In these cases the random selection was performed in the centre-of-mass system after which each particle was transferred to the laboratory system of coordinates.

MECHANISM OF INTERACTION OF FAST NUCLEONS WITH NUCLEI

649

either to point 2) or point 7) depending on whether the particle was a nucleon or a pion. As was mentioned in the previous section, in the calculation use was made of the characteristics of NN- and =N-interactions averaged over the values of isobaric spin. To single out charged particles in the total number of particles formed as a result of inelastic nucleon-nucleus collisions, we assumed that protons account for 50 % of all nucleons and 3 of all pions are charged. At high energies when many particles are produced this approximation is fully justified. Otherwise our calculations do not differ essentially from similar calculations performed by Metropolis et al. 23) . 5. Results of Calculations . Comparison with Experiment 5.1 . NUCLEON-NUCLEUS INTERACTION CROSS SECTIONS

Table 3 lists the values of the cross sections ar and aeel for an average light nucleus (N?4), an average heavy nucleus (Nb49.4 ) and an average nucleus (Ga31) of the NIKFI-R photoemulsion calculated by eqs. (2) and (3) . TABLE 3

Calculated cross-section values Type of nucleus Light nucleus

I

,

cr i

Orgel/ad

40± 4

0.30±0 .03

836±12

87_ 12

0.41±0 .06

1090±15

107±16

0.43±0.06

243± 5

Medium nucleus Heavy nucleus

' Orgel (102 cmz)

(l0E' CI11 2 j

I

I

'

6f

a5

50

100

150.

20

The solid line designates Fig. 3. Cross-sections of interaction of nucleons with nuclei at E = 9 GeV. cross-section the 4_-6t-and-dash line diffractional line the ?d, dashed inelastic scattering al,, the and . are 4e cross-sections al, designates an interpolationary line for the values of creel, and o given in the units of 10 -24 cm 2. are and calculated by the Monte-Carlo method . Cross-sections

creel

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V . S . BARASHENKOV, V . M . MALTSEV ANir E . K . MIKHUL

The probability of nucleon-nucleus collisions at which the energy transferred by the primary proton to a nucleon of the nucleus completely passes into the kinetic recoil energy of this nucleus must be small at high energies. If these collisions are neglected, the total cross section of inelastic processes ain - ar-Nel As is clear from fig. 3 the values ain thus obtained are very close to the curve ain = ain(A), calculated directly by an optical model (cf. sect. 2) ) . Table 3 also lists the ratios of the cross section asel to that of the diffractional scattering on the nucleus ad calculated by the optical model (cf. fig. 3). Approximately 3 of all cases of elastic scattering of a 9 GeV proton on the nucleus are elastic scattering on a bound nucleon in the nucleus. This agrees with the experimental results obtained in photoemulsion. 5.2. CHARACTERISTICS OF PARTICLES PRODUCED

Tables 4-6 and figs. 4--9 represent the available experimental data for s- and g-particles and the respective calculated quantities . Cases of diffractional scattering on nuclei are not included among nucleon-nucleus collisions, in accordance with the conditions of measurement in refs. 11, 6-10). The methodological conditions of measurements and the selection criteria for different types of nucleon-nucleus interactions as well as their analysis are different in all these investigations . Therefore direct comparison of measurements prove to be impossible, as a rule. The tables and figures indicate all results TABLE 4

Average number of particles produced in one nucleon-nucleus event Type of particles

s-particles

Group of light nuclei

Group of heavy nuclei

Exp.

I The ory (

Exp.

Theory

3.0±0.2 1)

2.9

3.5±0.3 1)

4.1

s-protons s-pions g-particles g-protons g-pions

1.4±0.1 1)

1 .5

4.1±0.5 1)

4.0

p rot. ) pions

Per average nucleus of photoemulsion (

Exp. 3.2 ±0.21) 3.7 X0.05 8) 1 .0 ±0.5 0) 0.68±0.07 7) 1 .010) 3.3 ±0.5 0) 3.8 -1-0 .3 7) 9 ) 3.110) 3.1 ±0.4 1 ) prot. 4"6 pions

Theory 3.7 0.9 2.8 3.2

") The number of a-mesons given here exceeds the number of all s-particles (see the first line of this table) and evidently is considerab' over estimates.

MECHANISM OF INTERACTION OF FAST NUCLEONS WITH NUCLEI

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TABLE 5

Average angle (in degrees) which contains half of the particles produced in the collision of a 9 GeV proton with nuclei Type of particles

(`soup of light nuclei Exp.

s-particles s-protons s-pions g-particles

Per average nucleus of photoemulsion

Group of heavy nuclei

Theory

Exp.

` Theory

22.5±1 1)

24

27.5±1 .5 1)

29

56.54-3 1)

48

65±3 1)

69

Exp.

Theory

25.0±1.5 1) --29 9) a) 36.5±8.8 11) 65±3 1)

28 22.5 30 63

8)

s) These values of angles were obtained only for stars with a number of relativistic tracks (of s-particles) tss ~; 3, a large number of narrow showers with it, < 3 being neglected. This may account for the fact that in ref. 9) larger values of 0j were obtained than in ref . 1) . TABLE 6

Average kinetic energy of particles (in GeV) produced in the collision of a 9 GeV proton with nuclei Type of particles

Group of light nuclei Exp.

Theory

Exp.

Theory

s-particles s-pions

g-protons g-pious

0.132±0 .020 1)

0.16

per average nucleus of photoemulsion

Group of heavy nuclei

,

0 .15

0.118±0 .012 1)

Exp.

` Theory

3.0 ±0.5 1 ) 3.5 ±0.5 7) a) , 0.85 -1-0.2 1) ' 0.60 ±0.18 6) 1 0.65 ±0 .2 7,9) 0.63 ± 0 .1 ") ~ 0.120-1-0.012 1) 0.040±0 .003 1)

2 .5 0. .52 0.15 0.048

s) This value is very close to the average kinetic energy of the protons produced in NN-collision .9 = 3.6+0.5 GeV. Since the spectrum ofprotons after nuclear collision should be considerably softer, the energy value obtained in ref . 7) is evidently overestimated .

50 40

40

30

30

0

20

10

10

l0

06

0.2

-02

-00

COO

10

0.6

02

-02

-06

COS0

(a) for a group of heavy Angular distributions of s-particles . a) is for a group of light nuclei,1) b) ; the dotted line is an . histograms from ref experimental designates nuclei . The dashed line experimental histogram from ref . 81) . Fig.

4.

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V . S . SARASSENKOV, V. M . MALTSEV AND E . K . MIKNUL

of measurement_-, known to us. Experimental values are given as a rule without critical appraisal . The data cited show that the experimental and theoretical characteristics of s- and g-particles are in good agreement .

9'0f 60 40 20 f0 Fig. 5. Angular distribution of s-pions produced in the interaction of 9 GeVT proton with the average nucleus of photoemulsion . The dashed line designates an experimental histogram from ref. 9).

06

02

-Q2

-R6 cmo

Fig. 6. Angular distribution of s-protons produced in the interaction of 9 GeV proton with the average nucleus of pho toemulsion . The dashed line designates an experimental histogram from ref. 9).

Fig. 7. Angular distribution of g-particles. a) is for a group of light nuclei, b) for a group of heavy nuclei . The dashed line designates an experimental histogram from ref. 1) .

The experimental data for b-particles known at present can also be interpreted in agreement with the results of the calculations of the intranuclear cascade : 1) The average experimental number of b-particles produced in a group of light nuclei of photoemulsions 1) n = 3.3±0.1 is close to the theoretical value 4 = 3.0.

MECHANISM OF INTERACTION OF FAST NUCLEONS WITH NUCLEI

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2) With allowance for the nucleons "evaporated" from the excited nucleus the experimental and theoretical numbers of particles produced in a group of heavy nuclei also prove to be nearly equal. -__-,

20 15 f0

Of

02

0.3

04

05

E

Fig. 8. Energy distribution of pions produced in the interaction of 9 GeV proton with the average nucleus of photoemulsion . The dashed line designates an experimental histogram plotted by the data of ref. 9). (Methodical conditions in this paper excluded the possibility of observing 7r-mesons with E > 0.54 GeV). Values of the kinetic energy of pions in the laboratory system of coordinates E are given in GeV.

0

tv

0.2

0.3

(a)

Of

0.2

0.3 (b)

0.4 £

Fig. 9. Energy distribution of g-particles . a) is for a group of light nuclei, b) for a group of heavy nuclei . The dashed line designates an experimental histogram from ref. 1). Values of the kinetic energy E are given in GeV.

3) The calculated pion spectrum has, in accordance with the experimental . 100 MeV. data of refs. 1, 9), a maximum in the energy region 504) The theoretical angular distributions of b-particles decrease very slowly with increasing angle 0 while the average angle which contains half of all bparticles emitted from the nucleus equals 70° to 90°. This also agrees with the results of the measurements 1 ) .

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V. S. BARASHENKOV, V . M . MALTSEV AND E . K. MIKHUL

Yet the results of the theoretical calculations of the characteristics of bparticles depend on the specific assumptions conccrning the model of the nucleus and are therefore less definite than the above-mentioned data for s- and g-particles. 5.3. PRODUCTION OF STRANGE PARTICLES

The production of K-mesons and hyperons in nucleon-nucleus collisions was studied in photoemulsion investigations ', s, 9.12,13) . The most detailed results are obtained in refs. 1, is) for K-mesons with E < 150 MeV. The results of the calculations of the intranuclear cascades for strange particles are now rather unreliable since the experimental data on the interaction of these particles with nucleons are quite insufficient . This especially applies to the interaction of hyperons . In calculations use has to be made of the angular

fo t 40 20

v I

i L_

_~7 -1 __-! I I

v I

0

Fig. 10. Angular distribution of K+-mesons with kinetic energy E S 150 MeV produced in the interaction of 9 GeV proton with the average nucleus of photoemulsion. The dashed line designates an experimental histogram from ref. is) .

I

,30 60 90 120 E

Fig. 11. Energy distribution of K+-mesons with kinetic energy E S 150 MeV produced in the interaction of 9 GeV proton with the average nucleus of photoemulsion. Thedashed line designates an experimental histogram from ref. 18) .

and energy distributions calculated by the statistical theory of multiple production . It is totally unknown, however, how well these distributions agree with experiments. Therefore at present we can refer only to very rough qualitative results of the calculations of intranuclear cascades with the participation of strange particles. Since K-mesons are produced already inside the nucleus and the cross section of their interaction with nucleons is less than the cross-sections of NN- and =N-interactions, K-mesons should on the average undergo a smaller number of interactions in the nucleus than nucleons or pions. Besides, since the probability of K-meson production rapidly decreases with the decrease of energy of colliding particles, the characteristics of K-mesons, should, in rough approximation, be determined largely by the first NN-collision.

MECHANISM OF INTERACTION OF FAST NUCLEONS WITH NUCLEI

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Figs. 10 and 11 represent the comparison of experimental distributions with the results of the calculations by the statistical theory of the multiple production of K-mesons in NN-collisions at E = 9 GeV. It can be seen that angular distributions are in good agreement but the experimental energy spectrum is "softer" . The evaluation of one collision of a K-meson in a nucleus changes little the theoretical histogram in fig. 10 (for comparison with the experimental data 13) ) the theoretical curve is averaged over very large angular intervals) but yields an energy distribution very close to the experimental figure. The experimental value 13) (K - /K+) ." Zoo « 1 of the ratio of the numbers of K-- and K+-mesons qualitatively agrees with the calculated value, though it is quantitatively 3-. 5 times as large t. 6. Conclusion The comparison of the results of the calculations of the intranuclear cascade with experimental data obtained by different authors, alongside the arguments put forth against the "tube mechanism" in ref. 1), makes it possible to claim that the intranuclear cascade mechanism occurs at E = 9 GeV as well as at lower energies . The opposite conclusion drawn by Friedlander 11 ) is based on the consideration of a narrow group of facts which besides, can be accounted for in terms of the intranuclear cascade mechanism tt . At energies E » 10 GeV both incident particles and nucle as are strongly compressed (in the centre-of-mass system). Therefore the time of the interaction with a nucleus is very small and the perturbation wave is unable to spread transversely further than by A/,u c. In this case interaction occurs only with a tube of nuclear substance cut by a primary particle . Yet in this case as well interaction can assume the form of consecutive interaction with separate nucleons of the tube, i.e., the form of an intranuclear cascade. Just which mechanism of interaction occurs in nucleon-nucleus collisions at very high energies is an open question at present . We are grateful to K. D. Tolstov for discussions of different problems involved in nucleon-nucleus interactions at high energies and to M. G. Shafranova for the discussion of experimental data.

It will be noted that in ref. 13 ) an analysis is made of only 80 tracks of K-mesons (77K+ and 8K-) . Therefore experimental errors are fairly large. 30) . tt A detailed analysis and criticism of the work by Friedlander is given in ref. t

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V . S . B .tRAMEIZKOV, V . M . MALTSEV AND E. K. MIKIIÜL

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