IL NUOVO CIMENTO VOL. 104 A, N. 12 Dicembre 1991

Production of Heavy Clusters in 4.5 A GeV/c Carbon- and Silicon-Nucleus Collisions.

TAUSEEF AHMAD, M. IRFAN and M. SHAFI

Department of Physics, Aligarh Muslim University - Aligarh 202002, India

(ricevuto il 23 Aprile 1991; approvato il 4 Giugno 1991)

S u m m a r y . - - Emission characteristics of clusters and heavy clusters are investi- gated by analysing the data on carbon- and silicon-nucleus interactions at 4.5 GeV per nucleon incident energy. The cluster size is found to be essentially insensitive to the nature of the projectile and target mass. There is a weak indication about the production of heavy clusters.

PACS 25.70.Np - Fragmentation and relativistic collisions.

1. - I n t r o d u c t i o n .

During the recent past, several attempts were made to investigate the mechanism of multihadron production in high-energy hadron-hadron[l-4], hadron-nucleus[5-7] and nucleus-nucleus [8, 9] collisions. The idea of the cluster formation in the interme- diate state of the multiparticle production in high-energy hadronic interactions has attained wide acceptability. It has been observed [10] that the relativistic pions pro- duced in an interaction are correlated amongst themselves. The observed correlations amongst the fast secondary pions may be attributed to the double step mechanism, i.e. subsequent to a collision, massive hadronic systems, like clusters, resonances or fireballs are formed which finally decay into the real physical particles. It is interest- ing to mention that quite useful and significant information about mechanism of mul- tiparticle production through the decay of clusters may be gleaned by examining the behaviour of the distributions of the rapidity differences between the n-th nearest neighbours.

In our earlier investigation [11], a significant clusterization effect was observed to occur in both carbon- and silicon-emulsion interactions data. In the present study, an attempt is made to study the emission characteristics of clusters and heavy clusters. Results based on the study of the rapidity-gap correlations and the production of heavy clusters investigated by examining n-particle rapidity gap distributions are presented in this paper.

1777

1778 TAUSEEF AHMAD, M. IRFAN and M. SHAFI

2. - E x p e r i m e n t a l d e t a i l s .

Two stacks of NIKFI-BR2 emulsion of dimensions (18.6 x 9.5 x 0.06)cm 8 and (16.9 x 9.6 x 0.06 )cm 8, each exposed to 4.5 GeV per nucleon 12C and 2sSi beams at Dubna Synchrophasotron, USSR, have been used in the present investigation. The details about the method of measurements, selection criteria, etc., are given in our earlier publication [11].

Random samples consisting of 852 and 1024 interactions produced in 4.5 A GeV/c carbon- and silicon-emulsion collisions, respectively, are analyzed to study the above stated problem. The following criteria are employed to select the shower tracks for carrying out the required analysis.

i) Relativistic charged particles having space angles less than 0o in the labora- tory frame, where the values of 00 are 2.00 ~ and 3.42 ~ for carbon- and silicon-nucleus interactions, respectively, are not included for the analysis. This has been done to ex- clude the contribution of the projectile fragments.

ii) Only events with Ns/> 4 are accepted for analysis.

3. - E x p e r i m e n t a l r e s u l t s .

In order to examine n-particle correlations, the charged shower particles in each event are arranged in decreasing order of their pseudorapidity (7 = - In tg 0/2) values and the differences between the consecutive particles are calculated. Several investi- gators [1-10] have reported that the rapidity difference distributions in high-energy hadron-hadron, hadron-nucleus and nucleus-nucleus interactions may be represented satisfactorily by the two-channel generalization of the Snider model [3]. According to the model, the rapidity density may be expressed as

(1) dn / dr~ = A exp [-Br~ ] + C exp [-Dr~ ],

where A, B, C and D are constants and dn/dri represents the cluster density. The first and the second terms of eq. (1) correspond, respectively, to the short- and the long-range correlations.

Rapidity-gap distributions between adjacent charged shower particles for carbon- and silicon-emulsion interactions are shown in fig. 1. A sharp and clear peak at a rela- tively smaller value of rapidity gap is observed in fig. 1, indicating thereby the pres- ence of two-particle correlations. The theoretical curve in the figure represented by solid line is drawn by using eq. (1) for silicon-emulsion interaction data. It may be mentioned that in order to avoid confusion, the curve corresponding to eq. (1) for car- bon-emulsion collisions is not shown in the same figure. The dash-dotted lines in the figure are the individual contributions of the two exponential terms in eq. (1). It is noticed from the figure that the dash-dotted line representing the contribution of the short-range correlation almost coincides with the solid curve in the region of lower values of the rapidity gaps, whilst the line representing the contribution of the long- range correlation is significantly far away from the solid curve in the region of lower rapidity gap values. This indicates that the major contribution to the two-particle correlation comes from the short-range correlation, while the contribution of the long-range correlation appears to be rather negligible.

The values of the parameters A, B, C and D occurring in eq. (1) are computed with the help of the CERN standard programme MINUIT and the errors as given in MI-

PRODUCTION OF HEAVY CLUSTER ETC.

101[ 1779

" \ , \ \. L 7

" ~ . L 7

\ .

\ F7 \ "7

\ L-7

10 -~ \ , ', [ - - L l ,

10-3 t

0

\

\

\

1.0 210 rapidity gap (r i)

I I l r 7 l i I

3.0

Fig. 1. - Two-particle rapidity gap distributions for carbon ( . . . . . ) and silicon ( The solid curve is drawn using eq. (1).

) projectiles.

NOS. The values of these parameters are tabulated in table I alongwith the values of z2/DF, where DF are the degrees of freedom. On comparing the values of the param- eters B and D obtained for 12C- and 2SSi-emulsion collisions at 4.5 GeV per nucleon, the values of these parameters are observed to be practically insensitive to the pro- jectile mass. Incidentally, the values of these parameters compare fairly well with those reported [6, 7] for hadron-nucleus interactions at high energies. Hence, it may be stated that the mechanism of multiparticle production in hadron-nucleus and nu- cleus-nucleus collisions is probably the same.

TABLE [. - Values of various parameters occurring in eq. (1)for carbon- and silicon-emulsion interactions at 4.5 A GeV/c.

Projectile A B C D ~ / D F

12C 2.38+2.17 6.52+1.31 0.55_+0.02 2.08_+1.19 0.09 2sSi 4.72 + 4.31 6.55 + 1.96 0.48 + 0.02 2.23 + 0.46 0.13

1780 TAUSEEF AHMAD, M. IRFAN and M. SHAFI

4. - Rapidity-gap correlat ion in different Ng-intervals .

For examining the dependence of the cluster size on the grey-particle multiplicity, N~, the data are divided into different Ng-intervals, i.e. Ng = 0, 1, 2-3, 4-5, 6-8 and I> 9.

Rapidity-gap distributions between adjacent charged shower particles for various Ng-intervals for carbon- and silicon-emulsion interactions are exhibited in fig. 2. The occurrence of clear and distinct peaks at relatively smaller values of the rapidity gaps would indicate the existence of two-particle correlation.

101

10 0

- "- ' ' ~l Ng>_9 10-11 J L~

r 10 ~

10 0

I f]

r J i r n

\ . \

i ' r n r n " - ~

=1

II

E

L] r l . =6+8

10-'b I " ' - . "~ ,:~" 1 i ~ ' ~ ! ~ . ~. ' , .~% , ~

10 -2

~ '~ --'l 77 =4,5 " " ' , ! , ' ' : ! ' ' l , r l

-~ \ LJ _J , F~ ! ! ',',k', !', , , , ' ' , ,,I , , , ~ , , I

0 1.0 2.0 0 1.0 2.0 3.0 rapidity gap (r i)

Fig. 2. - Two-particle rapidity gap distributions for different Ng-intervals in carbon- and silicon- nucleus interactions. The solid curves are drawn using eq. (1). - - 28Si, - - - 12C.

The solid curves in fig. 2 correspond to eq. (1) for the silicon-emulsion interac- tion data. It may be seen from the figure that the contribution of the short-range correlation is comparatively larger in comparison with the long-range correlation. The values of the parameters A, B, C and D occurring in eq. (1) for all Ng-intervals for carbon and silicon projectile are listed in table II alongwith the values of z2/DF for each fit.

PRODUCTION OF HEAVY CLUSTER ETC. 1781

TABLE II. - Values of various parameters occurring in eq. (1)for different Ng-intervals in car- bon- and silicon-nucleus interactions at 4.5 A GeV/c.

Carbon

Ng-bins A B C D z2/DF

Ng = 0 1.54 -+ 1.38 5.23 + 1.34 0.45 +_ 0.32 1.53 +_ 1.31 0.07 Ng = 1 1.50+ 1.21 9.00_+4.17 1.69_+ 1.52 2.14+ 0.43 0.07 N g = 2 , 3 2.92+1.79 3.79+2.63 0.29+0.04 1.30_+1.99 0.11 N g = 4,5 2.87_+1.62 5.78_+1.70 0.36+0.51 1.60_+0.57 0.11 Ng = 6-8 4.81 _+ 4.35 7.59 _+ 2.44 0.08 _+ 0.07 1.92 _+ 0.61 0.34 Ng>~9 3.36_+2.15 6.09_+2.11 1.25_+0.34 2.03_+0.21 0.06

Silicon

N~-bins A B C D z3/DF

Ng=O 3.13+2.42 3.88+2.42 0.16+0.07 1.01___0.22 0.11 Ng = I 3.83 _+ 1.68 5.00 _+ 0.61 0.06 + 0.03 1.30 +_ 0.20 0.05 N~=2,3 3.55+2.54 4.20+1.00 0.05+0.05 1.01+0.24 0.11 Ng = 4, 5 4.25 + 3.52 4.93 -+ 1.31 0.07 + 0.05 1.59 + 0.89 0.08 Ng=6-8 5.79+4.15 7.00+2.94 0.25+0.09 2.00+0.28 0.14 Ng~>9 6.67+2.95 8.20+6.87 0.16+0.47 2.15+1.13 0.06

5. - C l u s t e r s i z e .

The rapidi ty-gap distr ibutions can also be used to es t imate the cluster size and the cluster densi ty in the rapidi ty space. The cluster size can be de te rmined by using the following equations [12]:

(2) dn / dri ~- exp [ -pmri ]

for small values of ri ,

(3) dn /dr i ~ exp [ -~r i ]

TABLE I I I . - Values of cluster multiplicity occurring in eq. (2)for carbon and silicon projectiles at 4.5 A GeV/c.

m

12 C 2SSi

all events 3.13 2.94 Ng = 0 3.41 3.84 Ng = 1 4.20 3.85 Ng = 2, 3 2.92 4.15 Ng -- 4, 5 3.61 3.10 N~ = 6-8 3.95 3.50 Ng/> 9 3.00 3.81

1782 TAUSEEF AHMAD, M. IRFAN and M. SHAFI

for large values of r~, where p is the cluster density and m is known as the cluster multiplicity, defined as the number of showers in a cluster. The values of m, calculat- ed using eq. (2) for carbon- and silicon-emulsion interactions for all the events and for different Ng-intervals are listed in table III. The results obtained in the present study agree fairly well with the predicted value of m equal to 3.50 for 200 GeV pp in- teractions [3]. It is interesting to note that Ludlam and Slansky [13] have reported the value o f m equal to 4.0 +_ 0.8 at 205 GeV/c and 3.50 _+ 0.80 at 300 GeV/c by the fluctua- tion and analysis method. Thus, these results tend to reveal that the cluster multi- plicity is independent of the nature of the projectile.

6. - Short- and long-range correlat ions.

According to Snider [3], if more than two charged particles result from the same cluster, then two consecutive short gaps would occur in the rapidity space. Following Snider's suggestion, a small gap is defined to have ri ~< 0.1 and a large gap should sat- isfy the condition 0.8 ~< r i <- 1.0. For testing the validity of this idea, the behaviour of the distributions of the gaps occurring next to the short and the long gaps ri + ~ are ex- amined separately for both carbon- and silicon-emulsion interactions. These distribu- tions are plotted in fig. 3 and 4 for the gaps occurring next to the short and the long gaps. Clear and distinct peaks are observed at relatively lower values of r i+ 1. The

101[

I0 ~

7 .~ i0-I

10 .2

t - ~ 7

L J- 7

\.,~ L__J I A L__1

' ,~ II ;.

03 �9 i ~ ' - ~ . \

I I

\ I i I

0 1.0 2.0 r/+l

Fig. 3. - Distributions of rapidity gaps (r i + 1 ) next to a small gap (r i ~ O. 1). The solid curve is drawn using eq. (1). - - ~Si, - - - 12C.

PRODUCTION OF HEAVY CLUSTER ETC. 1783

101

10 ~ +

10 -1

7

L

1.0 ri+ 1

2 .0

Fig. 4. - Distributions of rapidity gaps ( r i + l ) next to a large gap (0.8 ~< r i ~ 1.0). - - 2SSi, _ _ _ 12C.

solid curve in the distribution of the gaps occurring next to the short gaps for silicon- emulsion interactions is represented by the following relation:

(4) dn /dr~+~=(4 .19+2 .26 )exp[ ( -5 .66+ l.O3)r~+~]+

+(0.01 + 0.007) exp [ ( - 0.83 + 0.25) r~+l]

and for carbon-emulsion collisions the following expression reproduces extremely well the data points:

(5) dn/dr~+l = (3.60 _+ 3.80) exp [ ( - 5.33 _+ 5.65) r~+i]+

+(0.59 +_ 1.01) exp [ ( - 1.97 ___ 2.54) ri+l] �9

The lines drawn by dashes and dots in fig. 3 are the contributions of the short- short and the short-long correlations. It may also be noted in fig. 3 that a major con- tribution to the correlation comes from the short-short correlation. Furthermore, it may be mentioned that the values of B are essentially the same for both carbon and silicon projectiles.

7. - Product ion of heavy clusters.

Adamovich et al. [12] have proposed a method for investigating the production mechanism of the heavy clusters in the interactions with shower particle multiplicity, Ns, nearly equal to the mean charged shower particle multiplicity, (Ns) , for the whole data. The rapidity interval nr k is defined as the difference of rapidities of two

113 - l l Nuovo Cimento A

1784 TAUSEEF AHMAD, M. IRFAN and M. SHAFI

particles in an event having n shower particles with k particles in between as

(6) ~rk = Vi + k- 1 - Vi

with l < . i < ~ n - k - 1 and O < . k < . n - 2 . In the present work, the values of (Ns > are found to be 7.67 _+ 0.19 and 11.26 + 0.33

for carbon- and silicon-nucleus collisions, respectively. Therefore, 123 interactions for 12C-nucleus interactions having Ns = 7, 8 and 9 and 93 events for silicon-nucleus inter- actions having N~ = 10, 11 and 12 were selected for the present analysis, which give 993 and 999 shower tracks respectively for '2C- and 2sSi-emulsion interactions.

According to Adamovich et al. [12], the production of the fireball types of heavy clusters should manifest its effect most significantly in the distributions having k i> (N~ >/2. In the present study, the values of (N~ > are approximately equal to 8 and 11 for carbon- and silicon-emulsion collisions, respectively. Therefore, the presence of two-bump structures should occur in the distributions for k t> 4 and k t> 5 for carbon- and silicon-emulsion interactions, respectively. The distribution of rapidity gaps nrk for k = 0 to 7 and k = 0 to 10 for carbon- and silicon-nucleus interactions are shown in fig. 5 and 6. From the figures, it is evident that there is no evidence for the occurrences of two-bump structure for the two cases. However, Goyal et al. [14] have obtained very clear evidence for the production of heavy clusters in nucleon-nucleon interactions at cosmic-ray energies -1000 GeV. Recently, Bell et al. [15] and Andersson et al. [16] have reported the production of heavy clusters in a-a, p-p and d-d interactions at ISR energies.

50

25

50 ~9

~ 0

200

100

1oo o 11~ ?

=0 10 0

4O

1.0 2.0 0 0 nr k

=7

=6

=4

1.0 2.0 3.0

Fig. 5. - Experimental distributions of rapidity intervals ~rk with k = 0 to 7 for carbon-emulsion interactions.

PRODUCTION OF HEAVY CLUSTER ETC. 1785

50-

0

50-

0

50

100

50

0

200

i00

~ k = 4 ~02

=3 5

rl0

_-2

0'

Jl :1 0

=0

0 1.0 2.0 3.0

25

:1o! =9

=8

=7

=6

5 =5

~ ~ n i 1.0 2.0 3.0 4.0

nr k

Fig. 6. - Experimental distributions of rapidity interval nr k with k = 0 to 10 for silicon-nucleus interactions.

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

From the above detailed investigation concerning the features of the rapidity-gap distributions and the production of heavy clusters produced in 1~C- and 2sSi-emulsion collisions, the following main conclusions can be drawn:

1) The mechanisms of multiple production of particles in nucleus-nucleus and hadron-nucleus interactions are perhaps the same.

2) The cluster size is independent of the nature and the energy of the projectile.

3) The contribution of the short-range correlation is rather larger in comparison with the long-range correlation for both the projectiles.

4) A two-bump structure has not been observed in both carbon- and silicon- emulsion interactions which would reveal that the heavy clusters are not produced in these interactions.

1786

R E F E R E N C E S

TAUSEEF AHMAD, M. IRFAN and M. SHAFI

[1] E. L. BERGER: Nucl. Phys. B, 85, 61 (1975). [2] L. FOA: Phys. Pep. C, 22, 1 (1975). [3] D. R. SNIDER: Phy8. Rev. D, 11, 140 (1975). [4] W. BURDETT, J. HANLON, R. S. PANVINI, E. 0. SALANT, W. H. SIMS, J. WATERS, M. S.

WEBSTER, n. R. KINSEY and T. W. MORRIS: Nucl. Phys. B, 48, 13 (1972). [5] M. IRFAN, H. KHUSHNOOD, A. SHAKEEL, M. ZAFAR and M. SHAFI: Phys. Rev. D, 39, 218

(1984). [6] TAUSEEF AHMAD, M. TARIQ, M. IRFAN and H. KHUSHNOOD: J. Phys. Soc. Jpn., 56, 2689

(1989). [7] TAUSEEF AHMAD, M. IRFAN and M. Z. AHSAN: Can. J. Phys., 68, 1192 (1990). [8] V. KAPOOR, n. K. SHIVPURI and S. K. JHA: Nuovo Cimento A, 85, 262 (1985). [9] V. S. SHUKLA, K. S. BHALLA, A. GILL, V. KUMAR, S. LOKANATHAN, A. BHASIN, V. K. GuP-

TA, S. KITROO, V. KUMAR, L. K. MANGOTRA, N. K. ROA, R. ARORA, V. S. BHATIA, M. KAUR and I. S. MITTRA: Mod. Phys. Lett. A, 3, 1411 (1988).

[10] I. M. DREMIN: Proceedings of the XII International Symposium on Multiparticle Dynam- ics (Notre Dame, USA, 1981), p. 261.

[11] TAUSEEF AHMAD, M. IRFAN and M. Z. AHSAN: to be published in Nuovo Cimento A. [12] M. I. ADAMOVICH, M. M. CHERNJAVSKII, I. M. DERMIN, A. M. GERSHKOVICH, S. P. KHAR-

LAMOV, V. G. LARIONOVA, M. I. TRETJAKOVA, E. I. VOLKOV and F. R. YAGUDINA: Nuovo Cimento A, 33, 183 (1976).

[13] T. LUDLAM and R. SLANSKY: Phy8. Lett. B, 48, 449 (1974). [14] D. P. GOYAL, S. ROY and S. SINGH: Phys. Rev. D, 26, 3273 (1982). [15] ABCDHLLW COLLABORATION: CERN preprint no. CERN-EP/85-188 (1985). [16] B. ANDERSSON, S. GARPMAN, G. GUSTAFSON, n. A. GUSTAFSSON, B. NILSSON-ALMQVIST, I.

OTTERLUND and E. STENLUND: Phys. Scr., 34, 51 (1986).