Research Journal of Recent Sciences ________________________________________________ ISSN 2277-2502
Vol. 1 (ISC-2011), 232-237 (2012)
Res.J.Recent Sci.

Some Aspects of Secondary Charged Particles Produced
in 4.5 A GeV/c 28Si-Nucleus Interactions
Shaikh Sarfaraz Ali1 and H.Khushnood2
Department of Physics, Jamia Millia Islamia, Jamia Nagar, New Delhi-110025, INDIA

Available online at, www.isca.in
(Received 15th October 2011, revised 10th January 2012, accepted 25th January 2012)

Abstract
Attempt has been made to study the characteristics of secondary charged particles produced in 4.5 A GeV/c 28Si-nucleus
interactions. The results reveal that the multiplicity correlations are not linear. These findings do not agree with those reported by
several workers. However, these correlations may be reproduced quite well by second order polynomial. It is also observed that the
dependence of mean normalized, RA and reduced multiplicity, RS on the multiplicity of different charged secondaries is linear up to
a certain value and then acquire almost a constant value. Results also reveal that the k th root of central moment increases with the
increase of <NS> and the values of normalized moments do not depend on the nature and energy of the projectiles. Finally, it is
observed that the integral multiplicity distribution of heavily ionizing tracks provides a method for selecting the disintegration
caused by the projectile due to different target nuclei of nuclear emulsion.
Keywords, Multiplicity correlations, mean normalized and reduced multiplicity, central moment, nuclear emulsion, etc.

Introduction
Study of relativistic heavy ion interactions has been carried
out by several workers1-9 during the recent years. One of the
important feature of relativistic heavy ion reactions is the
observation of collective behaviour of nuclear matter.
However, the first goal for such studies is to investigate the
correlations between the emitted particles in the nucleusnucleus collisions.

Black Particles: The tracks having relative velocity, b < 0.3
are termed as black tracks. The number of their tracks in an
event is denoted by Nb. They are generally alpha particles
and helium nuclei etc.
Grey Particles, The tracks with 0.3 £ b £ 0.7 are referred as
grey particles. The number of grey particles in an integration
is denoted by Ng. They are generally protons with a very
little admixture of slow pions.

In the present work an attempt has been made to investigate
the characteristics of different secondary charged particles
emitted in inelastic collisions of silicon nuclei with the nuclei
of nuclear emulsion at the momentum of 4.5 A GeV/c. At the
same time the nature of the dependence of various
parameters on the mass number of the projectile and on the
mass of the target nucleus are also studied. This will help us
to understand the dynamics of hadronization of final stage
charged secondaries produced in relativistic heavy ion
interactions.

Heavily ionizing Particles, The black and grey tracks taken
together are treated as heavily ionizing particles and denoted
as Nh (= Nb +Ng).

Material and Methods

The integral multiplicity distributions of heavily ionizing
particles, Nh, produced in 4.5 A GeV/c 28Si-nucleus
interactions is plotted in figure 1. It is interesting to note in
the figure that the distribution has two different slopes with
breaks approximately corresponding to CNO and Ag Br
constituents of the emulsion nuclei. A similar behaviour of
integral multiplicity distributions of heavily ionizing tracks is
also observed in 4.5 A GeV/c 12 C-nucleus interactions4. It is
reported that the multiplicity correlations between <Ns> Nb, <NS> - Nh and <Nb> - Ng acquire almost constant value
beyond Nb ~ 9 and Nh ~ 31 and Ng ~ 20 in both hadron-

In order to investigate the characteristics of secondary
charged particles, a random sample of 498 events produced
in 4.5 A GeV/c 28Si-nucleus interactions, have been
analyzed. All the relevant informations regarding the
emulsion stacks, method of measurement, selection criteria,
etc. may be found in our earlier publication8. All the
secondary charged particles produced in these interactions
may be classified in the following categories.

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Relativistic charged Particles, The tracks having b > 0.7 are
considered as relativistic charged particles. The number of
these particles in a star is represented by Ns. These are
generally charged pions.

Results and Discussions

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Research Journal of Recent Sciences ____________________________________________________________ ISSN 2277 - 2502
Vol. 1(ISC-2011), 232-237 (2012)
Res.J.Recent.Sci
nucleus and nucleus-nucleus collisions2,10,11. In order to
understand the nature of the multiplicity correlations, an
attempt has been made to investigate the multiplicity
correlations between <Ns> - Nb, <NS> - Nh and <Nb> - Ng.
For this purpose the regression of the type <Ni(Nj)>, where
Ni, Nj = Nb, Ng, Ns and Nh and i ≠j. In the present work
regression <Ns (Nh)>, <Ns(Nb)> and <Nb (Ng)> for 28Sinucleus reactions at 4.5 A GeV/c and their dependence on
the nature of the projectile are studied. The dependence of
<Ns> with Nb, Ng and Nh and <Nb> on Ng are displayed in
figures 2-4. The multiplicity correlations obtained in 28Sinucleus collisions may be represented by the following
second order polynomial quite well.
<Ns> = (5.47 ± 3.11) + (0.41 ± 0.35) N h +
(0.002 ± 0.008) Nh2
…………………….. (1)
<Ns> = (6.85 ± 1.82) + (0.69 ± 0.56) N b +
(0.008 ± 0.03) Nb2
……………………...(2)
<Nb> = (0.92 ± 0.02) + (1.41 ± 0.38) N g(0.03 ± 0.02) Ng2
……………………...(3)

reactions <Nch>PP at
RS = <Ns>AA / <Ns>PA

the

same

projectile energy
…………… (5)

It may be pointed out that the values of <Ns>AA have been
calculated using the following relations3.
<Ns>AA = 2.34 <Nch>PP - 4.12
…………(6)
The values of RA and RS are estimated and their dependence
with the number of black tracks, Nb produced in 4.5 A GeV/c
28
Si-nucleus interactions is shown in Fig.5. It is noticed in the
figure that both RA and RS increase linearly with increasing
the value of Nb up to Nb ~ 10. The experimental values of RA
and RS are found to satisfy the following relationship,
obtained by the method of least squares;
RA = (0.219 ± 0.07) Nb + (3.519 ± 1.15)
RS = (0.330 ± 0.114) Nb + (5.368 ± 1.73)

….…………(7)
…….………(8)

A similar behaviour of dependence of RA and RS with Nb is
also observed in case of 12C-nucleus reactions at 4.5 A
GeV/c3.

The continuous curve shown in figures corresponds to eqs.
(1-3) for 4.5 A GeV/c 28Si-nucleus interactions. It is reported
that the multiplicity correlations between <Ns> - Nh and
<NS> -Ng in case of hadron-nucleus collisions in the energy
range ~ (24-400) GeV11. and in 4.5 A GeV/c 12C-nucleus
reactions4 may be represented by the second order
polynomial. This indicates that the nature of the correlation
<Ns> - Nh is almost similar in both hadron-nucleus and
nucleus-nucleus collisions.

Figure 6 deals with the dependence of parameters RA and RS
with the multiplicity of grey particles, Ng. It may be noted
from the figure that the values of R A and RS increases with
increasing value of Ng up to Ng ~ 9. The following relations
obtained by the method of least square fit are found to satisfy
the experimental data quite well,

The mean normalized multiplicity RA defined as the ratio of
average number of relativistic charged particles produced in
hadron-nucleus and hadron-hadron collisions at the same
projectile energy is one of the most important parameter to
test the predictions of various theoretical models put forward
for explaining the mechanism of hadronization of final stage
charged particles produced in hadron-nucleus collisions. The
study of RA and its dependence on the nature and energy of
the impinging hadron has been investigated by several
workers in hadron-nucleus collisions at high energies10.
However, a little attention has been paid to study this
parameter in nucleus-nucleus interactions3. Thus, an attempt
has been made to investigate the dependence of the mean
normalized multiplicity, on the mass of the projectile and
target nucleus. Mathematically, RA may be given as;
RA = <Ns>AA / <Nch>PP
…………(4)

A similar result has also been reported by Saleem et al [6] in
the study of 12C-nucleus collisions at 4.5 A GeV/c. An
attempt has also been made to study the dependence of the
parameters RA and RS with the multiplicity of heavily
ionizing tracks, Nh. The variation of RA and RS with Nh for
28
Si-nucleus collisions is shown in figure 7. It is clear from
the figure that RA and RS increase linearly with increasing
value of Nh up to Nh ~ 28. The experimental value of RA and
RS are found to satisfy the following fits obtained by the
method of least squares.
RA = (0.221 ± 0.033) Nh + (1.721 ± 0.762)
………...(11)
RS = (0.334 ± 0.050) Nh + (2.601 ± 1.149)
………….(12)

Here <Ns>AA refers to to the average number of relativistic
charged particles produced in nucleus-nucleus interactions
and <Nch>PP is the average number of charged particles
emitted in Proton-Proton collisions at the same projectile
energy. The reduced multiplicity, RS is defined as the ratio of
the average number of relativistic charged particles produced
in nucleus-nucleus reactions, <Ns>AA and Proton-nucleus

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RA = (0.276 ± 0.009) Ng + (3.321 ± 1.32) ………………...(9)
RS = (0.437 ± 0.148) Ng + (4.860 ± 2.08) ……………….(10)

The normalized moments of the multiplicity distributions of
relativistic charged particles produced in high energy hadronnucleus collisions has been investigated by several workers
in the energy range ~ (50-400) GeV12. However, a little
attention has been paid to study the normalized moments of
the multiplicity distributions of relativistic charged particles
produced in nucleus-nucleus interactions1,3 . Thus, it was
considered worthwhile to investigate the normalized
moments of the distributions and their dependence on the
mass of the projectile and struck nucleus. The normalized
moments of the multiplicity distributions of relativistic
charged particles is defined as;
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Research Journal of Recent Sciences ____________________________________________________________ ISSN 2277 - 2502
Vol. 1(ISC-2011), 232-237 (2012)
Res.J.Recent.Sci
CK = <NSK> / <NS>K
………………….(13)
where K is a constant and can have different values 2, 3, 4
etc. For studying the dependence of C K on the size of the
target nucleus, the values of C2, C3 and C4 are calculated for
different groups of emulsion nuclei in 4.5 A GeV/c 28Sinucleus interactions. The values of CK obtained in 4.5 GeV/c
28
Si-nucleus reactions are listed in table-1 along with the
results obtained in12 C-nucleus reactions1,3 at the same
projectile energy.
It is interesting to note that the values of CK in 4.5 A GeV/c
12
C-nucleus reactions and 28Si-nucleus collisions are almost
consistent with constant with the statistical limits. It may be
further noted in the Table-1 that, the value of this parameter
is observed to increase with increasing value of k. On
comparing the findings of the present work with those
obtained in 50 GeV and 400 GeV hadron-nucleus
collisions12, it may be observed that the value of CK are very
similar in both type of interactions. The kth root of the central
moment, mK of the multiplicity distribution is also studied in
4.5 A GeV/c 28Si-nucleus collisions. The parameter mK is
defined as,
(mK)1/2 = (<(NS - <NS>)K>)1/2
……………(14)
In figure 7 we have plotted (m2)1/2, (m3)1/2, (m4)1/2 as a
function of <NS> for 28Si-nucleus interactions at 4.5 A
GeV/c.
It may be seen in the figure that the solid line which
represent the variation of the moments with <N S> fits the
experimental data quite well. On comparing these

observation with those obtained in high energy hadronnucleus collisions, it may be concluded that there is at least a
qualitative similarity in the mechanism of hadronization in
the final stage of high energy hadron-nucleus as well as
nucleus-nucleus reactions.

Conclusion
On the basis of the study of the present work we draw some
important conclusions which are summarized as follows,
i. The multiplicity correlations amongst <NS> - Nb, <Nb> Ng, <NS> - Nh are non-linear and may be represented quite
well by the second order polynomial. Thus, our findings are
in marked disagreement with those reported by other workers
in both hadron-nucleus and nucleus-nucleus interactions. ii.
The experimental values of RA and RS are found to increase
linearly with increasing value of Nb, Ng and Nh up to Nb ~ 10,
Ng up to Ng ~ 9, and Nh up to Nh ~ 28. iii. The values of
normalized moments are found to remain almost constant.
However, the value of this parameter increases with
increasing value of k. iv. The results reveal that the kth root
of the central moment increases with increasing value of
<NS>. v. On comparing the results obtained in 4.5 A GeV/c
nucleus-nucleus interactions with those obtained in high
energy hadron-nucleus collisions, we conclude that the
results both in hadron-nucleus and nucleus-nucleus
interactions are almost similar and the mechanism of
hadronization of final stage charged particles operating in
these reactions is perhaps the same.

Table-1
Values of normalized moments C2, C3 and C4 in nucleus nucleus reactions at 4.5 A GeV/c
Type of Interactions
C2
C3
C4
Reference
12
C-CNO
6
1.41 0.10
2.42 0.23
4.73  0.58






12







12







28







12







12







12







28

Si-CNO
C-Em
C-Em

Si-Em

C-AgBr
C-AgBr

Si-AgBr

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Present work
6
3
Present work
6
3
Present work

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Research Journal of Recent Sciences ____________________________________________________________ ISSN 2277 - 2502
Vol. 1(ISC-2011), 232-237 (2012)
Res.J.Recent.Sci

International Science Congress Association

235

Research Journal of Recent Sciences ____________________________________________________________ ISSN 2277 - 2502
Vol. 1(ISC-2011), 232-237 (2012)
Res.J.Recent.Sci

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Research Journal of Recent Sciences ____________________________________________________________ ISSN 2277 - 2502
Vol. 1(ISC-2011), 232-237 (2012)
Res.J.Recent.Sci

Acknowledgment
The authors wish to thank to staff of all clinical laboratories
of Valsad district, who gave their valuable support. The
authors also wish to thank management and staff of Shree
RamKrishna Institute of Computer Education and Applied
Sciences, Surat; Dolat Usha Institute of Applied Sciences,
Valsad.

References
1.

Qasim Raza Khan M., Ph.D. Thesis submitted to Aligarh
Muslim University, Aligarh (1988)

2.

Saleem Khan et al M., Multiplicity characteristics of 12Cnucleus interactions at 4.5 A GeV c-1, Can. J. Phys. 74,
651 (1996)

3.

Saleem Khan et al M., Production of secondary charged
particles in 12C-nucleus reactions at 4.5 A GeV per
nucleon, J. Phys. Soc. Jpn. 65, 801 (1996)

4.

Saleem Khan et al M., Study of disintegrations caused by
4.5 GeV carbon nuclei in nuclear emulsion, Nuovo
Cimento A, 108, 147 (1996)

5.

Singh et al Prithipal, Features of relativistic charged
particles produced in catastrophic destruction of heavy
emulsion nuclei at 4.5 A GeV/c, Can. J. Phys. 76, 559
(1998)

6.

Abd Allah et al N. N., Non-statistical fluctuations of
target fragments emitted in high energy nucleus-nucleus
collisions, Can. J. Phys. 80, 119 (2002)

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7.

El Naghy et al A., Comparative study for nucleus-nucleus
interactions and modified cascade evaporation model at
(4.1-4.5) A GeV/c, APHNS, Heavy Ion Phys.15, 131
(2002)

8.

Sarfaraz Ali et al Shaikh, Study of totally disintegrated
events caused by 4.5 A GeV/c 28Si with heavy emulsion
targets, Euro Phys. Lett. 65, 773 (2004)

9.

Khushnood et al H., Some aspects of multi particle
production in 4.5 GeV 28C-nucleus interactions, 6th
International Conference on Physics and Astro Physics of
Quark Gluon Plasma, Dec. 6-10,115 (2010) Goa, India

10. Khushnood et al H., A study of high energy hadron nucleus interactions, Can. J. Phys. 61, 1120 (1983)
11. Shakeel et al A., Multi particle production in 24, 50 and
400 GeV/c particle-nucleus interactions, Nuovo Cim.
76A, 699 (1983)
12. Khushnood et al H., Some interesting features of charged
particles produced in high energy hadron-nucleus
collisions, Can. J. Phys. 68, 67 (1990)

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