Vol.3, No.5, 408-413 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.35055
Nuclear fragmentation at 4.5 A GeV/c in 28Si with
emulsion interactions
A. Abd El-Daiem1*, A. Abdel-Hafiez2, M. A. Khalifa3
1Physics Department, Faculty of Science, Sohag University, Sohag, Egypt; *Corresponding Author:
2Experimental Nuclear Physics Department, Nuclear Research Center, Cairo, Egypt
3Mathematical Deparment, Faculty of Science, Tanta University, Tanta, Egypt
Received 11 February 2011; revised 13 March 2011; accepted 27 March 2011.
ABSTRACT
The experimental results of complete charge
distribution of projectile fragments (PFS) and
the total charge of the projectile fragments (PFS )
are presented. Also the multiplicity distributions
of (PFS) and the rapidity distribution of shower
tracks produced from events with nh = 0 from
28Si with emulsion at 4.5 A GeV/c are obtained.
Keywords: Multiplicity Distribution;
Total Chare and Rapidity Distribution
1. INTRODUCTION
Nuclear fragmentation and its possible connection
with a critical phenomenon of a phase transition has
been the subject intensive theoretical and experimental
investigation in the interaction of relativistic heavy nu-
clei nucleus collision [1,2] the overlapping region of
nuclear volumes is called the participant region, where
multiple productions of new particles occurs and the
matter breaks up into nucleons. An estimate the degree
of centrality of a collision of the nuclei can be made if
we determine the total charge Q of the non interacting
nucleons or fragments of the projectile nucleus, to which
we assign the relativistic particles emitted at an angel θ <
3˚ [3,4]. Then the number of interacting nucleons of the
projectile nucleus is on the average nint =28 − 2Q [5]. In
the collision of two nuclei, the elementary interaction is
more amplified than in the case of hadrons-nucleus in-
teraction. At such high energy (4.5 A GeV/c) the rapidity
gap between the projectile target fragmentation regions
is quite wide, which provides us with a good possibility
for testing the limiting fragmentation hypothesis [6,7] in
playing that no correlations exist between the projectile
and target fragments.
These results were obtained from the study of single
partied inclusive experiments where the degree of target
fragmentation can take any value. It is interesting to
compare these results with those of projectile fragments
angular distribution from the special class of events nh =
0, where there is no target fragmentation but only a pro-
jectile fragmentation.
2. EXPERIMENTS
In our experiments, the layers of photo emulsions
NIKFI-BR2, with dimensions of 20 cm × 10 cm × 600
µm were irradiated by the 28Si beam from the syncho-
phastron in the high energy laboratory of JINR, at Dubna
with an average beam momentum of 4.5 A GeV/c. Along
the track double scanning was carried out, fast in the
forward direction and slow in the backward direction.
The scanned beam tracks were further examined by
measuring the delta electron density on each of them to
exclude the tracks having the secondary particles is clas-
sified as follows:
1) Black particle tracks (nb) having a range L < 3 mm
in emulsion which corresponds to a proton kinetic en-
ergy of 26 MeV.
2) Grey particle tracks (ng) relative ionization I* (=
I/I0) < 1.4 and L > 3 mm which correspond to a proton
kinetic energy of 26 - 400 MeV, where I is the particle
track ionization and I0 is the ionization of a shower track
in the narrow forward cone of an opening angel of θ < 3˚
(the b and g particle tracks are called heavy ionization
particle tracks (nh)).
3) Shower particle (ns) having I* < 1.4 (tracks of such
type with an emission angel of θ < 3 were further sub-
jected to rigorous multiple scattering measurement for
moment determination and consequently, for separating
the produced pions and singly charged projectile frag-
ments (protons, deuterons, tritons).
A total of 1000 interactions of 28Si with the nuclei of
the emulsion were observed by following a primary
track length of 78.12 meters, which led to a mean free
path of λ = 8.71 ± 0.30 cm. In each event, the charge Z ≥

A. A. El-Daiem et al. / Natural Science 3 (2011) 408-413 409
2 of individual projectile fragments were determined by
the combination of several methods, which include grain
and delta ray densities. More details on the charge de-
terminations of projectile fragments are given in Refer-
ence [8]. Projectile fragments essentially travel with the
same speed as that if the parent beam nucleus, so the
energy of the produced projectile fragments as high
enough to distinguish them easily from the target frag-
ments.
3. THE TOTAL CHARGE OF THE
PROJECTILE FRAGMENTS (PFS)
In the Table 1 we have given the data obtained on the
average multiplicities of h and s particles as functions of
nint. It can be seen that the number of thin prongs in a
disintegration increases linearly with increase of nint, and
within experimental error this occurs in a completely
identical way for the light and heavy emulsion compo-
nents. This dependence of < ns > on Q is consistent with
the model of independent interactions and indicates a
decisive roll of the first interaction. In collisions of light
nuclei the values of < nh > do not depend on nint, while
for heavy nuclei they rise almost linearly.
In Figures 1(a) and (b) we have shown the distribution in
Q for events in standard emulsion, and also the distribu-
tions obtained by the different methods for three differ-
ent groups of nuclei, normalized to the corresponding
probability of inelastic interaction. It is evident that the
distributions in Q depend substantially on the type of
target nucleus. The average total charge for disintegra-
tion of an incident 28Si nucleus in hydrogen, light and
heavy emulsion nuclei were respectively 11.71 to 0.17,
9.62 ± 0.11 and 4.68 ± 0.16. Note that in Figures 1(a) and
(b) in the light emulsion nuclei (H,C,O) there are practi-
cally no central interactions (Q = 0), collisions with the
heavy component are characterized by a wide set of A
values. Study of the dependence of the total charge of
the spectator fragments on the impact parameter for
events produced in heavy emulsion nuclei. Figures 1(a)
and (b) show that for large impact parameters (nh  7)
this distribution is practically the same as the distribution
in Q for hydrogen of the emulsion and for 8 nh 15 it is
close the distribution for events in nuclei (C,N,O). For
large nh a dominance of central interactions is observed.
In order to see the dependence of the number of inter-
acting nucleons on the collision geometry, we have
shown in Figure 2 nint as a function of nh. This figure
indicate that even in collisions where no, or very little
Table 1. Experimental dependence of average multiplicities <nh> and <ns> on the number of interacting nucleon and the pa-
rameter Q.
target nucleus
AgBr CNO
<ns> <nh> <ns> <nh>
nint Q
1.0 ± 0.0 6.2 ± 0.6 1.0 ± 1.4 1.3 ± 1.9 0 14
3.0 ± 0.8 8.3 ± 0.5 2.5 ± 1.8 2.3 ± 2.2 2 13
5.8 ± 3.0 12.3 ± 3.9 3.4 ± 2.4 3.1 ± 2.4 4 12
5.6 ± 2.1 14.1 ± 4.7 4.1 ± 3.0 2.9 ± 2.4 6 11
6.4 ± 2.6 14.4 ± 4.8 5.9 ± 3.2 3.5 ± 2.4 8 10
8.8 ± 4.0 16.5 ± 6.7 6.4 ± 3.0 3.3 ± 2.3 10 9
10.4 ± 4.1 16.2 ± 6.7 8.2 ± 2.6 3.8 ± 2.2 12 8
13.3 ± 4.7 16.6 ± 7.4 10.0 ± 2.8 4.6 ± 1.9 14 7
13.8 ± 5.1 16.5 ± 7.4 12.3 ± 4.7 4.5 ± 1.8 16 6
16.5 ± 5.2 22.7 ± 8.8 12.6 ± 4.5 4.1 ± 2.1 18 5
19.7 ± 6.8 25.3 ± 9.2 11.4 ± 5.2 4.4 ± 1.5 20 4
22.0 ± 6.8 24.5 ± 9.4 17.7 ± 2.1 5.3 ± 1.3 22 3
22.7 ± 7.2 26.3 ± 9.7 17.6 ± 1.6 5.6 ± 1.0 24 2
26.6 ± 6.5 31.0 ± 6.9 26 1
32.2 ± 6.8 33.4 ± 7.6 28 0

A. A. El-Daiem et al. / Natural Science 3 (2011) 408-413 410
(a) (b)
Figure 1. Distribution in total charge Q of fragments of the incident 28Si nucleus with the groups of emulsion nuclei (a) and
distribution in Q for events in nuclei (a) and distribution in Q for events in heavy nuclei (AgBr) with different numbers of h-
particles (b). The dot. Dash histogram shows interactions in H, and the solid histogram in (CNO). The dashed histogram is in
(AgBr) nuclei, and the doted histogram is for center emulsion.

A. A. El-Daiem et al. / Natural Science 3 (2011) 408-413 411
Figure 2. Variation of <nint> with nh.
excitation of the target occurs (i.e. nh = 0 and 1).
Some of the nucleons of the projectile take part in the
interactions. We also observe that the mean number of
interacting projectile nucleons increases quickly as the
value of nh increases, as expected, but attains amore or
less constant value for extreme central collisions.
4. MULTIPLICITY DISTRIBUTIONS OF
PROJECTILE FRAGMENTS
In this part 950 28Si inelastic interactions emulsion
were measured, 856 events were observed to have emit-
ted projectile fragments, 90% o the total events represent
peripheral and quasi peripheral collisions. This percent-
age is about two times larger than the corresponding one
in interaction of a- particle with emulsion 9(9) at the
same energy per nucleon.The multiplicity distributions
of the emitted charge projectile fragments are shown in
Figures 3(a), (b) for a class of events without target
fragmentation as well as sample. It can be seen that there
is no great difference between these distributions.
5. ANGULAR DISTRIBUTIONS OF
PROJECTILE FRAGMENTS
Figure 4 represent the angular distribution of Z = 1,2
and Y3 projectil fragments, in terms of cosθ where θ is
the space angle between the emitted projectile fragments
and the beam direction. It can be seen clearly that the
angular distribution becomes narrow with increase of
fragment charge Z, in all these distributions there are
pronounced peaks cos θ = 1.
6. SOME FEATURES OF EVENTS WITH
PROJECTILE FRAGMENTATION
ONLY (nh = 0)
In the 94 events satisfying the criteria nh = 0 from our
sample of 950 inelastic interactions, the projectile frag-
ments are divided into Z = 1, 2, 3, ···, 14. We explicitly in
(a)
(b)
Figure 3. The multiplicity distribution of charged projectile frag-
ments z = 1, z = 2 and z = 3, (a) Total sample; (b) nh = 0.
Figure 4. The angular distribution of z = 1, z = 2 , z = 3 for a
class of events with nh = 0.
all the reaction produced observed in these 94 events
which are ordered according to the value of Z*, the total

A. A. El-Daiem et al. / Natural Science 3 (2011) 408-413 412
charge the emitted projectile fragments. The production
frequency of event s in 28Si with emulsion interactions as
a function of Zmax, the highest charged projectile frag-
ment emitted in the interactions, is shown in Figure 5. It
should be noted that the fragmentation probability is
higher for events with Zmax = 2, 6 and 8. This is inter-
preted as due to the structure of 28Si nucleus, which is an
even-even nucleus of total spin I = 0. This means that the
nuclear structure of the projectile may play an important
role in the fragmentation process. Figure 6 represent the
frequency distribution of Z*, the total charge of the
emitted projectile fragments in an interaction for our
sample of nh =0 events the distribution is smooth and the
frequency increases with Value of Z*.
The average value of Z* equals (11.9 ± 2.1) and the
average number of produced pions charged in these
Figure 5. The production frequency of nh = 0 events as a func-
tion of Zmax the highest charge of projectile fragments in an
event.
Figure 6. The production frequency of nh = 0 events as a func-
tion of Z* the highest charge of projectile fragments in an
event.
events equals (2.2 ± 1.2). Figure 7 illustrates the rapidity
(η = − ln tanθ/2) distribution for all shower tracks emer-
ged from stars of nh = 0 in comparison with correspond-
ing distributions of shower tracks from central event, i.e.
events with Z* = 0. A pronounced rapidity gap is ob-
served between the two distributions. The distribution of
central events extends from the target fragmentation
region to the projectile fragmentation region due to the
absence of the spectator and the complete dominance of
actors. The distribution from nh = 0 events is dominated
by the projectile spectators, thus it is mainly concen-
trated in the projectile fragmentation region.
7. CONCLUSIONS
From the investigation of particles emitted from 28Si
with emulsion collisions, we can make the following
conclusions:
1) We notice that the distribution in Q depend sub-
stantially on the type of nucleus and the average total
charge for this integration of an incident 28Si nucleus in
hydrogen, light and heavy emulsion nuclei were respec-
tively 11.71 ± 0.17, 9.62 ± 0.11 and 4.68 ± 0.16.
2) We observe that the mean number of interacting
projectile nucleons increases quickly as the value of nh
increases, as expected but attains a more or less constant
value for extreme central collisions.
3) The fragmentation probability is higher for events
with Zmax = 2, 6 and 8. This interpreted as due to the
structure of 28Si nucleus, which is an even – even nu-
cleus of total spin1 = 0.
4) The rapidity distribution of shower tracks from nh =
0 events has its peak the high rapidity region, i.e. the
projectile fragmentation region, it is separated by a
Figure 7. The rabidity (η = −ln tan θ/2) distribution of shower
tracks produced from events with nh = 0 and from central
events Z* = 0.

A. A. El-Daiem et al. / Natural Science 3 (2011) 408-413 413
measurable rapidity gap from the target fragmentation
region.
REFERENCES
[1] Goldhaber, A.S. (1974) Statistical models of fragmenta-
tion processes. Physics Letters, 47, 306.
[2] Goldhaber, A.S. and Heckman, H.H. Ann. (1978)
High-energy interactions of nuclei. Review of Nuclear
and Particle Science, 28, 161.
[3] Adamovish, M.I. et al. (1977) JINR Report El-10838
Dubna.
[4] Lindstrom, P.J., et al. (1976) Cross sections for produc-
tion of stable and long-lived nuclides by high energy
spallation of iron; cosmic ray implications. Preprint LBL,
3650.
[5] Fu, H. (2002) Target fragmentation in oxygen-emulsion
collisions at dubna and SPS energies. Chinese Journal of
Physics, 40, 159-167.
[6] El–Nagy, A. (1981) Fvosccti report. NF. 81/3, submitted
to IL Nuvo Cimento.
[7] Bucharest, D. and Kosice, L. (1974) Collaboration:
Dubna preprints. JINR, PI. 687.
[8] Adamovish, M.I. M.M., AygarwaI, Y.A., et al. (1999)
(EMu – 01 collaboration), Fragmentation and multifrag-
mentation of 10.6A GeV gold nuclei. European Physics
Journal A, 5, 429.
[9] Chernov, G.M., Gulamov, K.G., Gulyamov, U.G. and
Svechnikova, L.N. (1977) Multiplicity and angular dis-
tributions of charged particles in interactions of 56Fe in
emulsion at 2.5A GeV/c. Physics. A, 280, 478.
doi:10.1016/0375-9474(77)90616-9