Advances in High Energy Physics
dierent projectiles interactions with dierent targets, that is,
constituents of nuclear emulsion detector. ese calculated
nuclearreactioncrosssectionsareusedinthecalculation
ofaveragenumberofprojectileparticipants[()
proj
], target
participants [()
targ
],andbinarycollision[()
𝐶
]through the
following simple geometrical consideration []:
proj
=
𝑃
𝑃𝐴
𝑇
𝐴
𝑃
𝐴
𝑇
,
targ
=
𝑃
𝑃𝐴
𝑃
𝐴
𝑃
𝐴
𝑇
,
𝐶
=
𝑃
𝑇
𝑛𝑛
𝐴
𝑃
𝐴
𝑇
.
()
In the above equations,
𝑃𝐴
𝑇
is the total nuclear reaction
cross section of the proton with target, that is, each target
belongstothenuclearemulsiondetectorconstituent;con-
sider, as a target,
𝑃𝐴
𝑃
and
𝑛𝑛
are the total nuclear reaction
cross section of the proton with projectile and proton-proton
cross section. In addition,
𝐴
𝑃
𝐴
𝑇
is the total nuclear reaction
cross section of the projectile. e average numbers of
projectile participants [()
proj
], target participants [()
targ
],
and binary collision [()
𝐶
]are used in the shower particle
multiplicity calculation.
3. Results and Discussions
We have used the approach discussed in Section for the
calculation of total nuclear reaction cross section for proton-
emulsion (h-A),
56
Fe-Em,
84
Kr-Em,
132
Xe-Em,
197
Au-Em,
and
238
U-Em at incident engines ∼GeVpernucleon.ese
calculations have been performed in the Coulomb modied
Glauber model (CMGM) environment using parameters
related to the free space nucleon-nucleon interaction (
𝑁𝑁
)
and medium nucleon-nucleon interaction [(
−
)
𝑚
𝑁𝑁
].Taken
into consideration the calculation of total nuclear reaction
cross section (
𝑅
)is= , in the case without nuclear medium
eect. In the case with nuclear medium eect, we used =
. fm
−3
, =.fm
−3
,and=.fm
−3
, for the calculation
of total nuclear reaction cross section. Here, is the satura-
tion density of the normal nuclear matter, which ranges from
. to . fm
−3
[]. e calculated nuclear reaction cross
section with medium eects is represented as
𝑚
𝑅1
,
𝑚
𝑅2
,and
𝑚
𝑅3
.isNN interaction used in this calculation is dened
as the medium nucleon-nucleon interaction [(
−
)
𝑚
𝑁𝑁
] and
generally most of the previous calculations [, ] con-
sidered nuclear matter density =.fm
−3
only, in their
𝑚
𝑁𝑁
calculation. It is worth mentioning here that we have
performed all theoretical calculation of nuclear reaction cross
section in accordance with the zero-range approach. ese
nuclear reaction cross section values are plotted with respect
to the mass number of the dierent target of the nuclear
emulsion detector nuclei for dierent projectiles at incident
kinetic energy around GeV per nucleon in Figures and .
FromFiguresand,wemayseethatthetotalnuclear
reaction cross section with and without nuclear medium
eect increases with the mass number of target nucleus, in
case of all considered projectiles. From these Figures and ,
one can also observe that the nuclear reaction cross sections
𝑅
,
𝑚
𝑅1
,
𝑚
𝑅2
,and
𝑚
𝑅3
have very close value to each other in
case of the target mass number
𝑇
<40.etotalnuclear
reaction cross sections with medium eect,
𝑚
𝑅1
,
𝑚
𝑅2
,and
𝑚
𝑅3
,
have no signicant dependence in the mentioned range of
the nuclear matter density (). As shown in Figure , there
are many calculated/theoretical values of nuclear reaction
cross section for proton-emulsion (h-A); however, the nuclear
reaction cross sections without medium eect [()
𝑅
] have
always higher values than the nuclear reaction cross section
with medium eects. Figure shows the total nuclear reac-
tion cross section of the heavy projectiles-emulsion (A-A)
interactions for dierent projectiles as a function of the target
mass. e nuclear reaction cross section,
𝑅
,
𝑚
𝑅1
,
𝑚
𝑅2
,and
𝑚
𝑅3
values, for
56
Fe-Em and
84
Kr-Emvaluesareclosetoeach
other; however, the medium eect values for
𝑚
𝑅1
,
𝑚
𝑅2
,and
𝑚
𝑅3
aredominatingincaseof
132
Xe-Em and
238
U-Em, and some
place shows protrusions and it may be due to the variation in
the projectile mass and nuclear matter density. e nuclear
reaction cross section of
197
Au-Em shows the clear dierence
of medium eect ()
𝑅
and without medium eect and in that
graph the medium eect nuclear reaction cross section ()
𝑅
values are higher than other three values
𝑚
𝑅1
,
𝑚
𝑅2
,and
𝑚
𝑅3
.
e calculated total nuclear reaction cross section with
medium and without medium in case of proton-emulsion (h-
A)and
56
Fe-Em,
84
Kr-Em,
132
Xe-Em,
197
Au-Em, and
238
U-
Em at ∼ GeV/n are tabulated in Tables and . It is important
to note that the calculated nuclear reaction cross section
with medium eect
𝑚
𝑅2
isonlygiveninthetablebecausea
previous graph shows that
𝑚
𝑅1
,
𝑚
𝑅2
,and
𝑚
𝑅3
values are closer
to each other. It should be mentioned that the rst column
of the table refers to the constituent elements of the nuclear
emulsion, while the second and third column are related
to the mass number and root-mean-square (rms) radius of
the corresponding elements. In the present study, the rms
charge radius is not available for the three projectile nuclei,
56
Fe,
132
Xe, and
197
Au, and it has been calculated using the
following global expression []:
rms
=0.891
−1/3
1+1.565
−2/3
−1.04
−4/3
.
()
e h column referred to the chemical concentration
of the element nuclei, NIKFI (Br-) type of emulsion used for
56
Fe-Em, and
84
Kr-Em and ILFORD (G) type of emulsion
used in the case of
132
Xe-Em,
197
Au-Em, and
238
U-Em. e
sixth and seventh column referred to the calculated total
nuclear reaction cross section without medium (
𝑅
) and
with medium eect (
𝑚
𝑅2
)for interaction of proton-emulsion
(h-A) and dierent projectiles with the emulsion. e mul-
tiplied total nuclear reaction cross sections
(𝑚𝑙)
𝑅
and
𝑚(𝑚𝑙)
𝑅
were obtained from the calculated total nuclear reaction cross
sections
𝑅
and
𝑚
𝑅2
for the dierent projectiles multiplied
with individual emulsion nuclei’s (
1
H,
12
C,
14
N,
16
O,
32
S,
80
Br,
108
Ag, and
127
I) chemical concentration. e summation
value of
(𝑚𝑙)
𝑅
and
𝑚(𝑚𝑙)
𝑅
is divided by the sum of the chemical
concentration of the elements of the emulsion; one can get the