4 Study of Isospin Effects in Heavy-Ion Collisions at Intermediate Energies …
43
observables from low to relativistic energies. The isospin degree of freedom enters
into the calculations via symmetry potential, cross sections, and Coulomb interaction.
In this model, baryons are represented by Gaussian-shaped density distributions
f i (r, p, t) =
1
π 2 2 exp
−[r − r i (t)]
2 1
2L
× exp
−[p − p i (t)]
2 2L
2
. (4.1)
Nucleons are initialized in a sphere with radius R = 1.12 A
1/3 fm, in accordance with
liquid drop model. The Gaussian Width (interaction range of nucleons) in this model
is system size-dependent and its value varies from 8.66 fm
2 for
197
79 Au to 4.33 fm
2 for
40
20 Ca. This procedure of choosing system size-dependent value of Gaussian width
"L" leads to maximum stability of the density profile of the given nucleus. Each
nucleon occupies a volume of h
3 , so that phase space is uniformly filled. The initial
momenta are randomly chosen between 0 and Fermi momentum (p F ). The nucleons
of the target and projectile interact by two- and three-body Skyrme forces, Yukawa
potential, Coulomb interactions, and momentum-dependent interactions (MDI). In
addition to the use of explicit charge states of all baryons and mesons, a symmetry
potential between protons and neutrons corresponding to the Bethe–Weizsacker mass
formula has been included. The hadrons propagate using Hamilton equations of
motion:
dr i
dt
=
dH
dp i
;
dp i
dt
= −
dH
dr i
(4.2)
with
H = =T + +V
=
i
p
2
i
2m i
+
i
j>i
f i (r, p, t)V
i j
(r
, r)
× f j (r
, p
, t)dr dr
dp dp
.
(4.3)
The baryon potentialV
i j , in the above relation, reads as
V
i j
(r
− r) = V
i j
Skyrme + V
i j
Y ukawa + V
i j
Coul + V
i j
mdi + V
i j
sym
=
t 1 δ(r
− r) + t 2 δ(r
− r)ρ
γ −1
r
+ r
2
+t 3
exp(|(r
− r)|/μ)
(|(r − r)|/μ)
+
Z i Z j e
2
|(r − r)|
+t 4 ln
2
[t 5 (p
− p)
2
+ 1]δ(r
− r)
+t 6
1
0
T 3i T 3 j δ(r i
− r j ).
(4.4)