ABSTRACT
In this study the calculations of the total fusion reaction cross section?fus and the fusion barrier distributionDfus
have been performed for the systems 17F + 208Pb and 15C + 232Th which involving halo nuclei by using a
semiclassicalapproach.Thesemiclassical treatment is comprising the WKB approximation to describe the relative motion
between target and projectile nuclei, and Continuum Discretized Coupled Channel (CDCC) method to describe the
intrinsic motion for both target and projectile nuclei.For the sake of comparsion a full quantum mechanical have been
preforemd using the (CCFULL) code. Our theorticalrestulsare compared with the full quantum mechanical calculations
and with the recent experimental data for the total fusion reaction and the fusion barrier distribution. The comparsion with
experimental datashows that the full quantum mechanical calculations are shows more stability in the calculations of the
total fusion reaction cross section especially around the Coulomb barrier and also for the clalculation of the fusion barrier
distribution, therefore the semiclassical approach need to be improved especially in the region around the Coulomb
barrier.

1 INTRODUCTION
The interactions between two nuclei can lead to a variety of processes. In a semiclassical picture, it is customary to
use the impact parameter, or relative angular momentum, to distinguish between compound nucleus reactions (The fusion
reactions) and direct reactions; the latter take place for values of the impact parameter corresponding to grazing
trajectories, the former occur for more central interactions. In between, deep inelastic reactions show intermediate
behavior. The relative importance of the different mechanisms depends on a number of factors; among these, a very
important role is played by the kinetic energy and its value with respect to the amount of Coulomb repulsion between the
nuclei for a given trajectory (the ‘Coulomb sub-barrier’). At relatively high energies with respect to the barrier it is possible
to use geometrical models of the reaction process to provide independent descriptions of individual mechanisms: as,
Glauber models [1] for direct reactions, the onedimensionalsub-barrier penetration model for fusion [2].
The kinetic energy is small compared to the Coulomb sub-barrier height this independence no longer holds: the
behavior of a particular process can no longer be considered separately from the others. In scattering theory this is
expressed by the concept of coupling of the different reaction channels. The total wave function of the scattering problem
contains the entrance channel and all possible exit channels; the Hamiltonian connects these states by means of potential
terms, for example potentials that can create an excitation. For small kinetic energies, the contributions of these terms
become significant in the determination of the wave function of each channel. The effect of the couplings is
wellestablished, and visible on both the elastic scattering [3] and fusion reaction cross sections [4,5].
The aim of the presentstudy is to employ a semiclassical approach by adopting Alder and Winther theory originally
used to treat the Coulomb excitation of nuclei which is called Continuum-Discretized Coupled Channel (CDCC) method in
which Quantum and semiclassical approach have been implemented to calculate the total fusion reaction cross section
?fus and the fusion reaction barrier distribution Dfus for the systems involving light halo nuclei 17F + 208Pb and 15C + 232Th.
by using the FORTRAN codenamed (SCF) and compare our results with the full quantum mechanical calculations using
the coupled channel calculations (CC) with all order coupling using the computer code (CCFULL) and with the available
experimental data of complete fusion.

4 RESULTS AND DISCUSSION
The total fusion reaction cross section ???????? , and the fusion reaction barrier distribution ???????? have been calculated
by using a semiclassical treatment adopted the Coulomb excitations calculations from Alder and Winther (AW), and
implemented in a FORTRAN codenamed SCF for the systems 17F + 208Pband 15C + 232Th. For the sake of comparison with
other theoretical models using full quantum mechanics with all order coupling channels, we had performed calculations
using the famous fusion reaction code CCFULL for the same studiedsystems. The sameAküz-Winther potential
parameters, which used in the present calculations for two programs codes,aredisplayed in table 1.
Table 1. The parameters of Aküz-Winther potential along with terms of the Coulomb barrier: height,
radius, and curvature, Vb, Rb, and ??, respectively.
The fusion systems V0 (MeV) a0 (fm) r0 (fm) Vb (MeV) Rb (fm) ?? (MeV)
17F + 208Pb 80.1 0.66 1.2 83.9 11.91 4.9
15C + 232Th 80.5 0.65 1.21 59.2 12.41 4.3

Our semiclassical and full quantum mechanical calculations for 17F + 208Pbsystem are shown in figure 1. The
semiclassical calculations for the total fusion reaction cross section ???????? and the fusion reaction barrier distribution
????????without including the coupling channels effects between the elastic channel and the continuum are represented by the
dashed blue curve, while the calculations in case of including the coupling effects are represented by the solid blue
curve.The full quantum mechanical calculations using CCFULL code are presented by dashed and solid black curves for
the case of no-coupling and coupling included, respectively. The full quantum mechanical coupled channel calculations
performed by considering vibrational deformations for target nucleus with deformation parameter??0 = 0.157, adopted from
Ref. [15]withconsidering double phonon excitation, and the projectile nucleus taken to be inert.
The arrow in figure 1 and 2 represents the position of the Coulomb sub-barrier ???? . In the case of no-coupling both
semiclassical and full quantum mechanical calculations underestimate the experimental data of complete fusion reaction
cross section below the Coulomb sub-barrier, the inclusion of the coupling in both calculations shows that the the full
quantum mechanical are more closer than semiclassical treatmentones in comparison with the experimental data of
complete fusionbelow the Coulomb sub-barrier. The comparison of the calculated fusion reaction barrier distribution ????????
for both semiclassical and full quantal mechanical ones along with the experimental data of complete fusionextracted
using thethree-point difference method is shown in panel (b) in Figure 1.
The semiclassical and full quantum mechanical calculations for the total fusion reaction cross section ???????? and the
fusion reaction barrier distribution ???????? for 15C + 232Th system both with and without including the coupling effects is
presented in Figure 2.The semiclassical and fullquantum mechanical calculations without introducing the coupling
effectsrepresented by the dashed curves in blue and black, respectively.While,the calculations taking into consideration
the coupling effects represented by the solid blue and black curves, respectively. The coupling effect is taken between the
elastic channel and the continuum in our semiclassical calculations, while the coupling is considered as rotational
deformation in target nucleus with deformations parameters ??2 = 0.207 , and ??4 = 0.108adopted from Ref. [15], and
considered inert projectile nucleus. The semiclassical calculations including the coupling effects enhanced and brings the
calculated ???????? to the experimental values of complete fusion below the Coulombsub-barrier marked by the arrow. The
semiclassical method shows unstability around the Coulomb barrier even it reproduce the experiment, but still the
CCFULL calclations are more stable and reproduce the data better than the semiclassical approach.

5 CONCLUSIONS
The coupled channel effect between the elastic channel and the continuum is found to be very essential in the
semiclassical calculations which leads to improvement in the total fusion reaction cross section ???????? and the fusion
reaction barrier distribution ???????? around and below the Coulomb sub-barrier and brings the theoretical results closer to the
experimental data of complete fusion. The inclusion of the coupling channel effects by considering the target
hasrotationaldeformationin 17F + 208Pbsystem, and vibrationaldeformation with douple phonon excitation in 15C +
232Thsystem,enhances the full quantum mechanical calculations around and below the Coulomb sub-barrier. The
semiclassicaltreatment used in the present work shows unstability in the calculations around the Coulomb barrier, even if it
is able to reproduce the experimental data and still the semiclassical approach need more improvement especially around
the Coulomb barrier. This work can be extended to study more systems involving halo nuclei and medium and heavy
system to confirm it s validity to fusion reaction calculations using our semiclassical approach.