INTRODUCTION
Recently, extensive theoretical calculations have been done to explain the resonant structures, which usually observed in heavy ion transfer reaction, following the microscopic DWBA calculation (Farra, 2003a). The differential crosssection of two nucleon transfer of heavy ion reactions has been studied (Farra, 2003b) as a single directstep process. The differential cross section (ElAzab and Hassanain, 2004) of ^{6,7}Li elastic and inelastic scattering ^{12}C, ^{28}Ni targets in the energy range 1225 MeV were analyzed the coupledchannels mechanism. Nucleon pickup and striping reactions have been analyzed in terms of direct surface transfer reactions (Memaz et al., 1985) to continuum states. Multinucleon transfer reactions induced by heavy ions have been used in various contexts to study aspects of nuclear structure such as two particles (Tamura, 1974) and four particle (Lemaire, 1973) correlations. The angular distributions have been measured for ^{7}Li + ^{54}Fe at 48 MeV using finiterange DWBA calculations, employing real and imaginary Wood Saxon optical potential (Kemper et al., 1982) and have been reproduced reasonably well at energies below and above Coulomb barrier using the coulomb distorted Wave Born approximation (Lilley et al., 1987).
In the present study, the differential cross section of ^{16}O(^{6}Li,α)^{18}F heavy ion reactions with twoparticle transfer have been calculated. The direct transfer reaction is investigated using the exact finiterange DWBA calculations as a singlestep process. The optical potential is taken to have real and imaginary Gobbi potential (Kondo and Tamura, 1984) to generate the initial and final distorted waves.
FINITERANGE DIFFERENTIAL CROSS SECTION
The explicit transition matrix element of the T(A,C)R reaction with a transferred particle x is evaluated following the DWBA calculations. Therefore, the complete reaction transition T_{fi} (Farra, 2003c) is taken to have the following expression
Where and
are
the ingoing and outgoing distorted wave functions, φ’s are the bound
state wave functions and V_{ij }is the interaction potential between
the particle i and j, while, is
the optical potential generating the distorted waves. The differential cross
section for heavy ion reaction with particle transfer have been calculated in
terms of one step DWBA calculations (Farra, 2003c) and described by clear form,
which is given by
Where m_{ij }is the reduced_{ }mass_{ }of the particles
i and j, K_{i} and K_{f} are the wave vectors in the initial
and final channels, respectively, while J_{i} and μ_{i}
are the respective spin angular momenta of the particle i and its magnetic projection
on the zcomponent.
NUMERICAL CALCULATIONS AND RESULTS
Here, numerical calculations are carried out to find the angular distributions for ^{16}O(^{6}Li,α)^{18}F heavyion reactions, which proceed via direct two nucleon transfer processes at 34.0 and 48.0 MeV incident energies. In first set of calculations, the optical potentials describe the scattering of the heavy ions in both of the initial and final channels are taken to have Gobbi potential forms. These forms are used for the real and imaginary distorting potential in the initial and final channels together with a Coulomb potential. The nucleusnucleus interaction is expressed as:
Where V_{o, }R_{V} and a_{v} are the strength, radius and diffuseness of the real potential, while W_{o} and W_{E} describe an energy dependent absorptive potential, E_{c.m} is the center of mass energy of the ^{16}O + ^{6}Li channel, R_{W} and a_{w} describe the imaginary part and V^{C}(r) is the Coulomb potential due to a uniform sphere of radius R_{C} = r_{C}A^{1/3} and is given as
where r_{C} = 1.35 fm
The nuclear interactions describing the particlenucleus bound states are represented
by Yukawa potentials (Ass’ad, 2002).
Where R_{i }and R_{j} are the radii of the i and j nuclides
given by r_{o}A^{1/3}, a is the diffuseness of the potential.
represents
the interaction strength represents
the interaction strength given as:
The parameter C (i) which is appeared in Eq. 3 has the form
and another similar expression for C (j), while the bound state wavefunctions
for both initial and final channels are expressed to have Morinigo wavefunctions
(Ass’ad, 2002), with parameters determined to reproduce the particleparticle
binding energies which is given by:
Where
is
the binding energy.
The different parameters of the interactions are: V_{o} = 159.0 MeV,
W_{o }= 8.6 MeV, r_{o} = (1.18, 1.2, 1.25 fm), a = 0.65 fm and
the surface symmetry constant K_{S} = 3.0 which are chosen to fit the
static properties of nuclei. In general, the present spectroscopic factor is
extracted from the reaction, that is:
Where N is normalization factor for the reaction, i_{ }and j are the target spin and spin of the final state, respectively.
The parameters used above are found to reproduce the forward angle data reasonably
well and fair at the large angle. Therefore, the present optical potential obtains
the best fit to the data. The results obtained for the differential crosssections
at 0.34 MeV incident energy and r_{o} equal to 1.18 is shown in Fig.
1 by the solid with our calculations and the dash curve are compared with
previous calculations (Farra, 2003b) who used real and imaginary Wood Saxon
and Jdependent, respectively (WS+JD) optical potential (dashed) and experimental
data dots (Cook et al., 1984). In the same incident energy, the effect
of r_{o }is shown in Fig. 2.

Fig. 1: 
The differential crosssection of the ^{16}O (^{6}Li,^{
}α)^{ 18}F twonucleon transfer reaction (^{1+},
g.s.) at 34.0 Mev incident energy. The solid curve is the present calculations
using Gobbi potential, the dashed curve is the previous work taken from
(Farra, 2003b) and the dots are the experimental data taken from (Cook et
al., 1984) 

Fig. 2: 
The differential crosssection of the ^{16}O (^{6}Li,^{
}α)^{ 18}F twonucleon transfer reaction (^{1+},
g.s.) at 34.0 Mev incident energy using Gobbi optical potential, for different
r_{o}. The experimental data has been taken from (Cook et al.,
1984). 
At incident energy 0.48 MeV is shown in Fig. 3, the differential
crosssections given by the solid and dash curve are compared with previous
calculations (Cook et al., 1984) who used real and imaginary Wood Saxon
(WS+WS) optical potential (dashed) and experimental data dots (Cook et al.,
1984).

Fig. 3: 
The differential crosssection of the ^{16}O (^{6}Li,^{
}α)^{ 18}F twonucleon transfer reaction (^{1+},
g.s.) at 48.0 Mev incident energy. The solid curve is the present calculations
using Gobbi optical potential, the dashed curve and the dots are previous
work and the experimental data, respectively, are taken from (Cook et
al., 1984) 

Fig. 4: 
The differential crosssection of the ^{16}O (^{6}Li,^{
}α)^{ 18}F twonucleon transfer reaction (^{1+},
g.s.) at 48.0 Mev incident energy. The solid curves is the present calculations
using Gobbi potential (the differential crosssection have been multiplied
by 0.4 to fit the forward and backward angles), the dashed curve and the
dots are previous work and the experimental data, respectively, are taken
from reference (Cook et al., 1984) 
It is found our calculation is a little well at all the range of angles, to
get very well results we multiply the differential cross section by the factor
0.40 as shown in Fig. 4.
DISCUSSION
In this study, the^{ 16}O(^{6}Li,α)^{18}F heavy
ion reactions with two nucleon transfer have been studied using the DWBA calculations
as a single step process. The numerical calculations are carried out to find
the angular distributions of this reaction at incident energy 34.0 and 48.0
Mev. In Fig. 1, it seen that at large angle with Gobbi at
34.0 MeV was noticeably nearly good and significantly better than the previous
work. It is clear_{ }that the present data are good against the different
of the parameter r_{o}, we found the small values of r_{o }is
better fit for the forward angles but the large values of r_{o} is better
fit for backward angles as shown in Fig. 2. The spectroscopic
factor in the previous work is 0.77 but in our calculation is 0.78.
The use of 0.48 MeV shown in Fig. 3, WoodSaxoon potential
is better than Gobbi potential at forward angles, but at back angles Gobbi potential
gives better result than WoodSaxoon potential. If we multiply the differential
cross section by 0.4, the result is behaves very well for the whole range. Finally
the spectroscopic factor for this reaction at 0.48 incident energy is 0.84.
In conclusion, the use of Gobbi optical potential leads to a reasonable results
which are better than (WSWS) and (WSJD) potentials at large angles.