THE INFLUENCE CHANGING OF NUCLEAR POTENTIAL ON QUASI-ELASTIC SCATTERING IN 16 O+ 160 Gd AND 12 C+ 197 Au SYSTEMS †

In this research, the effect of changing the potential depth V 0 on the Quasi-elastic scattering and barrier distribution calculations have been studied using Wood-Saxon (WS) potential for 16 O+ 160 Gd and 12 C+ 197 Au systems. The chi square ( χ 2) is applied to compare the best fitted value of the diffuseness parameter between the theoretical calculations and the experimental data. The diffuseness parameter which used in this work is to be at standard value 0.63. The χ 2 was applied to most suitable the better fitted value of the potential depth V 0 . According to the results, we noticed that some systems achieved a good match between the theoretical calculations and experimental data of Quasi-elastic scattering ( d σ qel / d σ R ) and the distribution calculations at the standard value of the potential depth or at a value lower than the standard value and no match was achieved at a value greater than the standard value of the potential depth V 0 . We conclude that the values of quasi-elastic scattering values increase when the value of potential depth decreases.


INTRODUCTION
The potential between two nuclei interaction, which comprises the short-range attractive and absorptive nuclear potentials as well as the long-range Coulomb potential, has always been a fundamental topic in nuclear physics.The Coulomb contact between two nuclei is widely understood, but describing the nuclear component is significantly more complex.Over the last few decades, the optical model potential (OMP) has been widely used to characterize the nuclear component, and numerous alternative potential forms have been proposed to replicate a large amount of nuclear reaction data [1] [2].In addition to nuclear reactions driven by light particles, the optical system may also be involved in nuclear reactions between heavy ions.The nuclear potential is often assumed to be of Woods-Saxon type, with three parameters defining it: depth, radius, and diffuseness.The diffuseness parameter defines the nuclear potential's fall-off and hence has a direct impact on the barrier width and coupling strengths, which are first order dependent on the derivative of the potential [3][4] [5].Quasi-elastic scattering is defined as "the sum of elastic scattering, inelastic scattering, and transfer reaction [6] [7].Quasi-elastic scattering is similar to the fusion process [7], which is defined as the combination of two different nuclei to generate a composite system.The Negative of the first derivative of the ratio of quasi-elastic to Rutherford cross-section, dqel/dR, with regard to the energy E, or Dqel = d(dqel/dR)/dE, is used to determine the quasi-elastic barrier distribution [8].Several studies on quasi elastic scattering have been studied by Khalid S. Jassim for some heavy ions systems [9]- [11].They demonstrated the nucleus-nucleus potential for several heavy ions by a comprehensive investigation of the surface characteristics.The nuclear potential has been described using WS, singlechannel SC, and coupled-channel CC calculations, which were between the relative motion of colliding nuclei and their intrinsic motions, and they discovered that the best fitted value of the diffuseness parameter was obtained through a coupled-channel calculation with an inert target and excited projectile for the current work.
The aims of the present work is to study the influence changing of nuclear potential (potential depth V0) on quasielastic scattering in systems 16 O+ 160 Gd , 12 C+ 197 Au at surface diffuseness parameter it determined in earlier by the method chi square, we used The CQEL program [12] which contains all orders of coupling and is the most current iteration of the computer code CCFULL, was used to calculate single and coupled channels.

THEORY
The nucleus-nucleus potential is made up of two components, the first of which is the nuclear potential V n , which may be properly and appropriately described by the other two parts of the potential between two nuclei.The form for Woods-Saxon (WS) supplied by [13]: where r represents the distance between the projectile's mass number AP and the target's mass number A T at the center of mass, and R 0 stands for the system's radius:     .The second portion, which represents the Coulomb potential V C between two spherical nuclei with uniform charge density distributions when they are not interacting, is given by [13]: where r is the distance between the centers of mass of the colliding nuclei, Z p and Z T are the atomic numbers of projectile and target, respectively.The Coulomb potential is produced when the nuclei interact, and it is determined by [14]: where the projectile and target nuclei are represented by spheres of radii R c .Two nuclei collide as a result of the nuclear intrinsic motion and the relative motion of their centers of mass, r = (r, r).The following is the Hamiltonian system [15]: where V(r) is the bare potential in the absence of coupling where V(r) = V N (r)+V c (r), H 0 (ξ) is the Hamiltonian for the intrinsic motion, and V coup is the stated coupling r stands for the center of mass distance between the colliding nuclei.The Schrodinger equation to wave functions is given by [16]: Internal degrees of freedom have a limited spin in general.the coupling Hamiltonian may be expressed as [15]: The internal coordinate is used to create the harmonics and spherical tensors, which are represented by the notations  ȓ and  ), respectively.That when it was considered in V(r), the sum of all values of excluding for λ(r) = 0.For a constant total angular momentum J and its z-component M, the expansion basis for the wave function in Eq. ( 5) is given by [15]: where l stands for the orbital, I -internal angular momenta, and   the wave function for the internal motion that is give by the equation below [15] .
The total wave function  ⇀ . has been expanded as [16]: The Schrödinger equation [Eq.( 3)] can be written as a collection of linked equations for   : [16] ħ The coupling matrix elements ;ń.´.Í  , According to [15] are as follows: Where the reduced matrix elements in Eq. ( 8) is defined as follows [15]: where  ;ń.
´.Í  are separate of the index M, the index has been suppressed as seen in Eq (11).Coupled-channels equations are the name given to the equation (10).For heavy-ion fusion reactions, these equations are usually solved using the incoming wave boundary conditions [16]. where Following the determination of the transmission coefficients Tn lIJ , the penetrability through the Coulomb barrier is provided by: In contrast to the computation of fusion cross sections, the computation of quasi-elastic cross sections often requires a large value of angular momentum in order to yield convergent results.The potential pocket at (r = r abs ) grows shallow or even disappears for such a large angular momentum.The incoming flux in Eq (13) cannot, however, be clearly identified.The quasi-elastic problem frequently uses the regular boundary conditions at the origin in order to avoid using the incoming wave boundary conditions.When using the standard boundary conditions, a complex potential VN(r) = VN0(r)+iw(r) is needed to simulate the fusion reaction.After obtaining the nuclear S-matrix in Equation (Eq11).The scattering amplitude may be calculated using The Coulomb phase shift is  .andgiven by the equation, As for  , which is the Coulomb scattering amplitude and is determined by [16]: where η is the Somerfield parameter which is given by     /ћ , and utilizing Equation ( 16), the differential cross section may be evaluated May be evaluate the Rutherford cross section.
The distribution of the barrier of fusion is defined as [15]: The definition of the total scattering distribution of the barrier of scattering D tot (E) is [15].

RESULTS AND DISCUSSION
The single-channel and coupled-channel computations were performed with the CQEL program, which is the most recent edition of the computer code CCFULL [12].To eliminate systematic errors in the current study, the chi square technique χ 2 was used as a normalizing factor between the theoretical calculation and the experimental data.These computations were performed using a WS form for the nuclear potential, which has real and imaginary components.The imagined potential was utilized to explain the relatively low internal absorption following barrier penetration.The parameters of the actual potential were investigated in order to obtain the best fit to the experimental data, which was then replicated for all interactions.

16 O+ 160 Gd System
In this reaction were processed in two cases, the first case, where both the projectile and target nuclei were considered inert (SC) at three values of the real nuclear potential (potential depth V 0 ) (58.7, 83.7 and 108.7)MeV and we considered the diffusion parameter 0.50 fm.It was previously determined by χ 2 method as the best value for matching the experimental data with the theoretical data.In the second case, the target core 160 Gd was rotation this was deduced according to the ratio   ⁄ 3.3 with a deformation coefficient of  =0.280 and  = 0.065.We used the single-quadrupole and third-octupole phonon excitation to the state 2 + (0.075263 MeV), at coupled-channel (CC).While the projectile nucleus was 16 O vibration where   ⁄ 1.49 with a deformation coefficient of  = 0.364 with singlequadrupole phonon excitation to the state 2 + (6.9171 MeV) and the radius parameter r 0 =1.2 fm By the comparing between the experimental data and the theoretical calculations, we shown that in Table (1), we notice that the better value for the quasi-elastic scattering = 0.04873 at the depth potential V 0 = 58.7MeV,which was acquired from SC data analysis where the projectile 16 O nucleus and target 16 Gd nucleus are inert.It was shown by the hard red line in

12 C+ 197 Au system
In this reaction, the results were split into two stages.In the first stage, according to single channel (SC) calculations, the projectile and target nuclei were inert at various real nuclear potentials (potential depth V 0 ) (48.8, 58.8, and 68.8) MeV, and the diffusion parameter was 0.63 fm, which had previously been determined by the chi-square χ 2 method to be the nearest value between the experimental and theoretical data.In the second stage, at coupled-channel (CC) calculations, the projectile nucleus 12 C was rotation where   ⁄ = 2.9 with a deformation coefficient of  = 0.582 with single quadrupole phonon excitation to the state 2 + (4.43982 MeV).The target nucleus was 197 Au.In the rotation state, this was deduced according to the ratio  /  / ⁄ = 3.6 with a deformation coefficient of  =-0.131,  = -0.031.We excited the state 2 + (0.077351 MeV) with single-quadrupole and third-octupole phonons.The radius parameter r 0 is equal to 1.2 fm.The comparing between the experimental data and the theoretical calculations show in Table (2), from this table, We notice that the best value for the quasi-elastic scattering = 0.0508598 at the depth potential V 0 = 48.8MeV,which was obtained from SC data analyses when the projectile 16 O nucleus and target 197 Au nucleus are inert and it was represented by the hard red line in Fig. 2.a (A).This is the curve that is closest to the experimental data curve.The batter value for the distribution D = 0.0099349 at the same depth potential V 0 .Then, by using the coupled-channel accounts with a rotating target (T) and vibrating projectile (P), the better value of the quasi-elastic scattering = 0.0059362

CONCLUSIONS
In this research we concluded the following: 1-When the value of the potential depth decreases, it leads to a decrease in the value of the nuclear potential, and thus the height of the potential barrier will increase, the Quasi-elastic scattering calculations will increase, and the potential barrier distribution curve will shift to the right.2-When the potential depth increases, the nuclear potential also increases, so the potential barrier will decrease and lead to a decrease in semi-elastic scattering calculations and a decrease in the height of the potential barrier distribution and its shift to the left.

Figure 1a .
Figure 1a.The ratio of the quasi-elastic scattering to the Rutherford cross sections for 16 O+ 160 Gd system at sub-barrier energies.Banal A and B using the single channel and coupled-channels calculations, respectively.Figure 1.b.(C, D) shows the distribution at subbarrier energies, using the single and coupled channels calculations, respectively.

Figure 1 .
Figure 1a.The ratio of the quasi-elastic scattering to the Rutherford cross sections for 16 O+ 160 Gd system at sub-barrier energies.Banal A and B using the single channel and coupled-channels calculations, respectively.Figure 1.b.(C, D) shows the distribution at subbarrier energies, using the single and coupled channels calculations, respectively.
the depth potential V 0 = 58.8MeV.It was represented by the hard green line in Fig. 2.b (B) as the figure shows.It is the curve closest to the experimental data curve, with the best value for the distribution D = 0.0230850 at the depth potential V 0 = 48.8MeV represented by the red colored curve.

Figure 2 .
Figure 2.a.The ratio of the quasi-elastic scattering to the Rutherford cross sections for 12 C+ 197 Au system at sub-barrier energies.Banal A and B using the single channel and coupled-channels calculations, respectively.Figure 2.b.(C, D) shows the distribution at sub-barrier energies, using the single and coupled channels calculations, respectively.The experimental data are taken from Ref.[17].

Figure 2 .
Figure 2.a.The ratio of the quasi-elastic scattering to the Rutherford cross sections for 12 C+ 197 Au system at sub-barrier energies.Banal A and B using the single channel and coupled-channels calculations, respectively.Figure 2.b.(C, D) shows the distribution at sub-barrier energies, using the single and coupled channels calculations, respectively.The experimental data are taken from Ref.[17].

Table 1 .
The values of the WS potential's parameters and χ 2 fitting between experimental and theoretical data for the16

Table 2 .
The values of the WS potential's parameters and χ 2 fitting between experimental and theoretical data for the12 C+ 197Au reaction.