Alpha elastically scattered by light nuclei using semi-microscopic and full-microscopic method

ABSTRACT


Introduction
The study of alpha particle scattering on target nuclei like 6 Li, 7 Li, 9 Be, and 11  (1) In the full microscopic FM method, SPP was taken as a real and imaginary part of optical potential as: (2) Within this model, the nuclear interaction is connected with the folding         It also considers the relative speed between levels and the speed of light to overcome the Pauli effect through SPP.
This potential gave good results at alpha particle energies around 50 MeV, approximately with all nuclei.At higher energy, the fitting is good for forward angles only.The relations between J w , σ r , N r , W s and a s for the α+ 6,7 Li, α+ 9 Be, and B using the double folding model represents a sophisticated approach to understanding nuclear interactions at a microscopic level.The double folding model, based on the effective nuclear interaction potential, offers a powerful tool for investigating the elastic scattering of alpha particles on various nuclei.This model considers the nuclear densities of both the projectile (alpha particle) and the target nuclei, along with the effective nucleonnucleon interaction potential, to simulate the scattering process accurately.The folding model is one of the most widely used methods for determining the nucleus-nucleus interaction potential.There are many previous researches were studied alpha elastically scattered on light nuclei (Qaim et al., 2016The elastic scattering of alpha particles by light nuclei has been studied using a double folding model that employs SPP as the real part of the optical potential.This model incorporates the concept of Pauli nonlocality, which accounts for the exchange of nucleons between the target nuclei and the projectile alpha particles.The choice of target nuclei, including 6 Li, 7 Li, 9 Be, and 11 B for alpha particle scattering studies using the double folding model is motivated by their unique nuclear properties and relevance in nuclear physics research.These nuclei exhibit distinct characteristics that make them ideal candidates for investigating the elastic scattering of alpha particles and extracting valuable information about nuclear structure and nuclear reaction mechanisms (Alvarez et al., 2003; Chamon et al., 2002).This work aims to investigate the differential crosssections of alpha elastically scattered by light nuclei at low energies using semitheoretical model used in nuclear physics to describe heavy-ion nuclear interaction.It has been successful in explaining various aspects of heavy-ion scattering, including elastic and inelastic interactions.The model was developed by a team of researchers at the University of São Paulo and has been widely used in the field of nuclear physics.The SPP is based on a double folding potential, which is a mathematical representation of the interaction between two nuclei.This potential is calculated by folding the density distributions of the two nuclei with the nucleon-nucleon interaction.The model includes relativistic effects and is capable of describing the energy dependence of the optical potential, which is essential for understanding heavy-ion scattering.The SPP has been applied to a wide range of heavy-ion systems and has been shown to be effective in describing the elastic and inelastic scattering of various nuclei.It has also been used to study nuclear fusion and the properties of dense matter.The model continues to be an important tool in nuclear physics research, particularly in the study of heavy-ion interactions and nuclear reactions (Chamon et al.used to calculate the cross-section using double folding.It is based on SPP as the real part of the optical potential.The model has been used to calculate the total reaction cross-section (Chamon, 2007; Amer et al., 2021).In the semimicroscopic SM method, SPP was used as a real part of the optical potential whereas the imaginary part ( ) was used Woods-Saxon form as:

FRESCO
v is the local relative velocity between the interacting nuclei and c is the speed of light.The velocity dependence results from the effects of the Pauli non-locality, which comes from nucleon exchange between the alpha and the target.The relative velocity is given by (Chamon, 2007): by an iterative process.The folding potential V F (r) is calculated according to the relationship (Alvarez et al., 2003) : is a weakly bound nucleus and has two configurations, 3 He+ 3 H and d+α (Amar et al., 2022).Thus, for obtaining the information of the 6 Li configuration, alpha is used as a projectile.In our study, we compared the experimental data and the theoretical predictions for Alpha elastically scattered on 6 Li at the 29.4,50.5, 59.0, 104.0, and 166.0MeV energies are shown in Fig. (1).The potential parameters have been modified to reproduce differential cross-sections which are listed in Table (1).In the semi-microscopic model, the real part of optical model was taken as a Sao Paulo potential whereas the imaginary part was taken as Woods Saxon.The present analysis was performed using FRESCO (Thompson, 2006) with the parameters of the imaginary surface part.In the OM calculations, the Coulomb radius r c =1.3 fm was taken.To obtain the best fit of the calculations with the experimental data, the normalization factor N r and the imaginary surface potential parameters(W s and a s ) must be adjusted where r s = 1.292 fm was fixed.In the case of SM calculations (red lines), the N r was in the range of 0.9 -1.1.The reaction crosssection σ R has been calculated using Fig. (1): Alpha elastically scattered by 6 Li at 29.4 MeV(Matsuki, 1968), 50.5 MeV(Bragin et al., 1986), 59.0 MeV(Foroughi, et al., 1979), 104.0 MeV (Hauser et al., 1969), and 166.0 MeV(Bachelier et al., 1972) where the squares represent the experimental data, solid lines represent semi-microscopic model and dash-dot lines represent full microscopic model Fig. (3) based on the potential parameters, which are listed in Table(3)where r s =1.306 fm.To obtain a fit of the calculations with the experimental data, the N r and the imaginary potential parameters must be adjusted.These parameters were changed freely until the best fit was obtained.The N r factor was in the range of 0.9 -1.2.At 45.0 MeV, the calculated reaction cross-section gives its maximum value while the J w gives its minimum value.In the full microscopic method, the parameters N i and N R are varied freely until they obtain the best fit, as presented in Table(3).It should be noted that the FM analysis is satisfactory, especially at higher energies, as shown in Fig. (3).

Table ( 1
): Double folding of alpha elastically scattered by 6 Li using fresco code Alpha elastically scattered by 7 LiThe study of the 7 Li nucleus is of particular interest because it is an isotope

Table ( 2
): Double folding of alpha elastically scattered by 7 Li using fresco code

Table ( 3
): Double folding of alpha elastically scattered by 9 Be using fresco code

Table ( 4
): Double folding of alpha elastically scattered on 11 B using fresco code