Ex) Article Title, Author, Keywords
New Phys.: Sae Mulli 2022; 72: 893-899
Published online December 31, 2022 https://doi.org/10.3938/NPSM.72.893
Copyright © New Physics: Sae Mulli.
Yong Joo Kim*
Department of Physics, Jeju National University, Jeju 63243, Korea
Correspondence to:*E-mail: email@example.com
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The differential cross sections of 240 MeV 6Li elastic scattering on 24Mg, 28Si, 40Ca, 58Ni, 90Zr, and 116Sn targets are systematically analyzed using the eikonal model based on the Coulomb trajectories of colliding nuclei. The model calculations successfully reproduced the structure of the elastic scattering cross sections, and provided fairly good description of the experimental measurements. The oscillatory patterns shown in the experimental elastic angular distributions are well explained in terms of the strong interference between the near- and far-side scattering amplitudes. The reaction cross sections obtained from the analysis of 6Li elastic scattering on various targets from 24Mg to 116Sn are found to have linear dependence on the
Keywords: Elastic scattering, Eikonal model, Diﬀerential cross section, Reaction cross section, 6Li + nucleus
Most measurements in heavy-ion elastic scattering is the differential cross section. This physical quantity is calculated from the elastic scattering amplitude. The phase shift is an important factor in determining the scattering amplitude. The eikonal model[1-3] has been used for describing the high energy elastic scattering between heavy-ions. The basic assumption of this model is that its classical trajectory is little deflected from a straight line because the incident energy is sufficiently high. The eikonal phase shift is obtained from the integral equation by further approximating the Wentzel-Kramers-Brillouin (WKB)results. The only input to calculate the eikonal phase shift is the optical potential, and its parameters are usually determined by the
In the recent past, the elastic differential cross sections of 6Li projectile at 240 MeV have been measured[12-15] on 24Mg, 28Si, 40Ca, 58Ni, 90Zr, and 116Sn targets. Most theoretical studies employed optical and folding models for analyzing these elastic data. It is interesting to analyze the experimental measurements for 6Li + 24Mg, 28Si, 40Ca, 58Ni, 90Zr, and 116Sn elastic scatterings at 240 MeV by using the eikonal model based on the Coulomb trajectory of colliding nuclei. The purpose of this paper aims at a systematic analysis of 240 MeV 6Li elastic scattering from six different targets having various mass from 24Mg to 116Sn. The main points which will be of concern are the followings : (1) the best fit to the experimental data using the
This paper is organized as follows : In the next section, we briefly outline the theory related with the scattering amplitude and eikonal model. The results obtained from eikonal model calculation and their discussion are presented in section III. The concluding remarks are given in section IV.
The differential cross section for elastic scattering between two non-identical spin zero nuclei is given by the following equation :
The elastic scattering amplitude
Following the formalism of Fuller, the elastic scattering amplitude is decomposed in the near-side (
In the above equation,
In this section, the eikonal model mentioned in previous section is applied to the systematic analysis of 240 MeV 6Li elastic scattering from six targets (24Mg, 28Si, 40Ca, 58Ni, 90Zr, and 116Sn). The only input required for the eikonal model calculation is the nuclear potential. We use the optical Woods-Saxon squared potential given by Eqs. (9) and (10) as the nuclear potential. The parameter values of the nuclear potential are determined from the
Qualitative features of the
In order to examine the presence of nuclear rainbow, we plotted the deflection function
In a rainbow situation, the strong nuclear force attracts projectiles toward the scattering center and deflects them to negative scattering angles. As shown in Fig. 4, the
In Table 2, the physical quantities extracted from eikonal model analysis are collected. The
The reaction cross section
Within the framework of eikonal model,
In Fig. 5(a), the
In this paper, we systematically analyzed the differential cross sections for 240 MeV 6Li elastic scattering from six targets (24Mg, 28Si, 40Ca, 58Ni, 90Zr, and 116Sn) using the eikonal model based on the Coulomb trajectories of colliding nuclei. We have shown that the eikonal model provides a satisfactory account of elastically measured data of all 6Li + six targets scattering systems at 240 MeV. In this study, the calculated results yielded a successful reproduction of the elastic angular distribution structure, and gave fairly good quality of fit to the experimental measurements over the whole angles covered by the data for a wide mass range of target nuclei. Qualitative understanding of the elastic cross section can be gained by the near- and far-side decompositions of the elastic scattering amplitude. The strong interference between these two components of the scattering amplitude resulted in the oscillatory pattern appeared in the
The deflection function has a negative maximum value for each scattering systems, which indicates evidently a presence of an nuclear rainbow. The magnitude of nuclear rainbow angle became larger as the target mass increased. The critical angular momentum
Finally, our results confirm that the eikonal model calculation successfully reproduce the elastically measured scattering data of 6Li projectile on six targets having various mass from 24Mg to 116Sn at 240 MeV. Therefore, we can see that the eikonal model is a useful tool to be used in the analysis of the nucleus-nucleus elastic scattering data
This work was supported by the research grant of Jeju National University in 2022.