Extraction Of Reduced Distances And Coulomb Barrier Parameters From Elastic Scattering

Elastic scattering is a fundamental process in nuclear collisions,where elastic scattering data are dependent on energy,system,and angle.Nonetheless,the interaction distance D is a decisive physics quantity.The parameterisation method,which changes the energy and angle to the interaction distance,can more intuitively reflect the collision process.In bound nuclear systems,parametric methods can be utilized to combine elastic scattering data with different energies,particularly those close to the Coulomb energy region.The study of the interaction distance using parameterisation methods is crucial for a deeper understanding of different reaction angles.Currently,two typical reduced distances are being used.The first is the reduced critical interaction distanced_I,which is defined as the ratio of the elastic scattering cross section to the Rutherford value dσ_el/dσ_Rucould be set as 0.98.The second is the reduced strong absorption distance d_S,where dσ_el/dσ_Ru≈0.25,the corresponding angle isθ.The advent and development of radioactive nuclear beam facilities has enabled the experimental study of unstable nuclei,including those beyond the drip line,resulting in a large amount of new experimental data,including elastic scattering data.Currently,there is a clear pattern in the reduced critical interaction distance extracted from the scattering data,but there has been no systematic study of the strong absorption distance.In addition,studying the strong absorption distance can provide more information on the barrier radius and height,leading to a deeper understanding of the structure and reaction mechanism of peculiar nuclei.In this paper,we collected elastic scattering data from a series of different systems,including tightly bound nuclei,weakly bound nuclei and halo nuclei,and extracted the reduced strong absorption distance（d_S）and the reduced critical interaction distance（d_I）from the parameterisation of experimental elastic scattering angular distribution data to explore their systematic laws.This paper presents the main results of a study that extracted the d_Iand d_Sfrom elastic scattering data of various nuclear systems,including tightly bound nuclei,weakly bound nuclei,and halo nuclei.The study found that the average values of d_Iand d_Sfor halo nuclei are significantly larger than those for tightly bound and weakly bound nuclei.This is due to the long-range component of the Coulomb or nuclear potential of the target nucleus,which leads to large deformation or breakup of the valence nucleons weakly bound in the nucleus during the reaction process,reflecting the long tail property of the halo nuclear wave function.The overall effect is to reduce or eliminate the Coulomb rainbow and globally suppress the elastic scattering angular distribution.The comparison shows that the value of d _Ifor halo nuclei systems is significantly larger than that for tightly bound and weakly bound nuclei systems,indicating that the characteristics of halo nuclei may be more pronounced in the surface region.In contrast,d_Sremains unchanged with increasing system size,and a good linear relationship between d_Sand the system size was established,which can be used to estimate the Coulomb barrier radius.The study also extracted the barrier height V_B,which was found to have rules consistent with other theoretical barrier laws extracted from fusion reactions.These findings provide new information for predicting potential barriers and are of great importance for understanding the structure and reaction mechanisms of heavy ion nuclei.