The Experimental And Systematic Optical Potential Studies For Elastic Scattering Of Radioactive Ions

With the constructions and operations of large research facilities and the contin-uous developments of theoretical studies,the exploration of the structure and reaction mechanisms of far from the-stable line nuclei has gradually become one of the most widely researched objects in nuclear physics,and the elastic scattering,as one of the fundamental reaction channels in the nucleus-nucleus collisions,plays an important role in the intrinsic properties of nuclei,nucleus-nucleus interactions and their isospin de-pendence.At present,the experimental studies of the elastic scattering of radioactive nuclei from heavy targets mainly focus on the reaction energies around the Coulomb barrier,however,elastic scattering data at higher energies as well as those of complete isotope chains are of significance in systematically studying the dependence of elastic-scattering angular distributions on the incident energies and type of valence nucleon.Therefore,the elastic scattering experiments of¹¹C+²⁰⁸Pb at 275 Me V,¹³C+²⁰⁸Pb at 340 Me V,and¹⁴C+²⁰⁸Pb at 294 and 342 Me V were carried out at the Radioactive Ion Beam Line in Lanzhou（RIBLL-1）.In these experiments,two thin double-sided sil-icon strip detectors（DSSD）with 16 strips on both sides were placed upstream from the target to determine the position and direction of the incident particles.After the target,a detector array consisting of four sets ofΔE-E telescopes[DSSD+silicon detector（SD）]was used to identify the scattered particles and measure the position and energies of them.With theΔE-TOF particle identification method,the statistical distribution of the scattered particles were extracted in the offline data analysis,and the one of Ruther-ford scattering process was obtained by Monte Carlo simulation.The ratio of the above two statistical distributions at the corresponding angles is the elastic-scattering angular distributions of^11,13,14C on the²⁰⁸Pb target.The elastic scattering angular distributions of¹¹C,¹³C and¹⁴C,as weakly bound nuclei,show typical Fresnel-type distributions,and their Coulomb rainbow is not significantly suppressed,which is similar to the re-sults of proton-rich nuclei⁷Be,⁸B and⁹C nuclei previously measured by our research group,and significantly different from neutron-rich nucleus¹¹Be,suggesting that both the nucleon separation energy and the valence-nucleon type have important effects on the elastic-scattering angular distributions.In the further physical analyses（elastic scattering,breakup,and transfer reactions,etc.）of experimental data for^11,13,14C projectiles together with those of⁸B,⁹C,and11Be measured by our group previously,the information on nuclear many-body dynam-ics carried by experimental data can be obtained from relevant calculations and analyses with a reliable optical model potential.The systematic potential,with relatively smaller errors in mass and energy interpolation and extrapolation processes,is an important the-oretical tool for performing the optical model analysis and coupled channel calculations at a wider range of mass and energy.The existing systematics mainly focus on the light nuclei with<8,while there is a relative lack of potentials for heavier projectiles to satisfy the needs of experimental studies.In 2013,a new systematic nucleus-nucleus single-folding model potential（SNP）has been developed that can better reproduce the elastic-scattering and total-reaction cross sections for nuclei with?40,but does not reasonably described experimental data at lower energies due to its parameters being only applicable to incident energies above 10 Me V/nucleon.The present work is based on the nucleon-nucleus interaction given by the Bruyères Jeukenne-Lejeune-Mahaux（BJLM）model,and the optical model analysis of the elastic-scattering data of⁹Be projectile on different targets is performed within the framework of the single-folding model to extract a set of systematic potential parameters in the lower energy region.In the analysis,the renormalization factors_rand_iof the real and imaginary potentials are constrained using the experimental elastic-scattering an-gular distributions with the separate fitting and the simultaneous fitting methods,and the energy dependence of_rand_iis extracted by applying a simple linear functional form.The obtained results are further combined with the parameters of SNP to extend the energy range of applicability of potential parameters and arrive at an updated sys-tematic nucleus-nucleus potential（USNP）with the range of 16??209,V_B-100Me V/nucleon.It is found that the calculations using USNP can better fit the low-energy elastic-scattering data of^6,7Li,⁸B,⁹C,^9,10Be,^13,14C,^16,18O and other nuclei with?40 while remaining the prediction power of SNP for differential cross sections at higher energies and successfully predict the total-reaction cross sections in the low-and medium-energy regions.In addition,the potential depths corrected by new renormal-ization factors allow the volume integrals of the real and imaginary parts of potential to better satisfy the dispersion relation.Compared with a similar international work of the same time,Sao?Paulo potential version 2（SPP2）,both have comparable capabili-ties of data description at lower energies and the differential cross sections predicted by USNP are much closer to the experimental data（with smaller²values）than those predicted by SPP2 at higher energies(_lab>150 Me V).By discussing the potential depths and shapes of USNP and SPP2,it is found that the elastic-scattering data in the low-energy regions do not constrain the potential parameters well.The sensitivity of the total-reaction cross sections to the potential depths and radii was examined,confirming that the optical model potential radii is the main determinant of the elastic-scattering angular distributions,which explains the phenomenon that significantly different op-tical potentials can better describe the same experimental data.The present potential,USNP,is applied to the theoretical analyses of the elastic scattering data of^11,13,14C+²⁰⁸Pb at energies around six times the Coulomb barrier and accounts well for the corresponding data.In summary,the scattering data obtained in these experiments not only is used to study the nuclear mechanisms of the three carbon isotopes,but also verify the prediction-power and applicability of the present systematics,which in turn lays the foundation for the subsequent related studies.The optical model analysis pro-vides a reliable set of nucleus-nucleus interactions for future experimental studies of radioactive-ion from medium mass or heavy targets and their related calculations.