Puzzle of the Core–halo (\(^{9}\)Li–\(^{11}\)Li) Nuclei at Various Incident Energies and Nuclear Matter Radii

This work is devoted to study the structural and reactional properties of the prototypical example of the core–halo ( \(^{9}\) $_{}^9$ Li– \(^{11}\) $_{}^{11}$ Li) nuclei. The halo nucleus \(^{11}\) $_{}^{11}$ Li consists of a central core of \(^{9}\) $_{}^9$ Li surrounded by 2n–halo with very low separation energy \(\varepsilon _{2n}\) ${\epsilon }_{2n}$ = 378±5 KeV, reflecting the huge calculated root mean square radius value 4.11 fm. The elastic scattering potential at low and intermediate incident energies was a puzzle for decades of research on nuclear reactions. Single– and double–folding potentials describing the elastic scattering of \(^{11}\) $_{}^{11}$ Li from the proton and \(^{12}\) $_{}^{12}$ C, based on different effective interactions were constructed. Systematic comparison between the considered methods in terms of the renormalization coefficients is done. Based on the considered methods, the obtained potentials doesn’t need any renormalization in case of using real folding potential together with phenomenological imaginary potential and merely need renormalization almost approach unity in case of using complex folding potential to fit the total reaction cross sections and angular distributions along the measured data. Furthermore, correlations between real volume integrals and nucleon incident energies for the neutron drip–line \(^{11}\) $_{}^{11}$ Li nucleus were proven along the whole scale of energies.