Calculation of (135,137,138,139)LA(N,EL) scattering differential cross sections using the interaction potentials obtained from nucleon densities

Research in the field of nuclear physics often places great importance on nuclear reaction experiments. However, nuclear reaction experiments cannot be repeated multiple times. At this point, this gap is filled by theoretical calculations and simulation studies using different nuclear models. This study focuses on the correlation between nucleon densities, folding potential behavior, and elastic scattering cross-sections. Depending on the density, data on reaction parameters and cross-sections, which give the probability of the occurrence of the nuclear reaction, have been obtained. The nucleon density distributions within the nuclei of the Lanthanum isotopes, which are part of the lanthanide group elements, have been calculated using four different models. The ground state properties of nuclei, especially nucleon densities, are generally calculated using Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) approaches with Skyrme and Gogny interactions. The nucleon densities of Lanthanum isotopes have been calculated using the Skyrme interaction with the Woods-Saxon (WS) potential in the HF approach (SHF-WS), the Skyrme interaction with the Harmonic oscillator (HO) potential in the HF approach (SHF-HO), the Skyrme interaction in the HFB approach (HFB-S), and the Gogny interaction in the HFB approach (HFB-G). The best set was determined using the experimental charge radius. Based on these density data, nuclear potential parameters were identified using the single folding method along with the appropriate volume integral. Subsequently, using these parameters, elastic scattering cross-sections were calculated and compared with values found in the literature. The impact of the SHF-WS, SHF-HO, HFB-S, and HFB-G models on the results was observed. The aim was to theoretically obtain reaction data using an appropriate model and suitable volume integral for single folding for nuclei with available nucleon density data. Based on the reaction parameters, the angular distribution of differential cross-sections was obtained.