## 5 Conclusions
\({}^{182,184}\)W (open shell)  
* These isotopes may exhibit collective behaviors from the shell model perspective (e.g., surface vibrations). * Shell model: These collective modes cause oscillations or resonance structures in the angular distribution. * OMP: Does not include these effects \(\rightarrow\) fine structures in angular distributions cannot be explained, only average behavior is captured. \({}^{186}\)W (near closed shell)
* This isotope has a \"stiffer\" potential, with less absorption and smoother scattering. * Shell model: Surface collective effects are weak, and transitions between levels are limited. * OMP: The average parameterization generally fits better here, but shell closure effects at low energies can still make a difference. When calculating densities using the SHF-WS method, nucleon configurations are assigned according to the shell model. In the SHF-WS approach, placing protons and neutrons into energy levels based on the shell model allows for more precise calculations. Additionally, the density distribution having a WS form is also effective (Equation (3)). The parameters \(r_{v}\) (the radius parameter of the real potential) and \(a_{v}\) (the diffuseness parameter) used in the OMP generally yield results that are in good agreement with experimental scattering data. This outcome stems both from the intrinsic structure of the OMP and the physical significance of these parameters, and it can also be understood in relation to the shell model. Why are \(r_{v}\) and \(a_{v}\) consistent with experimental data? * \({}^{186}\)W (near closed shell)
* This isotope has a \"stiffer\" potential, with less absorption and smoother scattering. * Shell model: Surface collective effects are weak, and transitions between levels are limited. * OMP: The average parameterization generally fits better here, but shell closure effects at low energies can still make a difference. * They are geometrical parameters
* These parameters directly characterize the global structure of the nucleus: the total volume and surface thickness. * Especially in heavy nuclei (e.g., \({}^{182}\)W to \({}^{186}\)W), the nuclear volume and surface properties are relatively independent of shell structure, thus they can be accurately represented by an average effect. * Regions where the OMP achieves the most accurate fit
* The most significant contribution in scattering data is related to the overall size of the nucleus, which directly correlates with \(r_{v}\). * The surface potential diffuseness affects the spread of the potential and the total cross section; \(a_{v}\) effectively controls this. * Therefore, the general shape of the angular distribution can be well fitted using these two parameters. Shell model:
* Assumes nucleons occupy discrete energy levels in specific orbitals. This level structure mainly affects the internal nuclear structure and transition phenomena (resonances, spin splitting, etc.). However:
* \(r_{v}\) and \(a_{v}\) represent an average geometrical distribution of nucleon placement. * Shell effects only cause minor deviations in this average density distribution. * In other words, shell model details primarily influence reaction dynamics (resonances, fine structures, spin effects), rather than the overall potential shape. In conclusion:
* In other words, shell model details primarily influence reaction dynamics (resonances, fine structures, spin effects), rather than the overall potential shape. * Geometrical parameters like \(r_{0}\) and \(a_{v}\) are relatively independent of the shell model. * Therefore, the absence of shell model details in the OMP does not prevent these parameters from aligning well with experimental data.