Exploring the Giant Monopole Resonance in Superheavy Nuclei: A Theoretical Perspective

Within the relativistic mean-field (RMF) framework and employing the extended Thomas–Fermi approximation, we calculate the binding energies and charge radii of the recently synthesized superheavy nuclei with atomic nos. Z = 110–118. The calculated values are compared with results from relativistic Hartree calculations as well as with available experimental data to assess the reliability and predictive power of the employed methods. The study is further extended to investigate the collective vibrational properties of these superheavy nuclei by estimating the energies of their giant monopole resonances (GMR), commonly referred to as the “breathing mode.” These GMR energies are computed using both scaling and constraint approaches, and the results are benchmarked against those obtained from other theoretical models, such as the relativistic random phase approximation (RPA) and time-dependent mean-field calculations. To ensure a comprehensive analysis, comparisons are also made with known results for lighter nuclei, specifically zirconium (Zr) isotopes in the neutron number range N = 42–86 and oxygen (O) isotopes with N = 10–36. Finally, the nuclear incompressibility of the superheavy elements is estimated from the extracted GMR energies, providing insight into the equation of state and stiffness of nuclear matter in this extreme mass region.