Probing collectivity in nuclear binding energies from the viewpoint of the F-spin formalism

We aim to investigate binding energies of fp-shell nuclei using the supersymmetric model within the Interaction Boson Model-2, emphasizing the role of F-spin symmetry as a classification tool for collective dynamics. Since nuclear binding energies are strongly influenced by pairing correlations, an algebraic framework capable of distinguishing proton and neutron collective pairs is required. F-spin symmetry provides this framework by organizing bosons into multiplets according to their degree of proton–neutron coherence. In this work, we extended a supersymmetric Hamiltonian expressed as a linear combination of Casimir operators of the relevant subalgebras, supplemented by pairing contributions and explicit F-spin–breaking interactions. Ground-state energies and binding energies are evaluated, and deformation is analyzed using the quadrupole parameter β 2 . Color-mapped scatter plot visualizations of β 2 as a function of mass number and root mean square deviations demonstrate a satisfactory agreement with experimental data and reveal the influence of shell structure. This study also examines quantities sensitive to nuclear structure, including two-neutron separation energies and neutron-proton pairing gaps, to probe underlying nuclear properties. The results highlight F-spin as the key algebraic symmetry for describing the impact of pairing and collectivity on nuclear binding energies in the fp-shell.