Nuclear forces and nuclear excited states

In this work, the role of the central, spin-force and tensor forces of two-nucleon interaction in building the first 2$^+$ and 4$^+$ states of 20 sd-shell nuclei is studied. Calculations are performed within the framework of the nuclear shell model. It is shown that the central force predominantly contributes to the excitation energy. While the spin-orbit and tensor forces contribute relatively less, their roles are noted crucial in a few cases, such as in $^{22}$O. Further, it is demonstrated that the Hamiltonian projection approach should be preferred for rightly assessing the contributions of each force to the excitation energy.