In this paper we study the correlation between the evolution of nuclear collective motion and neutron-proton interactions. We construct empirical neutron-proton interactions (denoted by $V_{\mathrm{NP}}$) for nuclei in the $(28<Z<50,$ $50<N<82)$, $(50<Z<82,$ $50<N<82$), and $(50<Z<82,$ $82<N<126)$ major shells. The ratios between $V_{\mathrm{NP}}$ and $N_{\mathrm{n}}{N}_{\mathrm{p}}$ (the product of valence proton number and valence neutron number) are found to be different for particle-particle, particle-hole, and hole-hole regions of the same major shell, suggesting different average strengths of neutron-proton interactions for these regions. Very interestingly, collective observables of even-even nuclei, e.g., $2^{+}$ and $4^{+}$ state energies, which follow different trajectories in the $N_{\mathrm{n}}{N}_{\mathrm{p}}$ scheme for particle-particle, particle-hole, and hole-hole regions, are found to form one unified and compact trajectory if those collective observables are plotted in terms of total neutron-proton interactions, $V_{\mathrm{NP}}$.

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• Collective levels
• Nuclear forces
• Nuclear structure & decays
• Nucleon-nucleon interactions