2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/175635It has been shown recently that a simple formula in terms of the valence nucleon numbers and the mass number can describe the essential trends of excitation energies of the first $2^+$ states in even-even nuclei. By evaluating the first order energy shift due to the zero-range residual interaction, we find that the factor which reflects the effective particle number participating in the interaction from the Fermi orbit governs the main dependence of the first $2^+$ excitation energy on the valence nucleon numbers.9 pages, 5 figuresNuclear Theorytext