Origin of21+excitation energy dependence on valence nucleon numbers

Abstract

It 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.