Origin of $2_1^{+}$ 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.

9 pages, 5 figures

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