N_p N_n Scheme Based on New Empirical Formula for Excitation Energy

We examine the $N_p N_n$ scheme based on a recently proposed simple empirical formula which is highly valid for the excitation energy of the first excited natural parity even multipole states in even-even nuclei. We demonstrate explicitly that the $N_p N_n$ scheme for the excitation energy emerges from the separate exponential dependence of the excitation energy on the valence nucleon numbers $N_p$ and $N_n$ together with the fact that only a limited set of numbers is allowed for the $N_p$ and $N_n$ of the existing nuclei.