N_pN_n dependence of empirical formula for the lowest excitation energy of the 2^+ states in even-even nuclei

Abstract

We examine the effects of the additional term of the type $\sim e^{-{\lambda }^{\prime }{N}_p{N}_n}$ on the recently proposed empirical formula for the lowest excitation energy of the $2^{+}$ states in even-even nuclei. This study is motivated by the fact that this term carries the favorable dependence of the valence nucleon numbers dictated by the $N_p{N}_n$ scheme. We show explicitly that there is not any improvement in reproducing $E_x(2_1^{+})$ by including the extra $N_p{N}_n$ term. However, our study also reveals that the excitation energies $E_x(2_1^{+})$, when calculated by the $N_p{N}_n$ term alone (with the mass number $A$ dependent term), are quite comparable to those calculated by the original empirical formula.

Comments: 14 pages, 5 figures