We examine the effects of the additional term of the type ∼e−λ′Np​Nn​ 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 Np​Nn​ scheme. We show explicitly that there is not
any improvement in reproducing Ex​(21+​) by including the extra Np​Nn​
term. However, our study also reveals that the excitation energies
Ex​(21+​), when calculated by the Np​Nn​ term alone (with the mass number
A dependent term), are quite comparable to those calculated by the original
empirical formula.Comment: 14 pages, 5 figure