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

TL;DR

This paper investigates the impact of an $N_pN_n$ dependent term on an empirical formula for the lowest $2^+$ excitation energies in even-even nuclei, finding no improvement but comparable results with the original formula.

Contribution

It introduces an additional $N_pN_n$ term to the empirical formula and demonstrates that it does not enhance the accuracy of excitation energy predictions.

Findings

Adding the $N_pN_n$ term does not improve the empirical formula's fit.

The $N_pN_n$ term alone yields results comparable to the original formula.

The $N_pN_n$ dependence is significant but not sufficient for better predictions.

Abstract

We examine the effects of the additional term of the type $\sim e^{- \lambda' N_pN_n}$ 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 $N_pN_n$ scheme. We show explicitly that there is not any improvement in reproducing $E_x(2_1^+)$ by including the extra $N_pN_n$ term. However, our study also reveals that the excitation energies $E_x(2_1^+)$, when calculated by the $N_pN_n$ term alone (with the mass number $A$ dependent term), are quite comparable to those calculated by the original empirical formula.