Rotational energy term in the empirical formula for the yrast energies in even-even nuclei

TL;DR

This paper links an empirical formula for yrast energies in even-even nuclei to rotational energy, improving understanding and parameter consistency by interpreting a key term as rotational energy.

Contribution

It introduces a novel interpretation of the empirical formula's first term as rotational energy, enhancing the understanding of nuclear excitation energies.

Findings

Parameters align with rigid rotor model predictions

Better fit to experimental data with rotational interpretation

Consistent parameter values across analysis methods

Abstract

We show that part of the empirical formula describing the gross features of the measured yrast energies of the natural parity even multipole states for even-even nuclei can be related to the rotational energy of nuclei. When the first term of the empirical formula, $\alpha A^{-\gamma}$, is regarded as the otational energy, we can better understand the results of the previous analyses of the excitation energies. We show that the values of the parameters $\alpha$ and $\gamma$ newly obtained by considering the $\alpha A^{-\gamma}$ term as the rotational energy of a rigid rotor are remarkably consistent with those values extracted from the earlier `modified' $\chi^2$ analyses, in which we use the logarithms of the excitation energies in defining the `modified' $\chi^2$ values.