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

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.