Average Multiplicity of Unresolved Photon Cascades in the De-excitation of Highly Excited Compound Nuclei

Heavy ion (HI, $\mathrm{xN}$) reactions leading to ${}_{}{}^{158}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{160,162,164}{}_{}{}^{}\mathrm{Er}$, and ${}_{}{}^{170,172}{}_{}{}^{}\mathrm{Hf}$ were studied in order to determine the average multiplicity of the unresolved photons underlying discrete spectra of rotational band transitions observed in rare-earth even-even nuclei. The average multiplicity is found to be small (6), independent (to the accuracy of this experiment) of the ground-state rotational band level in which the cascade terminates.