Power-law intensity distribution in $γ$-decay cascades

We show that the distribution of $\gamma$-decay intensities from heavy nuclei follows a power law. This is similar to the long-reported result that the distribution of electromagnetic emission line intensity from many-electron atoms follows a power law, however we find that in heavy nuclei the distribution always has a specific index 1, i.e., Zipf's law. This phenomenon is observed all 27 data sets having sufficient $\gamma$-ray intensity entries in the National Nuclear Data Center database, regardless of the reaction type or nuclei involved. This agreement can be understood from combining two statistical models: exponentially increasing level density, and independently distributed line strengths among all the excited states. We also present a joint probability distribution of the $\gamma$-ray energy and intensity, which may be used to estimate the gamma strength function for highly excited nuclei.

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