Abstract

In neutron resonances, which are long believed to be a form of quantum chaos, simple regular family structures are found for many even-even nuclei in the several tens of keV to MeV region. Resonance energies can be written by simple arithmetic expressions with good accuracies, where separation energies ${S}_{n}$ and $G$ play essential roles and where $G\ensuremath{\approx}34.5\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ is almost equal to the Fermi energy. Family structures are described for the observed resonances in ${}^{40}\mathrm{Ca}$, ${}^{54}\mathrm{Cr}$, ${}^{64}\mathrm{Ni}$, ${}^{90}\mathrm{Zr},$ and ${}^{208}\mathrm{Pb}$. Statistical probability tests are performed for the appearance of these family structures. A classical dynamic model of the compound nucleus is proposed where the recurrence of multiple oscillators produces ``breathing'' and seems to successfully reproduce observed resonance families.

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