Regular family structures observed in neutron resonance energies: Breathing model of the compound nucleus

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 ≈ 34.5 MeV is almost equal to the Fermi energy. Family structures are described for the observed resonances in 40 Ca, 54 Cr, 64 Ni, 90 Zr, and 208 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.