Restoration of Wigner’s Sypersymmetry in Heavy and Superheavy Nuclei

Abstract

Various aspects of restoration of Wigner’s supersymmetry [SU(4) symmetry] in heavy and superheavy nuclei are analyzed by comparing the results of calculations with experimental data. The energy differences between the giant Gamow–Teller and analog resonances ($E_{\mathrm{G}}$ and $E_{\mathrm{A}}$) are given according to calculations within the theory of finite Fermi systems for 34 nuclei for which experimental data are known. The calculated energy differences $\Delta E_{\mathrm{G{-}A}}$ of $E_{\mathrm{G}}$ and $E_{\mathrm{A}}$ tend to zero in heavier nuclei, demonstrating the restoration of Wigner’s SU(4) symmetry. Also, the isotopic dependence of the Coulomb energy difference between neighboring nuclear isobars is analyzed within the SU(4) approach for more than 400 nuclei in the mass-number range of $A=5{-}244$. The restoration of Wigner’s SU(4) symmetry in heavy nuclei is confirmed. It is shown that the restoration of Wigner’s SU(4) symmetry is compatible with the possible existence of an island of stability in the region of superheavy nuclei.