Restoration of Wigner supersymmetry in heavy and superheavy nuclei

The possibility of the restoration of Wigner supersymmetry ($\mathrm{SU(4)}$ symmetry) in heavy and superheavy nuclei has been analyzed by comparing the calculations with experimental data. The differences between the energies of the giant Gamow–Teller resonance ($E_G$) and analog resonance ($E_A$) calculated within the finite Fermi system theory for $33$ nuclei for which experimental data exist are presented. The energy differences $\Delta E_{G-A}$ between $E_G$ and $E_A$ tend to zero in heavier nuclei, demonstrating the restoration of Wigner $\mathrm{SU(4)}$ symmetry. The energy differences $\Delta E_{G-A}$ have also been calculated for heavy and superheavy nuclei located on the betastability line in the mass number range of $A=140$–$290$. In the $\mathrm{SU(4)}$ approach, the isotopic dependence of the difference between the Coulomb energies of neighboring isobar nuclei has been analyzed for more than $400$ nuclei in the mass number range of $A=3$–$244$. The restoration of Wigner $\mathrm{SU(4)}$ symmetry in heavy and superheavy nuclei has been confirmed. It has been shown that the restoration of $\mathrm{SU(4)}$ symmetry does not contradict the possibility of the existence of the “island of stability” in the region of superheavy nuclei.