Tin Anomaly in Coulomb Energies and Analog Resonances of Neutron-Rich Tin Isotopes

Abstract

An anomaly in the distribution of Coulomb energies of tin isotopes (Sn anomaly) is determined. This anomaly manifests itself as follows: in the mass-number ($A$) dependence of $\Delta E_{\mathrm{C}}A^{1/3}$ for the isotopes ${}^{\mathrm{112-132}}$Sn, experimental data on $\Delta E_{\mathrm{C}}$ show a linear dependence close to a constant. The Coulomb energy difference $\Delta E_{\mathrm{C}}(A,Z)$ between the Sn–Sb neighboring isobaric nuclei is approximated by a two-parameter expression. The energies of isobaric analog resonances, $E_{\mathrm{AR}}$, for the isotopes ${}^{\mathrm{110-140}}$Sn are calculated both on the basis of the resulting approximation within a phenomenological model and on the basis of the microscopic theory of finite Fermi systems. The results are compared with experimental data on $E_{\mathrm{AR}}$, and it is found that the phenomenological model describes the energies $E_{\mathrm{AR}}$ quite accurately, and so do the new self-consistent relativistic model.