Parameter-Independent Symmetries in Nuclear Structure - Bonatsos, D.; Lenis, D.; Minkov, N.; Raychev, P. P.; Terziev, P. A. (HNPS Advances in Nuclear Physics, 2021)
The E(5) symmetry describes nuclei related to the U(5)–SO(6) phase transition, while the X(5) symmetry is related to the U(5)–SU(3) phase transition. A chain of potentials interpolating between the U(5) symmetry of the 5-dimensional harmonic oscillator and the E(5) symmetry is considered. Parameter independent predictions for the spectra and B(E2) values of nuclei with R_4= E(4)/E(2) ratios 2.093, 2.135, and 2.157 (compared to the ratio 2.00 of the U(5) case and the ratio 2.20 of the E(5) case) are derived numerically and compared to existing experimental data, suggesting several new experiments. Furthermore, an exactly soluble model with R_4 = 2.646 is constructed and a chain of potentials interpolating between this new model and the X(5) symmetry is considered. Parameter independent predictions for the spectra and B(E2) values of nuclei with R_4 ratios 2.769, 2.824 and 2.852 (compared to the ratio 2.904 of the X(5) case) are derived numerically and compared to existing experimental data, suggesting several new experiments.