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Parameter-Independent Symmetries in Nuclear Structure

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Published: Aug 30, 2021
DOI: https://doi.org/10.12681/hnps.3344
D. Bonatsos
D. Lenis
N. Minkov
P. P. Raychev
P. A. Terziev
Abstract

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.

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References
F. Iachello, Phys. Rev. Lett. 85 (2000) 3580.
F. Iachello, Phys. Rev. Lett. 87 (2001) 052502.
A. Bohr, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 26 (1952) no. 14.
E. Chacon and M. Moshinsky, J. Math. Phys. 18 (1977) 870.
L. Wilets and M. Jean, Phys. Rev. 102 (1956) 788.
G. Rakavy, Nucl. Phys. 4 (1957) 289.
D. R. Bes, Nucl. Phys. 10 (1959) 373.
M. Moshinsky, J. Math. Phys. 25 (1984) 1555.
F. Iachello and A. Arima, The Interacting Boson Model (Cambridge Univesrity Press, Cambridge, 1987).
D. Troltenier, J. A. Maruhn, and P. O. Hess, in Computational Nuclear Physics 1. Nuclear Structure, ed. K. Langanke, J. A. Maruhn, and S. E. Koonin (Springer, Berlin, 1991) p. 105.
T. M. Corrigan, F. J. Margetan, and S. A. Williams, Phys. Rev. C 14 (1976) 2279.
W. Greiner and J. A. Maruhn, Nuclear Models (Springer, Berlin, 1996).
C. M. Bender, S. Boettcher, H. F. Jones, and V. M. Savage, J. Phys. A 32 (1999) 6771.
H. J. Korsch and M. Gluck, Eur. J. Phys. 23 (2002) 413.
N. Minkov and W. Scheid, INRNE Soa preprint (2003).
D. Bonatsos, D. Lenis, N. Minkov, P. P. Raychev and P. A. Terziev, N.C.S.R. Demokritos preprint DEM-NT-03-01, to appear in the Proceedings of the XXII International Workshop on Nuclear Theory (Rila Mountains, Bulgaria, 2003), ed. V. Nikolaev.
F. Iachello, in Mapping the Triangle: International Conference on Nuclear Structure, ed. A. Aprahamian, J. A. Cizewski, S. Pittel, and N. V. Zamr (American Institute of Physics, 2002), Vol. CP638, p. 1.
R. F. Casten and N. V. Zamr, Phys. Rev. Lett. 85 (2000) 3584.
A. Frank, C. E. Alonso, and J. M. Arias, Phys. Rev. C 65 (2001) 014301.
N. V. Zamr et al., Phys. Rev. C 65 (2002) 044325.
D. Bonatsos, D. Lenis, N. Minkov, P. P. Raychev and P. A. Terziev, N.C.S.R. Demokritos preprint DEM-NT-03-02, to appear in the Proceedings of the XXII International Workshop on Nuclear Theory (Rila Mountains, Bulgaria, 2003), ed. V. Nikolaev.
R. F. Casten and N. V. Zamr, Phys. Rev. Lett. 87 (2001) 052503.
R. Krucken et al., Phys. Rev. Lett. 88 (2002) 232501.
M. A. Caprio et al., Phys. Rev. C 66 (2002) 054310.
P. M. Davidson, Proc. R. Soc. 135 (1932) 459.
D. J. Rowe and C. Bahri, J. Phys. A 31 (1998) 4947.