### Group contractions and conformal maps in nuclear structure models

#### Abstract

Group contraction is a procedure in which a symmetry group is reduced into a group of lower symmetry in a certain limiting case. Examples are provided in the large boson mumber limit of the Interacting Boson Approximation (IBA) model by a) the contraction of the SU(3) algebra into the [R5]SO(3) algebra of the rigid rotator, consisting of the angular momentum operators forming SO(3), plus 5 mutually commuting quantities, the quadrupole operators, b) the contraction of the O(6) algebra into the [R5]SO(5) algebra of the ∞-unstable rotator. We show how contrac- tions can be used for constructing symmetry lines in the interior of the symmetry triangle of the IBA model.

In mathematics, a conformal map is a function which preserves angles. We show how this procedure can be used in the framework of the Bohr Hamiltonian, leading to a Hamiltonian in a curved space, in which the mass depends on the nuclear deformation Ø, while it remains independent of the collective variable ∞ and the three Euler angles. This Hamiltonian is proved to be equivalent to that obtained using techniques of Supersymmetric Quantum Mechanics.

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R. Le Blanc, J. Carvalho, and D. J. Rowe, Phys. Lett. B 140, 155 (1984).

D. J. Rowe, Prog. Part. Nucl. Phys. 37, 265 (1996).

H. Ui, Prog. Theor. Phys. 44, 153 (1970).

D. Bonatsos, S. Karampagia, and R.F. Casten, Phys. Rev. C 83, 054313 (2011).

J. Meyer-ter-Vehn, Phys. Lett. B 84, 10 (1979).

J. P. Elliott, P. Park, and J. A. Evans, Phys. Lett. B 171, 145 (1986).

D. Bonatsos, S. Karampagia, and R.F. Casten, these proceedings.

C. Quesne and V. M. Tkachuk, J. Phys. A: Math. Gen. 37, 4267 (2004).

A. Bohr, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 26, no. 14 (1952).

B. Podolsky, Phys. Rev. 32, 812 (1928).

D. Bonatsos, P. E. Georgoudis, D. Lenis, N. Minkov, and C. Quesne, Phys. Rev. C 83, 044321 (2011).

D. Bonatsos, P. E. Georgoudis, D. Lenis, N. Minkov, and C. Quesne, these proceedings.

DOI: http://dx.doi.org/10.12681/hnps.2506

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