Quantum groups in nuclear spectra

We demonstrate how quantum algebras (quantum groups), which are nonlinear generalizations of the usual Lie algebras, can be used for constructing nuclear Hamiltonians which, in addition to the deformed symmetry su_q(2), also obey the usual su(2) symmetry underlying physical angular momentum. In particular, the rotational invariance under the usual physical angular momentum of the su_q(2) Hamiltonian for the description of rotational nuclear spectra is explicitly proved and a connection of this Hamiltonian to the formalisms of Amal'sky and Harris is provided. Furthermore, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITOs) under su_q(2) and use of q-deformed tensor products and q-deformed Clebsch–Gordan coefficients. The rotational invariance of this su_q(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved, a simple closed expression for its energy spectrum (the "hyperbolic tangent formula") is introduced, and its connection to the Harris formalism is established. Numerical tests in a series of Th isotopes are provided. The way in which the same techniques can be used for the description of magic numbers and supershells in metal clusters is also briefly mentioned.