Rotationally Invariant Hamiltonians for Nuclear Spectra Based on Quantum Algebras

The rotational invariance under the usual physical angular momentum of the ${\mathrm{su}}_{q}(2)$ Hamiltonian for a description of rotational nuclear spectra is explicitly proved, and a connection of this Hamiltonian to the formalisms of Amal'sky and Harris is provided. In addition, a Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITO's) under ${\mathrm{su}}_{q}(2)$ and the use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this ${\mathrm{su}}_{q}(2)$ 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.