Construction of SO(5)>SO(3) spherical harmonics and Clebsch-Gordan coefficients

Abstract

The SO(5)>SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1,1)xSO(5) basis. We present a computer code for explicit construction of the SO(5)>SO(3) spherical harmonics and use them to compute the Clebsch-Gordan coefficients needed for collective model calculations in an SO(3)-coupled basis. With these Clebsch-Gordan coefficients it becomes possible to compute the matrix elements of collective model observables by purely algebraic methods.

LaTeX (RevTeX), 15 pages; to be published in Computer Phys. Comm.

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• Racah's method for general subalgebra chains: Coupling coefficients of SO(5) in canonical and physical bases
• Description of the low-lying collective states of ${}^{96}$Zr based on the quadrupole-collective Bohr Hamiltonian
• Evolution of the phenomenologically determined collective potential along the chain of Zr isotopes
• Applications of the Capelli identities in physics and representation theory
• Triaxial projected shell model study of $\gamma$-bands in atomic nuclei