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

TL;DR

This paper develops a computational framework for constructing SO(5)>SO(3) spherical harmonics and their Clebsch-Gordan coefficients, facilitating algebraic calculations in nuclear collective models.

Contribution

It introduces a computer code for explicit construction of SO(5)>SO(3) spherical harmonics and computes Clebsch-Gordan coefficients for nuclear model applications.

Findings

Provided a computational tool for spherical harmonics construction.

Enabled algebraic calculation of matrix elements in nuclear models.

Facilitated the use of SO(5)>SO(3) harmonics in collective model diagonalization.

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.