The quadrupole collective model from a Cartan–Weyl perspective

The matrix elements of the quadrupole variables and canonic conjugate momenta emerging from collective nuclear models are calculated within an SU(1, 1) × O(5) basis. Using a harmonic oscillator implementation of the SU(1, 1) degree of freedom, one can show that the matrix elements of the quadrupole phonon creation and annihilation operators can be calculated in a pure algebraic way, making use of an intermediate state method.