2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166181The matrix elements of the quadrupole variables and canonic conjugate momenta, emerging from collective nuclear models are calculated within a $SU(1,1)\times O(5)$ basis. Using a harmonic oscillator implementation of the SU(1,1) degree of freedom, it can be shown 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.Special issue of journal of physics for the QTS5 conferenceNuclear Theorytext