2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124756The matrix elements of the quadrupole collective variables, emerging from collective nuclear models, are calculated in the natural Cartan-Weyl basis of O(5) which is a subgroup of a covering $SU(1,1)\times O(5)$ structure. Making use of an intermediate set method, explicit expressions of the matrix elements are obtained in a pure algebraic way, fixing the $γ$-rotational structure of collective quadrupole models.submitted to Journal of Physics ANuclear Theorytext