The s and d bosons into the Shell Model SU(3) wave functions

Abstract

The Shell Model SU(3) symmetry was discovered by Elliott in 1958 and since then has been the algebraic realization of the Nuclear Shell Model. It is considered to be a fermionic nuclear model, since it tackles with the occupancies of the orbitals by nucleons. Elliott proved that the SU(3) symmetry appears in the LS (spin-orbit) coupling scheme of the nucleons. On the other side the Interacting Boson Model was proposed by Arima and Iachello in 1975 and it is a boson model. The bosons in the Interacting Boson Model are being derived by nucleon pairs. But the mapping (Otsuka-Arima-Iachello mapping) of the nucleon pairs into bosons is functional only in the jj coupling scheme and so it is applicable only in the U(5) and O(6) limits of the Interacting Boson Model. But what is the origin of the s and d bosons in the SU(3) limit of the Interacting Boson Model? Hereby I demonstrate that the s and d bosons are present into the spatial Shell Model SU(3) wave functions and that they derive from pairs of harmonic oscillator quanta.