摘要
The structure of the irreducible collective spaces of the group Sp(12,R),which many-particle nuclear states are classified according to the chain Sp(12,R)⊃U(6)⊃SO(6)⊃SU_(pn)(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM),is considered in detail.This chain of the PNSM was recently shown to correspond to a microscopic shell-model version of the Bohr-Mottelson collective model.The construction of the relevant shell-model representations of the Sp(12,R)group along this chain is considered for three nuclei with varying collective properties and from different mass regions.It is shown that the SU_(pn)(3)basis states of the Sp(12,R)representations belonging to the SO(6)irreps with seniorityυ≥υ0,withυ0 denoting the maximal seniority SO(6)irrep contained in the Sp(12,R)bandhead,are always Pauli allowed,but organized in a different way into different SO(6)shells.This is in contrast to the case of filling the levels of the standard three-dimensional harmonic oscillator and using the plethysm operation.Although the SU_(pn)(3)multiplets withinυ<υ0 are not all Pauli forbidden,it is safe to discard them.The results obtained in the present work are important for the practical application of the microscopic version of the Bohr-Mottelson collective model.
