SO（8）对关联和代数壳模型中的SU（3）四极基底（英文）

建立了SO（8） 同位旋标量、同位旋矢量及总的配对基与微观壳模型坐标空间部分的Elliott SU（3） 基之间的对应关系。从该代数间的互补关系导出了在壳模型的粒子数守恒代数U（4Ω） 中所包含的具有同位旋T 及自旋S 的Wigner 超多重态（不可约） 表示。其重要性在于，该结果能用于研究对相互作用和四极-四极相互作用在核谱中的竞争效应并揭示其配对基中的SU（3） 组份。虽然仅展示了该理论对ds 壳的计算，其方法也适用于研究多壳的情形。We establish a correspondence between the SO(8) isoscalar, isovector and total pairing bases and the Elliott's SU(3) basis in the algebraic structure of the spatial part of the microscopic shell model. It is derived from the complementarity of these algebras to the same T, S, (S,T) irreducible representations (irreps) of the Wigners supermultiplets, contained in the shell-model number-conserving algebra U(4Ω). This important result allows for the evaluation of the content of SU(3) irreps into the different types of pairing bases which leads to an investigation of the complementarity and competitive effects of pairing and the quadrupole-quadrupole interactions on the energy spectra of the nuclear systems. The theory is valid for any shell and for a number of shells as well, but we illustrate it with the results for a single ds-shell.

Correlations of the SO(8) Pairing and SU(3) Quadrupole Bases in the Algebraic Shell Model

We establish a correspondence between the SO(8) isoscalar, isovector and total pairing bases and the Elliott's SU(3) basis in the algebraic structure of the spatial part of the microscopic shell model. It is derived from the complementarity of these algebras to the same T, S, (S,T) irreducible representations (irreps) of the Wigners supermultiplets, contained in the shell-model number-conserving algebra U(4Ω). This important result allows for the evaluation of the content of SU(3) irreps into the different types of pairing bases which leads to an investigation of the complementarity and competitive effects of pairing and the quadrupole-quadrupole interactions on the energy spectra of the nuclear systems. The theory is valid for any shell and for a number of shells as well, but we illustrate it with the results for a single ds-shell.