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New results for the missing quantum numbers labeling the quadrupole and octupole boson basis

A. Gheorghe·A. A. Raduta
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Abstract

The many $2^k$-pole boson states, $|N_kv_kα_k I_kM_k>$ with $k=2,3$, realize the irreducible representation (IR) for the group reduction chains $SU(2k+1)\supset R_{2k+1}\supset R_3\supset R_2$. They have been analytically studied and widely used for the description of nuclear systems. However, no analytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$'s IR, determined by the reduction $R_{2k+1}\supset R_3$, is available. Thus, the number of distinct values taken by $α_k$ has been so far obtained by solving some complex equations. Here we derive analytical expressions for the degeneracy $d_v(I)$ characterizing the octupole and quadrupole boson states, respectively. The merit of this work consists of the fact that it completes the analytical expressions for the $2^k$-pole boson basis.

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A. Gheorghe, A. A. Raduta. 2004-10-27. New results for the missing quantum numbers labeling the quadrupole and octupole boson basis. https://doi.org/10.1088/0305-4470%2F37%2F45%2F013

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