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

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

2004-05-24

arxiv.org/abs/nucl-th/0405065v2

J.Phys. A37 (2004) 10951-10958

Physics

Nuclear Physics

Nuclear Theory

10pages

Scientific paper

10.1088/0305-4470/37/45/013

The many $2^k$-pole boson states, $|N_kv_k\alpha_k I_kM_k>$ 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 $\alpha_k$ 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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