Eigen-Property of Single-j System and Seniority Conservation Condition

Wang Xiaobao (王小保); Qi Chong (亓冲); Xu Furong (许甫荣)

doi:10.1088/1009-0630/14/5/08

Plasma Science and Technology > 2012 > 14(5): 383-385. > DOI: 10.1088/1009-0630/14/5/08

Wang Xiaobao (王小保), Qi Chong (亓冲), Xu Furong (许甫荣). Eigen-Property of Single-j System and Seniority Conservation Condition[J]. Plasma Science and Technology, 2012, 14(5): 383-385. DOI: 10.1088/1009-0630/14/5/08

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Eigen-Property of Single-j System and Seniority Conservation Condition

1 School of Physics, and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China 2 KTH (Royal Institute of Technology), Alba Nova University Center, SE-10691 Stockholm, Sweden

Funds: supported by the Natural Science Foundation of China (Nos. 10735010, 10975006), the Chinese Major State Basic Research Development Program (No. 2007CB815000). Qi C. has been supported by the Swedish Research Council (VR).

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Received Date: May 16, 2011

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Abstract

Abstract

In this paper we study the system with three nucleons within a single-j shell, which can be described as the angular momentum coupling of a nucleon pair and the odd nucleon. The overlaps between these non-orthonormal states form a special matrix coincidental with the one obtained by Rowe and Rosensteel. They proposed a proposition related to the eigenvalue problems of that matrix and dimensions of the associated subspaces. We prove their proposition with the help of the symmetric properties of the six-j symbols. We also derive algebraic expressions for eigen energies as well as conditions for conservation of seniority through the decomposition of the angular momentum.
- seniority,
- single-j shell,
- conservation condition

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