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 ...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.展开更多
基金supported by National 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)
文摘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.
