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Abstract
In this paper we consider a basis for N boson states classified by the chain of groups U(6)⊇U(3)⊇U(2)⊇U(1). We determine analytical expressions for the matrix elements of the boson creation and annihilation operators, as well as for the U(6) generators, with respect to that basis. For such purpose, we use the Wigner–Eckart theorem with respect to U(3) and calculate the reduced matrix elements of the appropriate irreducible tensors from their matrix elements between highest weight states. Then we apply the transformation brackets from the chain U(6)⊇U(3)⊇U(2)⊇U(1) to the physical chain U(6)⊇SU(3)⊇SO(3)⊇SO(2) to obtain the matrix elements of the above-mentioned operators in a basis corresponding to the latter. The matrix elements so determined can be used either in the nuclear interacting boson model of Arima and Iachello or in the microscopic nuclear collective model of Vanagas et al.
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