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Abstract
The procedure for constructing the non-canonical basis corresponding to the reduction SO(5)⊃ SU 2( T)× U 1 valid for the arbitrary irreducible representations of the group SO(5) is developed. The proof of the completeness of this basis is given and the matrix elements of the generators are calculated in this basis. The matrix of the operator B introduced by Flowers and Szpikovsky, and specifying the effective number of alpha-like four-nucleon cluster in a nucleus is obtained and some of its general properties are discussed.
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