Abstract
A calculation method is developed which enables algebraic treatment of the isospin-fixed (or seniority-fixed or S-fixed) high moment of energy spectra in a many-body configuration. Essential is to get a recursion relation for the average energy of a many-body interaction and to solve it as a boundary condition problem. Shell model techniques and the branching diagram are well used. As a simple application of the result, the first three moments with isospin being fixed are evaluated for the case of the (Og9/2)n configuration.

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