Relationship between states of partially and almost filled shells

3 Relationship between states of partially and almost filled shells 

Since the number of electrons in the lN configuration is uniquely determined by the value of the z-projection of quasispin momentum, then the quasispin method provides us with a common approach to the spin-angular parts of the wave functions of partially and almost filled shells that differ only by the sign of that z-projection. The phase relations between various quantities will then uniquely follow from the symmetry 

Usually, the phase factor here is chosen in some arbitrary manner, fixing the relationships between the partially and almost filled shells [14, 23]. As is seen from (16.38), in the quasispin method these relationships are given rigorously and uniquely. 

In exactly the same way, for operators Uk and Vkl we obtain the relationship between the submatrix elements defined relative to the wave functions of partially and almost filled shells 

The connection between appropriate quantities for partially and almost filled shells can be established by another method - by going over from the particle representation to the hole one. According to the results of Chapters 2, 13 and 14, the wave function of the completely filled shell is at the same time the vacuum state for holes 

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