Mirror reflection symmetry and the phase relations for partially and almost filled shells of equivalent atomic electrons

The mirror reflection symmetry which consists in the correlation of the substitution j → −j −1 with the reflection of the coordinate system and of m → −m with the reflection of the space with respect to the xy‐plane has been applied to the quasi‐spin formalism. The phases of the wave functions of the shell of equivalent atomic electrons treated as partially filled, as they relate to those when the same shell is treated as almost filled, have been established. The mirror reflection symmetry has been generalized for the supplementary quantum numbers used for distinguishing the terms of the same kind. The phases of the coefficients of fractional parentage of almost filled shell enabling us to determine them from those of partially filled shell have been specified. Corresponding phase relations for the matrix elements of operators have also been considered.