Rydberg symmetry properties

A detailed discussion of the symmetry properties of Hund s case (a) basis functions, InJOASE), is presented in Section 3.2.2.1 followed in Section 3.2.2.2 by a brief summary of the symmetry properties of other classes of basis functions, such as those that are expressed in ion-core Rydberg electron) form and those that specify molecule-fixed R-axis (Sr, 1r, sr, jR) rather than z-axis projection quantum numbers. 

In this book, we adopt a form in which the function is expressed as a linear combination of spherical harmonics. This form is particularly appropriate for systems with near-spherical symmetry (such as Rydberg states or molecules which conform to Van Vleck s pure precession hypothesis [68, 69]) and is also consistent with the spirit of spherical tensors, which have the same transformation properties under rotations as spherical harmonics. The functional form of the ket rj, A) is written... 

For molecules, just as for many-electron atoms, one uses equation (2.8) to describe the series. As before, the quantum defect p characterises the whole Rydberg series but now absorbs the influence of the molecular core. In practice, its value still depends largely upon the atomic symmetry of the Rydberg orbital (more detail on its properties for polyatomic molecules will be given in section 3.11). 

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