Molecular Rydberg states quantum defects

QUANTUM DEFECT THEORY OF THE DYNAMICS OF MOLECULAR RYDBERG STATES... 

We consider the QDO method to be a useful tool for estimating transition probablities between molecular Rydberg states. A drawback of our method is its empirical character in that it requires the quantum defects for the states involved in transitions as an input. However, the well established correspondence between the energy levels of a Rydberg molecule and those of its united atom limit (9), as well as the regular behavior of the quantum defects along a Rydberg series are very helpful in their estimations. 

A central feature of molecular quantum defect theory is the use of frame transformations. These provide an elegant way of treating the breakdown of the Bom-Oppenheimer approximation that occurs systematically once an electron is excited into a high Rydberg state. 

There are two parameters in the atomic coulomb functions, the effective nuclear charge and the quantum defect. The values of these were taken by Johnson and Rice from available spectral data. The effective atomic charge was adjusted to give the correct ionization potential of the molecule, 9.25 eV, requiring thereby z = 0.8243. The quantum defects of carbon were taken from the appropriate atomic series and were 1.04 for the 5-state and 0.73 for the p-states. It is interesting to compare the calculated molecular quantum defects (i.e., those corresponding to the Johnson-Rice LCAO function) with those which can be obtained from the various benzene Rydberg series.218 The asymptotic form of the elu orbital constructed from s atomic functions is... 

The investigation of Rydberg states in the far UV spectra of molecules may. also contribute to the interpretation of PE spectra. From the quantum defects and the number of Rydberg series that converge on a given limit, the ionized molecular orbital can be deduced. The convergence limit of a series corresponds to an ionization energy in the PE spectrum. 

Ross and Jungen (1999) have used differences between ab initio ion-core and Rydberg state potential curves to determine quantum defect functions. Thus the independent quantum defect functions associated with the atom-like Hel(°) and the molecular H 1) are, respectively, ai(R) and ai (R). 

The quantum defect is about 1.0 for user orbitals of molecules composed of atoms between Li and N, since these orbitals penetrate into the molecular core (cf. Mulliken, 1964) and consequently are strongly modified by the presence of inner electrons of the same sa symmetry. The quantum defect is of the order 0.7 for npa and npn orbitals, which are less modified by the core, and nearly zero for ndcr, ndir, and ndS orbitals, which have no precursors in the core. For a given molecule this quantum defect is roughly independent of the ion state to which the Rydberg series converges (see, for example, for O2, Table 1 of Wu, 1987). 

From the optically pumped atomic or molecular Rydberg levels neighboring levels can be reached by microwave transitions, as was mentioned above. This triple resonance (two-step laser excitation plus microwave) is a very accurate method to measure quantum defects, fine-structure splitting, and Zeeman and Stark splitting in Rydberg states [592]. 

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