Rydberg scale

As one proceeds to the heavier particle type atoms, the effective Rydberg scales by the ratio of particle mass to electron mass. This has the effect, for example, of moving low Z pionic spectra into the soft X-ray region of one to a few kilovolts. 

For all calculations, the choice of AO basis set must be made carefully, keeping in mind the scaling of the two-electron integral evaluation step and the scaling of the two-electron integral transfonuation step. Of course, basis fiinctions that describe the essence of the states to be studied are essential (e.g. Rydberg or anion states require diffuse functions and strained rings require polarization fiinctions). 

Such long lifetimes are puzzling in view of the well-known n3 scaling of Rydberg state lifetimes observed from linewidths of resolvable series and predicted by theory. The n3 scaling derives from a fundamental property of Rydberg states. The normalization factor in the radial part of the Rydberg orbital scales as n 3/2. Thus... 

SEPARATION OF TIME SCALES IN THE DYNAMICS OF HIGH MOLECULAR RYDBERG STATES... 

There are many motivations for the study of the unusual dynamics of high Rydberg states of molecules. The two that most capture my imagination are the exceptionally wide range of time scales involved (Fig. 1) and the unusual limiting situation of a very slow electron being perturbed by the faster motion of the nuclei in the core about which it revolves. What this means is that, as one varies the hydiogenic principal quantum number n, it is possible... 

R. D. Levine The latest results for benzene as reported by Prof. Neusser suggest that benzene is the molecule we should study at all time scales. In other aromatic molecules (and also in other molecules [U. Even et al., J. Phys. Chem. 98, 3472 (1994)]) you have reported that there are at least two times scales for the decay of high Rydberg states. A faster (hundreds-of-nanosecond) scale and a slower one (microsecond range). Even the faster time scale is two to three orders of magnitude slower decay than one would expect from an extrapolation of the decay measured at low or intermediate n Rydberg states. 

The classical trajectory simulations of Rydberg molecular states carried out by Levine ( Separation of Time Scales in the Dynamics of High Molecular Rydberg States, this volume) remind me of the related question asked yesterday by Prof. Woste (see Berry et a]., Size-Dependent Ultrafast Relaxation Phenomena in Metal Clusters, this volume). Here I wish to add that similar classical trajectory studies of ionic model clusters of the type A B have been carried out by... 

For small nonpolar species such as H2 and N2 the dominant interaction between the Rydberg electron and the nuclear vibrational and rotational motion occurs within a small radius around the ionic core, which is traversed in a fraction of a femtosecond. This short encounter justifies the sudden treatment of vibration and rotation in MQDT theory, while also permitting Bom-Oppenheimer estimates of the necessary quantum defect functions. It is also central to the n-3 scaling law because the core transit time is almost energy independent, while the Rydberg orbit time increases as n3. 

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