Helium Rydberg state

Energies and Asymptotic Analysis for Helium Rydberg States, G. W E Drake... 

In this paper we examined quantum aspects of special classical configurations of two-electron atoms. In the doubly excited regime, we found quantum states of helium that are localized along ID periodic orbits of the classical system. A comparison of the decay rates of such states obtained in one, two and three dimensional ab initio calculations allows us to conclude that the dimension of the accessible configuration space does matter for the quantitative description of the autoionization process of doubly excited Rydberg states of helium. Whilst ID models can lead to dramatically false predictions for the decay rates, the planar model allows for a quantitatively reliable reproduction of the exact life times. 

Also as in the case of helium, asymptotic expansion methods can be applied to the Rydberg states of lithium and compared with high precision measurements [73,74]. This case is more difficult because the Li+ core is a nonhydrogenic two-electron ion for which the multipole moments cannot be calculated analytically, and variational basis set methods must be used instead. However, the method is in principle capable of the same high accuracy as for helium. 

G.W.F. Drake High-Precision Calculations for the Rydberg States of Helium in Long Range Casimir Forces Theory and Recent Experiments in Atomic Systems, ed. by F.S. Levin, D.A. Micha (Plenum Press, New York, 1993), pp. 107-217... 

Korona T, Jeziorski B, Moszynski R, Diercksen GHF (1999) Degenerate symmetry-adapted perturbation theory of weak interactions between closed- and open-shell monomers application to Rydberg states of helium hydride. Theor Chem Acc 101 282-291... 

Results of similar accuracy are now available for all the higher-lying Isnl L Rydberg states of helium up to n = 10 and L = 7 (see Drake [35] and earlier references therein). One might object that these long strings of figures are just... 

Hydrogen [54] and helium [55] atoms are known to exhibit regular/chaotic dynamics in the presence of external field of different colors and intensities. Chaotic ionization from the Rydberg states of the atoms [54,55] has been very intriguing for the experimentalists. Both QFD [56,57] and quantum theory of motion (QTM) [58,59] have been able to explain the quantum domain behavior of the classically chaotic systems [60], In QFD, the quantum dynamics is mapped onto that of a probability fluid of density and current density p(r, t) and j(r, t) respectively obtainable as solutions to the QFD equations. The fluid moves under the influence of the classical Coulomb potential augmented by a quantum potential defined as... 

This simple orbital model in Figure 12.25 is not entirely consistent with the available experimental data. Indeed, Kropp called the isolated carbon-carbon double bond "one of the most deceptively simple chromophores available to the organic chemist." ° Even though the end absorption apparently includes the n,ii transition, there is evidence that there may also be weak absorption due to tc —> c and Rydberg transitions. In alkenes, the Rydberg state is thought to result from promotion of an electron from the n orbital to a carbon orbital that has the characteristics of a 3s orbital in helium. 

The Rydberg state of alkene is designated as n, R(3s), to specify that one electron from the n bond remains in the n orbital and the other has been shifted to the Rydberg orbital, which resembles the 3s orbital of a helium atom. The Rydberg state of an alkene is considered to have a partially ionic stmcmre such that a net positive charge remains on a carbon atom. The Rydberg state of ethylene is shown below. 

L. Argenti, Rydberg and autoionizing triplet states in Helium up to the N = 5 threshold, At. Data Nucl. Data Tables 94 (2008) 903. 

On increasing the temperature, B and even C free excitons are thermally populated and their contribution can be observed in the bandedge luminescence of undoped GaN (see FIGURE 1). At helium temperature weak luminescence peaks located 19 - 20 meV higher in energy than the A line [6,13,19,21] are frequently observed. Their attribution to n - 2 states of the A exciton can be used to evaluate the A Rydberg. Doing so leads to values of 25 2 meV. 

There is no problem with the existence of the Rydberg regime. Its existence is guaranteed on the basis of the elementary independent particle model, an excellent approximation of the helium states in the Rydberg regime where n m. 

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