What's a Rydberg state, anyway?

A Rydberg state is a state of an atom or molecule in which one of the electrons has been excited to a high principal quantum number orbital. Classically, such a state corresponds to putting one electron into an orbit whose dimensions are very large compared to the size of the leftover ion core. Among the novel properties of these states are extreme sensitivity to external influences such as fields and collisions, extreme reactivity, and huge probabilities for interacting with microwave radiation. A wide variety of types of experiments of current interest in atomic, molecular, and optical physics involve the use of Rydberg states.


Spectroscopically, we talk about a Rydberg series as being the set of bound states of the excited electron for a given set of excited electron angular momentum quantum numbers and ion core state. If we include all of the corresponding free electron states, we have what the quantum defect theory folks would call a channel. For a channel that is not interacting with any others, the Rydberg state energies follow a simple formula, the Rydberg formula
                                        En,g = - (Ry)/(n - mg)2

where n is the principal quantum number, Ry is the Rydberg constant for the system, g represents all of the other quantum numbers, and mg is the marvelous quantum defect. The quantum defect describes how much the Rydberg series departs from the behavior of the Rydberg states of atomic hydrogen, and is directly related to the interaction of the excited electron with the leftover ion core.


It starts to get really interesting when you consider an energy region where there are states associated with more than one channel present. These different channels might, for instance, be associated with different spin-orbit states of the ion core in an atom or different rotational and vibrational states of a molecular ion core. Additional interactions which have been neglected in the definition of the channels give rise to couplings between the states of the different channels, leading to complicated energy shifts and intensity variations in the Rydberg series. If, in one or more of the channels in the energy range of interest, the excited electron is unbound (open channels), this channel interaction leads to a mixing of the bound states (in closed channels) with the unbound states and the process of autoionization. Spectra of the atom or molecule in a region of autoionization show broadened, asymmetric lines described by a thing called a Beutler-Fano profile. Multichannel quantum defect theory (MQDT) provides a unified treatment of coupled channels, both open and closed.


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