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*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
E_{n,g }= -
(Ry)/(n - m_{g})^{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 m_{g} 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.

Last Updated: July 9 1997 Webmaster