Quantum Defect in Rydberg Atoms
The quantum defect of a Rydberg atom refers to a correction applied to the equations governing Rydberg atom behavior to take into account the fact that the inner electrons do not entirely screen their associated charge in the nucleus. It is used particularly for the alkalis that contain a single electron in their outer shell.
The perfect 1/r potential in the hydrogen atom leads to an electron binding energy given by
- ,
where R is the Rydberg constant, h is Planck's constant, c is the speed of light and n is the principal quantum number.
For multi-electron atoms in Rydberg states with a low value of the orbital angular momentum, there is a high probability of finding the excited electron near the nucleus where it can polarize or even penetrate the ion core, modifying the potential. The resulting shift of the energy levels is represented mathematically as an angular momentum dependent quantum defect, δl:
- .
The largest shifts occur when the orbital angular momentum is equal to 0 (normally labelled 's') and these are shown in the table for the alkali metals:
| Element | Configuration | n* | δs |
|---|---|---|---|
| Li | 2s | 1.59 | 0.41 |
| Na | 3s | 1.63 | 1.37 |
| K | 4s | 1.77 | 2.23 |
| Rb | 5s | 1.81 | 3.19 |
| Cs | 6s | 1.87 | 4.13 |
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