The Lamb Shift

The Lamb shift is the small energy difference between the 2s and 2p levels of hydrogen, which the Dirac theory predicts to be degenerate; its existence revealed that the quantized electromagnetic field shifts atomic levels.

Definition

The Lamb shift is the small upward shift of the 2s₁⁄₂ level of hydrogen relative to the 2p₁⁄₂ level—states the Dirac equation predicts to be exactly degenerate—caused by quantum-electrodynamic radiative corrections such as vacuum polarization and the electron's self-energy.

Scope

This topic covers the Lamb shift: its experimental discovery by Lamb and Retherford in 1947, Bethe's non-relativistic estimate, and its interpretation as a radiative correction arising from the interaction of the bound electron with the fluctuating quantized electromagnetic field. It treats the shift as the founding empirical motivation for quantum electrodynamics and as a benchmark for precision tests of that theory.

Core questions

• Why does the Dirac equation predict the 2s and 2p levels of hydrogen to be degenerate?
• What experiment first measured the splitting between them?
• What quantum-electrodynamic effects produce the Lamb shift?
• Why was the Lamb shift pivotal for the development of QED?

Key concepts

• 2s–2p degeneracy in Dirac theory
• Electron self-energy
• Vacuum polarization
• Renormalization
• Quantum electrodynamics
• Precision hydrogen spectroscopy

Key theories

Discovery of the Lamb shift

Using microwave resonance on a beam of metastable hydrogen, Lamb and Retherford showed the 2s₁⁄₂ and 2p₁⁄₂ levels are not degenerate but split by about 1000 megahertz, contradicting the Dirac prediction.

Radiative QED interpretation

Bethe's 1947 calculation attributed the shift to the electron's interaction with the quantized radiation field (its self-energy), and the full renormalized QED treatment that followed accounted for the shift to high precision.

Clinical relevance

Measurement of the Lamb shift provides one of the most precise tests of quantum electrodynamics and contributes to determinations of the Rydberg constant and the proton charge radius; the discrepancy between hydrogen and muonic-hydrogen determinations of that radius—the proton-radius puzzle—drew on Lamb-shift spectroscopy.

History

In 1947 Lamb and Retherford applied wartime microwave techniques to hydrogen and found the 2s–2p splitting that Dirac theory forbade. Within weeks Bethe produced a finite estimate by subtracting an infinite free-electron self-energy, an early instance of renormalization, and the result spurred the full development of quantum electrodynamics by Feynman, Schwinger, and Tomonaga.

Key figures

• Willis Lamb
• Robert Retherford
• Hans Bethe
• Richard Feynman

Seminal works

• lamb1947
• bethe1947

Frequently asked questions

Why is the Lamb shift important if it is so small?

Its smallness is the point: it cannot be explained by the Coulomb or Dirac theory and required the quantized electromagnetic field. Its measurement and successful calculation established quantum electrodynamics as a quantitatively accurate theory.

What is vacuum polarization?

Vacuum polarization is the QED effect in which the electromagnetic field briefly creates virtual electron–positron pairs that screen a charge. It is one of several radiative corrections contributing to the Lamb shift, alongside the larger electron self-energy term.