Two levels that should have coincided
In 1947, Lamb and Retherford used microwaves to investigate hydrogen and found a small separation between two excited energy levels that theory placed together. The S level was above the P level by an amount corresponding to roughly one gigahertz, or a billion microwave oscillations per second.
The result posed a precise problem for the successful Dirac theory of hydrogen. It explained important details of the fine structure but gave these two states the same energy. The experiment focused on that particular relationship.
Read the evidence: W. E. Lamb Jr. and R. C. Retherford (1947), Fine Structure of the Hydrogen Atom by a Microwave MethodLamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243
Let long-lived atoms report a transition
Some atoms in the beam occupied a metastable state: an excited state that survived long enough to reach a downstream target. On striking the metal, these atoms released detectable electrons and produced a current.
A related excited state had a much shorter lifetime. If a microwave transferred an atom into it, the atom quickly decayed and no longer reached the target as a metastable atom. The current fell. The researchers had converted a hard-to-see internal change into a count of surviving atoms.
The initial report held the microwave frequency fixed and varied the magnetic field. The field changed the atomic level spacing until the transition matched the microwaves. A dip in downstream current marked the conditions where atoms were readily transferred out of the long-lived state.
Read the evidence: Lamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243
Infer the separation without a magnetic field
The observed transitions changed with the magnetic field. Their pattern allowed the researchers to infer the separation of the two levels at zero field. The equation defines the usual positive Lamb shift. The state labels identify the excited S and P levels with total electronic angular momentum one half; h is Planck’s constant, which converts frequency into energy. The relevant structures are treated separately in this definition.
The original paper reported an approximate one-gigahertz separation. Its figure caption explicitly said that a translated comparison curve was not the best fit. The short-lived state’s natural width, hyperfine structure, strong microwave excitation and field inhomogeneity all broadened the signal. Field calibration also limited the precision.
Read the evidence: Lamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243
Include the atom’s electromagnetic interaction
Bethe responded in the same year with a calculation of electromagnetic energy shifts. An electron in an atom also interacts with the electromagnetic field. Effects absent from the ideal Dirac–Coulomb problem became visible in this small energy difference.
The result helped drive the development of quantum electrodynamics and set a target for increasingly precise comparisons. Later experiments and calculations would account for smaller corrections. The clear achievement in 1947 was to separate two levels that should have coincided: a current dip pointed directly to a relationship the theory needed to repair.
Read the evidence: H. A. Bethe (1947), The Electromagnetic Shift of Energy Levels, Phys. Rev. 72, 339Lamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243