The fine-structure constant *α* determines the strength of the electromagnetic interaction. The size of this important natural constant has been determined in various ways: by means of the hyperfine structure of myonic atoms; by measuring the magnetic moment of the proton or of the electron; and via the quantum Hall effect. In a completely different way, Dr. Eckhard Krüger, Dr. Wolfgang Nistler and Dr. Winfried Weirauch determined the fine-structure constant by carrying out velocity measurements on neutrons. The three physicists employed at PTB were awarded the 1996 Helmholtz Prize for their work in the field of "Precision Measurement of Physical Quantities".

The fine-structure constant *α* = *e*^{2}/(2*ε*_{0}*hc*) stands in a simple relation to the electron mass *m*_{e} and to the Rydberg constant *R*_{∞} (which is known very precisely from measurements of atomic spectra): *α*^{2} = 2*hR*_{∞}/(*m*_{e}*c*). If in an experiment, both the wavelength λ and the velocity *v* of neutrons are measured, the following result is yielded according to the de Broglie relation: *h*/*m*_{n} = λ*v*. Since the quotient of the neutron mass and the electron mass *Q* = *m*_{n}/*m*_{e} is also very precisely known, *α* can be determined very accurately by precision measurements of λ and *v*: *α*^{2} = (2*R*_{∞}*Q*/*c*) ∙ (*h*/*m*_{n}).

Eckhard Krüger and his colleagues measured the wavelength and the velocity of neutrons at the high-flux reactor of the Institut Laue-Langevin in Grenoble and determined the quotient *h*/*m*_{n} with a relative uncertainty of 7.7 ∙ 10^{-8} from this. In their experiment, they modified Fizeau's classical experiment for measuring the speed of light, where a light beam passes through a gear wheel rotating at frequency *f*, is reflected by a mirror that is placed far away, and traverses the gear wheel again. If the distance between the gear wheel and the mirror is continuously altered, then the brightness of the returning light varies. If the mirror has been shifted between two brightness maxima by Δ*L*, the speed of light is *v* = 2*f*Δ*L*.

Instead of a gear wheel, the three researchers allowed spin-polarized neutrons to pass through a special magnetic coil which periodically changed the spinning direction of the neutrons at a frequency of *f* = 750 kHz. The neutrons hit a silicon crystal which, due to Bragg reflection, only reflected neutrons that had a certain, very precisely known wavelength λ of about 0.25 nm. These neutrons passed the coil again and hit a Heusler crystal which reflected the neutrons differently well, depending on their spinning direction. Finally, a detector measured the intensity of the reflected neutron beam. This intensity changed periodically when the distance between the coil and the silicon crystal was altered. The researchers measured the distance difference Δ*L* for successive intensity minima with the aid of laser interferometry.

According to Fizeau's formula, they obtained the velocity *v* of the neutrons. From λ and *v*, they calculated *h*/*m*_{n} and from this, finally, the fine-structure constant *α*. They obtained the reciprocal value of 1/*α* = 137.036 010 8, which had a relative uncertainty of 3.9 ∙ 10^{-8}, comparable to the relative uncertainties of the former values for 1/*α* that had been determined in a different way. The experiment was terminated in 1996, as it was not possible to reduce the measurement uncertainty significantly with this measurement method. The value acknowledged today for 1/*α* is 137.035 999 11, with a relative uncertainty of 3.3 ∙ 10^{-9}.