Determination of the fine-structure constant by a precise measurement ofh/mn: the final result

At the high-flux reactor of the Institut Laue-Langevin in Grenoble (France), a beam of neutrons with a well-known wavelength was produced by Bragg reflection in a perfect silicon crystal; the velocity of these neutrons was measured using a very precise time-of-flight method. According to the de Broglie equation, the product of the wavelength and the velocity is equal to h / m n ( h Planck constant, m n neutron mass). From the value of h / m n determined in this way the value of the fine-structure constant infinity was derived. The results of a first series of measurements have already been published. The results of a second series are now available. They are in excellent agreement with the previous results. The final values following from all the experimental data of both series are h / m n = 3.956 033 332 (290) × 10 -7 m 2 s -1 (relative uncertainty 7.34 × 10 -8 ) and α -1 = 137.036 010 62 (5 03) (relative uncertainty 3.67 × 10 -8 ), the uncertainties being one-standard-deviation estimates.