Determination of the fine-structure constant by measuring the quotient of the Planck constant and the neutron mass

A beam of neutrons with an identical and well-known wavelength was produced by Bragg reflection in a perfect silicon crystal; the velocity of the neutrons was measured using a very precise time-of-flight method. According to the de Broglie equation, the product of these two quantities is equal to the quotient h/m_n (h Planck constant, m_n neutron mass). The result is h/m_n=3 956 033 320(302)×10⁷ m² s^-1 (relative uncertainty: 7.7×10^-8). From this value, a value of the fine-structure constant α was derived, leading to α^-1 =137 036 011 28(5 24) (relative uncertainty: 3.9×10^-8 ). The experiment was carried out at the high-flux reactor of the Institut Laue-Langevin in Grenoble, France