Abstract. After an improvement on the theory of the neutron-gravity-refractometer and after refinements of the experimental procedure we have performed new measurements of the absolute value of the neutron-proton scattering amplitude at low neutron energies. In order to obtain and to confirm a very high accuracy we carried out neutron-reflection experiments on 18 various liquids of 11 different organic substances containing the elements carbon, hydrogen and/or chlorine. Compounds with fluorine and bromine were used to measure the scattering amplitudes of these elements. We found the coherent scattering amplitudes of the bound atoms to be: a, = -3.7409 (11)fm, ac=6.6484(13)fm, acl=9.5792(8)fm, av= 5.66(2)fm and a~r=6.79(2)fm. The low energy (n, p)-parameters a t and a~ were calculated with the present a H and a new value of the (n, p) scattering cross-section cr 0. By comparing the measured a c with values obtained from precise transmission experiments we could determine the gravitational acceleration gj of the free neutron in terms of the local value g. We found the two values to be equal: gf =0.9996(7)g.
At the high-flux reactor of the Institut Laue-Langevin in Grenoble the fine-structure constant was determined by measuring the quotient of the Planck constant and the neutron mass . The results have already been published. In order to evaluate the measurement data, the lattice parameters of several silicon crystals must be known very accurately. As these parameters can now be determined in a more direct way than in the past, the results of the experiment have been re-evaluated. The values obtained by the re-evaluation are (relative standard uncertainty ) and (relative standard uncertainty ), the uncertainties being one-standarddeviation estimates. These values differ from those obtained in the first evaluation by only about 15 % of their uncertainties.
The quotient hlm, ( h Planck constant, mn neutron mass) has been measured with a relative uncertainty of 7,7 x lo-*. The result is hlm, =3,956033 320(302) x lo-' m2s-*. To obtain it, 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, hlm, is equal to the product of these two quantities. From h/m, the value of the fine-structure constant Q can be derived. The measured value of hlm, leads to 137,03601082(5 24) (relative uncertainty 3,9 x The experiment was carried out at the high-flux reactor of the Institut Laue-Langevin in Grenoble, France.
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