Studies of the Optics of Neutrons. I. Measurement of the Neutron-Proton Coherent Scattering Amplitude by Mirror Reflection

Abstract

Measurements were made of the ratio, $\frac{{a}_{\mathrm{C}}}{|{a}_{\mathrm{H}}|}$, of the carbon to the hydrogen coherent scattering amplitudes, using liquid hydrocarbon mirrors with various ratios of hydrogen to carbon atoms. In two of these measurements the reflected neutron intensity from different liquids was compared for a fixed angle of reflection. In two other measurements the angles were determined for which the same reflected intensity was obtained.Our most accurate value for the ratio of the nuclear amplitudes, after various corrections, is $(\frac{{a}_{\mathrm{C}}}{|{a}_{\mathrm{H}}|})(\mathrm{nuclear})=1.775\ifmmode\pm\else\textpm\fi{}0.004$. Combining this value with the presently accepted value of the carbon nuclear scattering amplitude, ${a}_{\mathrm{C}}=(6.64\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm, we find the best value for the proton scattering amplitude is ${a}_{\mathrm{H}}=(\ensuremath{-}3.74\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm.