Gravitational Acceleration of Free Neutrons

Abstract

The gravitational acceleration of free neutrons from the Oak Ridge Research Reactor has been measured in the evacuated 180-m flight path at Oak Ridge National Laboratory. The transmission edges associated with the $〈100〉$ and $〈002〉$ lattice spacings in a polycrystalline beryllium filter have been used to define particular neutron velocities ${v}_{\mathrm{hkl}}=(\frac{h}{2m{d}_{\mathrm{hkl}}})$ in the "slow beam." Boral filters permitted the selection of a "fast beam" which did not fall appreciably. The differences between the vertical positions of the slit image formed by the "fast beam" and of the two transmission edges (12.7 and 15.5 cm lower) have been determined with the aid of least-squares fits to theoretical curves. An x-ray examination of the beryllium filter established the values for $2{d}_{\mathrm{hkl}}$. We find the acceleration of free neutrons due to gravity to be $g=975.4\ifmmode\pm\else\textpm\fi{}3$ cm/${\mathrm{sec}}^{2}$ [(100) planes] and $g=973.1\ifmmode\pm\else\textpm\fi{}7$ cm/${\mathrm{sec}}^{2}$ [(002) planes]. These may be compared with the local value $g=979.74$ cm/${\mathrm{sec}}^{2}$ and McReynolds' early result $g=935\ifmmode\pm\else\textpm\fi{}70$ cm/${\mathrm{sec}}^{2}$. A recent suggestion of Spitzer that there might be a difference in $g$ for the two vertical neutron-spin projections \ifmmode\pm\else\textpm\fi{}\textonehalf{} does not appear to be present. No splitting greater than a few percent of $g$ is found.