DIRECT MEASUREMENT OF THE ACCELERATION DUE TO GRAVITY OF NEUTRONS

Since the gravitational constant is a universal constant, independent of the nature of the interacting bodies, there can be no doubt that the acceleration due to gravity for nucleons must be the same as for massive bodies. The author of the reviewed note*) carried out an experiment directly confirming this obvious conclusion in the case of neutrons. For the measurements, a well-collimated horizontal beam of free neutrons from a nuclear reactor was used. The collimator consisted of two slits (made

) A. Mc Reynolds, Phys. Rev. 83*, 172 (1951).

from boron carbide and lucite) measuring \(0.75 \times 50\) mm, installed in the boiler shielding and separated from one another by a distance of 150 cm. The position of the beam was observed at a distance of 11.6 m from the collimator. For this purpose, a slit 9 mm wide was placed before a proportional counter with \(\mathrm{BF}_3\), serving as the detector, and the counting rate was measured as a function of the height of the slit. If \(r_1\) and \(r_2\) are, respectively, the distance from the entrance slit of the collimator to its exit slit and to the detector slit, then, as is easy to see, the displacement of the beam under the action of gravity should be equal to

\[ d=-\frac{g}{2v^2}\left(r_2^2-r_1r_2\right). \]

What was measured directly, however, was not the displacement itself, but the difference between the displacements of two beams formed by neutrons of different velocities:

\[ \Delta=d_1-d_2=-\frac{g}{2}\left(r_2^2-r_1r_2\right)\left(\frac{1}{v_1^2}-\frac{1}{v_2^2}\right). \]

The first beam was the beam of thermal neutrons emerging directly from the boiler, with a Maxwellian velocity distribution and a distribution maximum corresponding to \(0.07\) eV \((v_{\mathrm{av}}=3.95\cdot 10^5\ \mathrm{cm/sec})\). The second beam was obtained from the first by filtering it (before the collimator) through 25 cm of BeO. Special measurements showed that in this case

\[ \frac{1}{v_{\mathrm{av}}}=\frac{6.5}{4.5\,(9.00\times10^4)^2}\ \mathrm{sec^2/cm^2}. \]

Since the beams are rather strongly spread out in velocity, by the time they reach the detector they are also considerably spread out in the magnitude of the displacement \(d\); the half-width of the beams is then about 10 mm. However, the curve of the beam-intensity distribution with height has the correct form, with a clearly expressed maximum. Therefore the relative displacement of the curves obtained for the two beams can readily be measured.

The value thus obtained,

\[ \Delta=1.22\pm0.06\ \mathrm{mm}, \]

which is the mean of several measurements, gives for the acceleration of free fall of neutrons in the Earth’s gravitational field the value

\[ g=935\pm70\ \mathrm{cm/sec^2}, \]

which, within the limits of accuracy, agrees with the usual value.

R. G.