  The general relativistic gravitomagnetic clock effect consists in the fact
that two point particles orbiting a central spinning object along identical,
circular equatorial geodesic paths, but in opposite directions, exhibit a time
difference in describing a full revolution. It turns out that the particle
rotating in the same sense of the central body is slower than the particle
rotating in the opposite sense. In this paper it is proposed to measure such
effect in an Earth laboratory experiment involving interferometry of slow
neutrons. With a sphere of 2.5 cm radius and spinning at 4.3 x 10^4 rad/s as
central source, and using neutrons with wavelength of 1 Angstrom it should be
possible to obtain, for a given sense of rotation of the central source, a
phase shift of 0.18 rad, well within the experimental sensitivity. By reversing
the sense of rotation of the central body it should be possible to obtain a
0.06 fringe shift.
