Search for quantum states of the neutron in a gravitational field: gravitational levels

The neutron could occupy quantum stationary states if it is trapped between the Earthʹs gravitational field on one side and the Fermi quasi-potential of a mirror on the other side. The quantum states cause a strong variation in neutron density, both for separate energy levels and for a mixture of low-energy states. The use of a position sensitive UCN (ultracold neutron) detector allows simultaneous measurement of the position probability density distribution in the total range of interest and increases significantly the statistics, making possible such an experiment. In this article we describe a specially developed neutron spectrometer and a method of measurement of such quantum states.