We propose to apply Ramseys method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a vertical mirror. This method allows a precise measurement of quantum mechanical phaseshifts of a Schrodinger
wave packet bouncing off a hard surface in the gravitational field of the earth. Measurements with ultra-cold neutrons will offer a sensitivity to Newtons law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism.
We present a case study on a new type of cold neutron beam station for the investigation of angular correlations in the beta-decay of free neutrons. With this beam station, called PERC, the active decay volume lies inside the neutron guide, and the c
harged neutron decay products are magnetically guided towards the end of the neutron guide. Hence, the guide delivers at its exit a beam of decay electrons and protons, under well-defined and precisely variable conditions, which can be well separated from the cold neutron beam. In this way a general-purpose source of neutron decay products is obtained which can be used for various different experiments in neutron decay correlation spectroscopy. A gain in phase space density of several orders of magnitude can be achieved with PERC, as compared to existing neutron decay spectrometers. Neutron beam related background is separately measurable in PERC, and magnetic mirror effects on the charged neutron decay products and edge effects in the active neutron beam volume are both strongly suppressed. Therefore the spectra and angular distributions of the emerging decay particles will be distortion-free on the level of 10^-4, more than 10 times better than achieved today.
