Investigation of quantum neutron states in the terrestrial gravitational field above a mirror

Weakly bound states of neutrons in gravitational fields

“…In our consideration, we suggest, that due to the Pauli exclusion principle there should exist, close to the NS surface, an analogy of the Fermi like surface, which can play the role of a mirror as is the case of the experiments conducted with the UCN in the Earth's gravitational field [11][12][13][14][15].…”

“…The present research, which used the works of [11][12][13][14][15] as a foundation devised a simple manner in which to consider the energy of UCN weakly bound quantum states in the Earth's gravitational field. Comparison of our results with the results of the above cited papers is presented in the Table 1.…”

“…Theoretical consideration of a neutron's energy spectrum and its wave functions in the Earth's gravitational field, as cited in the [15], can be found in a number of works, including, for example [17][18][19]. In this section, by using pure methodic reasoning, we present a simple and transparent derivation of the main relationships of these results.…”

“…In this section we begin with a simple theoretical estimation because of the [11][12][13][14][15] approach, for the quantum effects on the NS surface. Introducing new notations: M N S -NS mass, M E -Earth mass, we can derive using the framework of the nonrelativistic approach of gravitational acceleration on the NS surface which is equal to:…”

“…Certainly, the many recent works devoted to this research subject indicate that the solution of the UCN storage problem can give us an unique capability to carry out a very precise experiments in the field of neutron physics and neutron interferometry in gravitational fields [9,10]. In this paper, we will begin by reviewing some pertinent recent experimental results and measurements of UCN weakly bound quantum states in the weak gravitational field of the Earth [11][12][13][14][15]. After that, we will present a simple sketch of some of the other possible applications of these results to astrophysics and gravity.…”