Comment about constraints on nanometer-range modifications to gravity from low-energy neutron experiments

A topic of present interest is the application of experimentally observed quantum mechanical levels of ultra-cold neutrons in the earth’s gravitational field for searching short-range modifications to gravity. A constraint on new forces in the nanometer-range published by Nesvizhevsky and Protasov follows from inadequate modelling of the interaction potential of a neutron with a mirror wall. Limits by many orders of magnitude better were already derived long ago from the consistency of experiments on the neutron-electron interaction.