How to Strengthen Constraints on Non-Newtonian Gravity from Measuring the Lateral Casimir Force

It has been known that in the nanometer interaction range the available experimental data do not exclude the Yukawa-type corrections to Newton's gravitational law, which exceed the Newtonian gravitational force by many orders of magnitude. The strongest constraints on the parameters of Yukawa-type interaction in this interaction range follow from the experiments on neutron scattering and from measurements of the lateral and normal Casimir forces between corrugated surfaces. In this work, we demonstrate that by optimizing the experimental configuration at the expense of the higher corrugation amplitudes and smaller periods of corrugations it is possible to considerably strengthen the currently available constraints within the wide interaction range from 4.5 to 37 nm. We show that the maximum strengthening by more than a factor of 40 is reachable for the interaction range of 19 nm.