  In this work, we consider the Yukawa-type and power-type non-Newtonian
corrections, which induce amplification of gravitational interaction on
submillimeter scales, and analytically calculate deviations produced by the
atomic gravitational field on the energy levels of hydrogen-like ions.
Analyzing ionic transitions between Rydberg states, we derive prospective
constraints for non-Newtonian corrections. It is shown that the results also
provide stronger constraints, due to the high accuracy for Rydberg transition
measures into optical spectrum frequency range, than the current empirical
bounds following from Casimir force measurements.
