Spectroscopic tests for short-range modifications of Newtonian and post-Newtonian potentials

There are theoretical frameworks, such as the large extra dimension models, which predict the strengthening of the gravitational field in short distances. Here we obtain new empiric constraints for deviations of standard gravity in the atomic length scale from analyses of recent and accurate data of hydrogen spectroscopy. The new bounds, extracted from transition, are compared with previous limits given by antiprotonic Helium spectroscopy. Independent constraints are also determined by investigating the effects of gravitational spin–orbit coupling on the atomic spectrum. We show that the analysis of the influence of that interaction, which is responsible for the spin precession phenomena, on the fine structure of the states can be employed as a test of a post-Newtonian potential in the atomic domain. The constraints obtained here from transition in hydrogen are tighter than previous bounds determined from measurements of the spin precession in an electron-nucleus scattering.