  We consider the role of high-lying Rydberg states of simple atomic systems
such as $^1$H in setting constraints on physics beyond the Standard Model. We
obtain highly accurate bound states energies for a hydrogen atom in the
presence of an additional force carrier (the energy levels of the Hellmann
potential). These results show that varying the size and shape of the Rydberg
state by varying the quantum numbers provides a way to probe the range of new
forces. By combining these results with the current state-of-the-art QED
corrections, we determine a robust global constraint on new physics that
includes all current spectroscopic data in hydrogen. Lastly we show that
improved measurements that fully exploit modern cooling and trapping methods as
well as higher-lying states could lead to a strong, statistically robust global
constraint on new physics based on laboratory measurements only.
