  New unification theories predict Large Extra Dimensions (LEDs). If that is
the case, gravity would be stronger at short ranges than what Newtonian gravity
predicts. LEDs could also have effects at atomic level. In this paper we
propose a new method to constrain the size of gravity-only LEDs by analyzing
how these LEDs modify the energy of the atomic transitions 1s-2s and 2s-2p
(Lamb shift), for the particular case of the hydrogen and muonium atoms. We
estimate these effects by using Bethe's non-relativistic treatment of Lamb
shift. For the particular case of three LEDs, which may be a candidate to
explain the interaction mechanism of dark matter particles, we have found that
current knowledge in atomic spectroscopy could constrain their sizes to be less
than 10 * 10^(-6) m. Although our contributions do not reach the sensitivity
given by SN1987a, they are still slightly better than recent constraints given
by Inverse Square Law tests of Eot-Wash group at Washington University, which
gave R3 < 36.6 * 10^(-6) m.
