EN
We reconsider the idea in spectroscopy of detecting
extra dimensions by regarding the nucleus as a
homogeneous sphere. In our results, it turns out that the
gravitational potential inside the nucleus is much stronger
than the potential induced by a particle in the same regime
in ref. [16], and thus a more significant correction of the
ground state energy of hydrogen-like atoms is obtained,
which can be used to determine the existence of ADD’s extra
dimensions. In order to get a larger order of magnitude
for the correction, it is better to apply our theory to high-Z
atoms or muonic atoms, where the volume of the nucleus
can’t be ignored and the relativistic effect is important. Our
work is based on the Dirac equation in aweak gravity field,
and the result is more precise.