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. , 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.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.