SciELO - Scientific Electronic Library Online

vol.58 issue4Simulación de adsorción en superficies a partir de cálculos ab initio sobre nano-clusters de átomos de oroCorrosion resistance and biocompatibility of zirconium oxynitride thin film growth by rf sputtering author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • Have no similar articlesSimilars in SciELO


Revista mexicana de física

Print version ISSN 0035-001X

Rev. mex. fis. vol.58 n.4 México Aug. 2012




Estimation of length scale of RS II-p braneworld model through perturbations in Helium's atom ground state energy


N. Garrido and H.H. Hernández


Universidad Autónoma de Chihuahua, Facultad de Ingeniería, Nuevo Campus Universitario, Chihuahua, Chih., México, e-mail:;


Recibido el 20 de marzo de 2012;
aceptado el 24 de abril de 2012



We put to the test an effective three-dimensional electrostatic potential, obtained effectively by considering an electrostatic source inside a (5+p)-dimensional braneworld scenario with p compact and one infinite spacial extra dimensions in the RS II-p model, for p = 1 and p = 2. This potential is regular at the source and matches the standard Coulomb potential outside a neighborhood. We use variational and perturbative approximation methods to calculate corrections to the ground energy of the Helium atom modified by this potential, by making use of a 6 and 39-parameter trial wave function of Hylleraas type for the ground state. These corrections to the ground-state energy are compared with experimental data for Helium atom in order to set bounds for the extra dimensions length scale. We find that these bounds are less restrictive than the ones obtained by Morales et. al. through a calculation using the Lamb shift in Hydrogen.

Keywords: Brane-worlds; extra dimensions phenomenology; Helium atom; perturbative methods; variational methods.


PACS: 31.15.xp; 31.15.xt; 04.50.-h; 31.15.-p





This work was supported by Mexico's National Council for Science and Technology (CONACyT) grant CONACyT-CB 2008-01-101774.



1. Th. Kaluza, Sitzungober. Preuss. Akad. Wiss. Berlin K1 (1921) 966.         [ Links ]

2. O. Klein, Z. Phys. 37 (1926) 895.         [ Links ]

3. K. Akama, Lect. Notes Phys. 176 (1982) 267-271.         [ Links ]

4. V.A. Rubakov and M.E. Shaposhnikov, Phys. Lett. B 125 (1983) 136.         [ Links ]

5. M. Visser, Phys. Lett. B 159 (1985) 22.         [ Links ]

6. N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, Phys. Rev. Lett. 83, 3370-3373(1999).         [ Links ]

7. L. Randall and R. Sundrum, Phys. Rev. Lett. 83 (1999) 3370-3373.         [ Links ]

8. L. Randall and R. Sundrum, Phys. Rev. Lett. 83 (1999) 4690-4693.         [ Links ]

9. V.A. Rubakov, Phys. Usp. 44 (2001) 871-893.         [ Links ]

10. A. Perez-Lorenzana, An introduction to the Brane World (2004). arXiv:hep-ph/0406279v2        [ Links ]

11. R. Maartens, Living Rev. Rel. 7 (2004) 7.         [ Links ]

12. S.L. Dubovsky, V.A. Rubakov, and P.G. Tinyakov, JHEP 0008 (2000)041.         [ Links ]

13. R. Linares, H.A. Morales-Tecotl and O. Pedraza, Phys. Rev. D81 (2010) 126013.         [ Links ]

14. M. Frank, N. Saad and I. Turan, Phys. Rev. D78 (2008) 055014.         [ Links ]

15. H. A. Morales-Tecotl, O. Pedraza and L.O. Pimentel, Gen. Rel. Grav. 39 (2006) 1185-1202.         [ Links ]

16. R. Linares, H. A. Morales-Tecotl, O. Pedraza and L.O. Pimentel, Phys. Rev. D 84 (2011) 126007.         [ Links ]

17. H.A. Bethe, E.E. Salpeter, Quantum mechanics of one and two electron atoms First edition (Springer-Verlag OHG, 1957).         [ Links ]

18. Y. Liu, X. Zhang and Y. Duan, Mod Phys. Lett. A 23 (2008) 1853-1860.         [ Links ]

19. E.A. Hylleraas, Z. Phys. 54 (1929) 347.         [ Links ]

20. T. Kinoshita, Phys. Rev. 105 (1957) 1490.         [ Links ]

21. The exact relativistic formulation for the two electron system cannot be written in closed form, and certain methods in the form of relativistic corrections to the non-relativistic formulation as a series expansion in powers of the fine structure con-stant α. have to be applied. One of the most prominent corrections is expressed in the Breit equation (see [17]).

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License