Rydberg states of hydrogen-like ions in braneworld

Abstract

It has been argued that precise measurements of optical transition frequencies between Rydberg states of hydrogen-like ions could be used to obtain an improved value of the Rydberg constant and even to test Quantum Electrodynamics (QED) theory more accurately, by avoiding the uncertainties about the proton radius. Motivated by this perspective, we investigate the influence of the gravitational interaction on the energy levels of Hydrogen-like ions in Rydberg states within the context of the braneworld models. As it is known, in this scenario, the gravitational interaction is amplified in short distances. We show that, for Rydberg states, the main contribution for the gravitational potential energy does not come from the rest energy concentrated on the nucleus but from the energy of the electromagnetic field created by its electrical charge, which is spread in space. The reason is connected to the fact that, when the ion is in a Rydberg state with high angular momentum, the gravitational potential energy is not computable in zero-width brane approximation due to the gravitational influence of the electrovacuum in which the lepton is moving. Considering a thick brane scenario, we calculate the gravitational potential energy associated to the nucleus charge in terms of the confinement parameter of the electric field in the brane. We show that the gravitational effects on the energy levels of a Rydberg state can be amplified by the extra dimensions even when the compactification scale of the hidden dimensions is shorter than the Bohr radius.

References in corpus (14)

• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Particle Physics Implications of a Recent Test of the Gravitational Inverse Square Law
• The Proton Radius Puzzle
• Review of short-range gravity experiments in the LHC era
• Constraints on extra dimensions from precision molecular spectroscopy
• Fundamental constants and tests of theory in Rydberg states of hydrogen-like ions
• Effective description of brane terms in extra dimensions
• Using Muonic Hydrogen in Optical Spectroscopy Experiment to Detect Extra Dimensions
• Extra dimensions and atomic transition frequencies
• Constraints on extra dimensions from atomic spectroscopy
• Is the proton radius puzzle evidence of extra dimensions?
• Exploring Extra Dimensions in Spectroscopy Experiments
• Searches for Extra Spatial Dimensions with the CMS Detector at the LHC
• Dirac Hamiltonian and Reissner-Nordstrom Metric: Coulomb Interaction in Curved Space-Time

Cited by in corpus (5)

• Spectroscopic tests for short-range modifications of Newtonian and post-Newtonian potentials
• Submillimeter constraints for non-Newtonian gravity from spectroscopy
• Hunting for extra dimensions in black hole shadows
• Neutron interferometry and tests of short-range modifications of gravity
• Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds