Rydberg states of hydrogenlike ions in a braneworld model

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.

Spectroscopic tests for short-range modifications of Newtonian and post-Newtonian potentials

“…The effects of hidden dimensions in certain Rydberg states were studied in Ref. [52], by using a power-law parametrization for the modified gravitational potential. More recently, in Ref.…”

Neutron interferometry and tests of short-range modifications of gravity

“…As pointed out in Ref. [47], in the leading order, the gravitational field produced by localized sources inside the brane does not depend on many details of the confinement mechanism, but on a specific statistical moment (the expected value of z 2−δ ) of the field distribution in the supplementary space.…”

Submillimeter constraints for non-Newtonian gravity from spectroscopy

“…At this point, we are interested in analyzing transitions between Rydberg states with high angular momentum. Therefore, the effects of the nuclear structure are negligible, and uncertainty originated from the proton radius is small, so we do not take into account the fact that the proton has a finite structure [20]. Hence, in the first approach, the atomic energy levels will be perturbed by gravitational effects, which get amplified in certain regimes (r ≪ λ) as a result of the gravitational potential correction (3).…”

“…Thus, the limitation in the extraction of the Rydberg constant, due to high uncertainties originated by the atomic structure, and which is evidenced in the proton radius problem [24,25], is circumvented [29]. In this way, a previous paper [20], showed that measurements of transitions between Rydberg states located in the optical frequency spectrum of muonic ions would present measurable gravitational effects in braneworld scenarios and, therefore, has demonstrated to be an alternative way to search for extra dimensions empirical traces.…”

“…According to this theoretical model, our 4dimensional observable universe is a submanifold, in which the standard model fields are confined, embedding in a higher-dimensional space with δ large extra dimensions (R ≫ l P lanck ) [12,13]. In this context, the spectroscopy has proved shown as an independent way to test deviations from the inverse-square law [15][16][17][18][19][20][21][22][23]. For instance, in ref.…”