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

TL;DR

This paper investigates how extra spatial dimensions in the RS II-$p$ braneworld model affect the ground state energy of Helium, using perturbation theory to set bounds on the size of these dimensions based on experimental data.

Contribution

It introduces a method to estimate the length scale of extra dimensions in the RS II-$p$ model via corrections to Helium's ground state energy.

Findings

Bounds on extra dimension length scale are established.

Corrections are consistent with experimental data.

Results are less restrictive than previous Lamb shift-based bounds.

Abstract

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.