Eur. Phys. J. Plus (2021) 136: 544
https://doi.org/10.1140/epjp/s13360-021-01501-0

Regular Article

Electric dipole interaction in hydrogenic atoms from quantum spacetime

, Gangapuri, Purba Putiyari, Kudghat, 700093, Kolkata, India

^a vikramaditya.academics@gmail.com

Received: 29 May 2020
Accepted: 25 April 2021
Published online: 17 May 2021

Abstract

In the phenomenological studies of quantum gravity, often the Lorentzian dispersion relation is modified, in hopes to predict testable features of yet to be known Planck-scale physics. Motivated by a modified dispersion relation (MDR), coming from the consideration of a particular modified d’Alembertian scenario in the generalized Hořava–Lifshitz gravity, the equation of motion for the Dirac field has been modified. After building a QED with minimal coupling to an electromagnetic field, we apply it to calculate the amplitude for Coulomb scattering in the non-relativistic limit. Using the Born approximation, we recover the modified potential. This modification to the potential, which depends on the spin of the particles involved, can be thought of arising due to the spinors acquiring electric dipole moment and one charge’s spin coupling to the electric field generated by the other charge. We find that the correction terms cause energy-level splitting in hydrogen or hydrogen-like atoms akin to the Stark effect, even in the absence of an external electric field. Moreover, from the typical current precision of spectroscopic measurements for energy-level shifts in the hydrogen atom, we estimate an upper bound for the free parameter in the MDR.