Atomic effects in Carroll–Field–Jackiw Lorentz-violating electrodynamics

We investigate novel atomic effects in the ground state of the hydrogen atom within the CPT-odd electromagnetic sector of the Standard Model Extension (SME), governed by Carroll-Field-Jackiw (CFJ) electrodynamics, where Lorentz violation is induced by the background vector ( k A F ) μ . Treating this background vector perturbatively up to second order, we employ standard Rayleigh–Schrödinger perturbation theory to compute corrections to the ground-state energy. The induced electric quadrupole moment is then obtained analytically through the Dalgarno–Lewis method. By considering the complete spectral resolution of the Coulomb problem, including both bound and continuum states, we show that the continuum sector provides the dominant contribution to the quadrupole moment and that the full spectral result agrees with the analytic expression. Based on this induced quadrupole moment, we derive the interaction energy and force between two hydrogen atoms in their ground state. Furthermore, the emergence of a torque in the two-atom system is predicted, and an order-of-magnitude estimate for this effect is provided. The results can be applied in a wide range of situations, from the modeling of anisotropic materials in condensed matter physics to theories beyond the Standard Model in fundamental physics.