Regular Article

Retaining hypothetical photon mass in atomic spectroscopy models

Aix-Marseille Université, CNRS, Laboratoire PIIM, UMR 7345, Centre de Saint-Jérôme, 13397 Marseille Cedex 20, France

^a e-mail: joel.rosato@univ-amu.fr

Received: 21 August 2018
Received in final form: 2 October 2018
Published online: 10 January 2019

Abstract

We revisit the formalism involved in atomic spectroscopy modeling under the assumption that the photon has a finite mass. Starting from the Proca Lagrangian, we build a Hamiltonian suitable for the calculation of line shapes and intensities. Two consequences of finite photon mass are: (i) a dispersion of electromagnetic waves propagating in free space; (ii) the occurrence of a longitudinal polarization state. We illustrate these effects by addressing the spontaneous emission of a massive photon by an excited atom. The Einstein A coefficient and the power spectrum are calculated as an example. If the photon has a finite mass, deviations to standard formulas are showed to occur at energies comparable to the mass energy. A discussion based on the current upper bound estimates for the photon mass is done.