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.
Graphical abstract
Similar content being viewed by others
References
A.S. Goldhaber, M.M. Nieto, Rev. Mod. Phys. 82, 939 (2010)
L.-C. Tu, J. Luo, G.T. Gillies, Rep. Prog. Phys. 68, 77 (2005)
A.S. Goldhaber, M.M. Nieto, Rev. Mod. Phys. 43, 277 (1971)
M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018)
D.D. Ryutov, Plasma Phys. Control. Fusion 49, B429 (2007)
L. Bonetti et al., Phys. Lett. B 768, 326 (2017)
L. Bonetti et al., Phys. Lett. B 757, 548 (2016)
A. Retinò, A.D.A.M. Spallicci, A. Vaivads, Astropart. Phys. 82, 49 (2016)
P. Egorov et al., Mon. Not. R. Astron. Soc. 437, L90 (2014)
A. Accioly, J. Helayël-Neto, E. Scatena, Phys. Rev. D 82, 065026 (2010)
W. Greiner, J. Reinhardt, Field Quantization (Springer, Berlin, 1996)
J.D. Jackson, Classical Electrodynamics (Wiley, Hoboken, 1999)
C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley, New York, 1989)
C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992)
G. Nienhuis, Physica 66, 245 (1973)
M. Baranger, Spectral line broadening in plasmas, in Atomic and Molecular Processes, edited by D.R. Bates (Academic Press, New York, 1962), p. 493
H.R. Griem, Spectral Line Broadening by Plasmas (Academic Press, New York, 1974)
S. Alexiou, High Energy Density Phys. 5, 225 (2009)
E. Stambulchik, High Energy Density Phys. 9, 528 (2013)
M.A. Gigosos, J. Phys. D: Appl. Phys. 47, 343001 (2014)
J. Rosato, High Energy Density Phys. 22, 60 (2017)
J. Rosato et al., Phys. Rev. E 79, 046408 (2009)
C. Cohen-Tannoudji, B. Diu, F. Laloë, in Quantum Mechanics (Wiley, New York, 1991), Vol. 1
H.A. Bethe, E.E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer-Verlag, Berlin, 1957)
J. Alexander, S. Gulyaev, Astrophys. J. 828, 40 (2016)
G. Peach, J. Astrophys. Astron. 36, 555 (2015)
S.V. Stepkin et al., Mon. Not. R. Astron. Soc. 374, 852 (2007)
E. Churchwell, P.G. Mezger, Astrophys. Lett. 5, 227 (1970)
J.K.G. Watson, J. Phys. B: At. Mol. Opt. Phys. 39, L291 (2006)
J.D. Hey, J. Phys. B: At. Mol. Opt. Phys. 47, 165701 (2014)
K. Ferrière, Rev. Mod. Phys. 73, 1031 (2001)
F. Nicastro, S. Mathur, M. Elvis, Science 319, 55 (2008)
D.R. Inglis, E. Teller, Astrophys. J. 90, 439 (1939)
G. Herzberg, Molecular Spectra and Molecular Structure (D. Van Nostrand Company Inc., Princeton, 1950)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rosato, J. Retaining hypothetical photon mass in atomic spectroscopy models. Eur. Phys. J. D 73, 7 (2019). https://doi.org/10.1140/epjd/e2018-90427-9
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2018-90427-9