A nonlinear electrodynamical shift of spectral lines in the hydrogen atom and hydrogen-like ions

Денисов, В И; Kravtsov, Nikolai V; Krivchenkov, I. V.

doi:10.1134/s0030400x06050018

Cited by 12 publications

(6 citation statements)

References 9 publications

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“…Of particular interest here is the role of particles, which both source and respond to nonlinear fields [7,8]. In addition to providing a vehicle for thinking carefully about nonlinearity (in preparation for other nonlinear studies, like GR, say [9]), the particulars of Born-Infeld have current proponents from string theory (by now, this is established enough to warrant a chapter in [10]), general relativity, atomic physics [11,12] and spectroscopy [13]. Our work serves both as an attempt to collect and compare known spectra, as well as present the results of the Dirac spectrum, all in a unified language.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Born–Infeld effects on the relativistic hydrogen spectrum

Franklin¹,

Garon²

2011

Physics Letters A

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The Born-Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the relativistic Dirac equation, and a form of the Born-Infeld potential that approximates the self-field corrections of the electron. Using these together, we can establish that if the Born-Infeld nonlinear electrodynamics is to be physically relevant, it must contain a fundamental constant that is well-below the original value proposed by Born. This work extends the original Schrödinger spectrum from [1] for the self-field correction, and shows that using the Dirac equation introduces minor corrections -but also gives access to a range for the fundamental constant that is below that attainable from non-relativistic considerations.

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Section: Introductionmentioning

confidence: 99%

“…Previous work on spectra has focused on this "test-particle" approximation (as in [14,13]), where only the single-particle Born-Infeld point potential is used. This approach is justified in the limit that the proton charge is much larger than the electron's, so that the electron's contribution to the total Born-Infeld field is negligible.…”

Section: Introductionmentioning

confidence: 99%

Approximate Born–Infeld effects on the relativistic hydrogen spectrum

Franklin¹,

Garon²

2011

Physics Letters A

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“…In Heisenberg-Euler nonlinear electrodynamics, the angles given by (21) and (22) can reach a few arcseconds. The expression for the time delay (20) in this case takes the form …”

Section: The Calculation Of Nonlinear Effects In the Gravitational Anmentioning

confidence: 99%

“…At electromagnetic fields on the order of B ϳ E ϳ 10 5 G, which can be created in terrestrial labs, the nonlinear effects are so small [21][22][23][24][25][26][27][28][29][30][31][32] that current experimental techniques do not allow us to detect them. However, nature comes to our rescue with astrophysical objects with much higher field strengths: neutron stars have a field strength of B ϳ 10 12 G, pulsars have a field strength comparable to B q ϳ 10 13 G [33, 34], and magnetars even have a field strength (B ϳ 10 16 G) that exceeds B q [35].…”

Section: Introductionmentioning

confidence: 99%

Effects of nonlinear electrodynamics in the magnetic field of a pulsar

Denisov

2014

Can. J. Phys.

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The eikonal method was used to construct differential equations for beams of electromagnetic waves in magnetic and gravitational fields of pulsars, according to the nonlinear electrodynamics of the vacuum. Integrating these equations using successive approximations allows us to find the ray equations and a parametric form of the law of motion for these beams' electromagnetic pulses. It is shown that the electromagnetic pulse passing through the magnetic field of the pulsar propagates as two normal waves, arriving at the detector along two different rays and spending different amounts of time in transit. The angles of rays' bending because of the nonlinearity of the electrodynamics of the vacuum and the delay time of the electromagnetic signal carried by one normal wave relative to the other normal wave are calculated. The magnitude of these effects is evaluated.Résumé : Utilisant la méthode de l'eikonale, nous construisons des équations différentielles pour décrire des faisceaux d'ondes électromagnétiques dans les champs magnétique et gravitationnel d'un pulsar, en accord avec l'électrodynamique du vide. Intégrer ces équations par approximations successives nous permet de trouver les équations des rayons (lumineux) et les lois du mouvement sous forme paramétrique pour ces impulsions électromagnétiques. Nous trouvons que les impulsions électromag-nétiques passant à travers le champ magnétique du pulsar, se propagent sous la forme de deux ondes normales vers le détecteur en suivant deux rayons différents, en des temps différents. Les angles de fléchissement des rayons proviennent de l'électrodynamique non linéaire du vide et nous calculons le délai en temps entre les deux ondes. Nous évaluons la grandeur de ces effets. [Traduit par la Rédaction]

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“…The nonlinear correction is considered to affect such as the radiation from pulsars [1,2] or neutron stars [3], the Wichmann-Kroll correction [4] on the Lamb shift, and the interaction between a nucleus and electrons through the Uehling potential [5][6][7]. The most widely considered theories are the Heisenberg-Euler model [8,9] and the Born-Infeld model [10], which is sometimes applied to calculate a hydrogen atom [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic resonance of nonlinear vacuum in one-dimensional cavity

Shibata

2021

Eur. Phys. J. D

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Nonlinear corrections on electromagnetic fields in vacuum have been expected. In this study, we have theoretically considered nonlinear Maxwell’s equations in a one-dimensional cavity for a classical light and external static electromagnetic fields. A general solution for the electromagnetic corrective components including that of a longitudinal standing wave was derived after a linearization. The main purpose is to give a detailed feature of the previously reported resonant behavior [Shibata, Euro. Phys. J. D 74:215 (2020)], such as the effect of external static fields and the polarization fluctuation. These results favor the development of new and effective method for experiment. Graphic abstract

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A nonlinear electrodynamical shift of spectral lines in the hydrogen atom and hydrogen-like ions

Cited by 12 publications

References 9 publications

Approximate Born–Infeld effects on the relativistic hydrogen spectrum

Approximate Born–Infeld effects on the relativistic hydrogen spectrum

Effects of nonlinear electrodynamics in the magnetic field of a pulsar

Electromagnetic resonance of nonlinear vacuum in one-dimensional cavity

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