Quantum transitions of relativistic electrons in a superstrong magnetic field

Sokolov, A. A.; Zhukovskii, V. Ch.; Nikitina, N.S.

doi:10.1016/0375-9601(73)90557-4

Cited by 24 publications

(4 citation statements)

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“…Fitting the data with transitions to the ground state excluded again yielded a = 0.042 and we found that excluding ground state transitions has little effect on the equilibrium spin polarization at weak magnetic fields. Beyond the critical field we found that transitions to the ground state are almost solely responsible for spin polarizing an electron, as has also been noted in [41]. This can be explained because the dominant and spin orbit mixing terms, which have a ratio of √ E 0 + m e / √ E 0 − m e , become nearly equal for N ≥ 1 in the strong field limit and thus the spin flip rates in both directions should be roughly equal.…”

Section: Numerical Resultssupporting

confidence: 81%

Radiative spin polarization of electrons in an ultrastrong magnetic field

2019

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We calculate the spin flip rates for an electron in a homogeneous magnetic field for low excitations (N ≤ 5). Our results apply for all field strengths including those beyond the critical field strength at which the spin contributes as much to the electron's energy as its rest mass. Existing approximations either assume that the electron is in a sufficiently highly excited state such that its orbit can be assumed to be classical or the magnetic field be weak compared to the critical field. The regime of high mangetic field strength and low excitations is therefore poorly covered by them. By comparing our calculations to different approximations, we find that in the high field, low excitation regime the spin flip rates are lower and the equilibrium spin polarization is less pure then one would get by naively applying existing approximations in this regime.

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Section: Numerical Resultssupporting

confidence: 81%

Radiative spin polarization of electrons in an ultrastrong magnetic field

2019

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“…However, the expressions for n → 0 quantum cyclotron transition rates derived in Eq. ( 9) of Sokolov, Zhukovskii & Nikitina (1973) and Eq. (2.56) of White (1974) reduce exactly to Eq.…”

Section: Asymptotic Limitsmentioning

confidence: 99%

“…For cyclotron scattering in higher harmonics l > 0, the intermediate sums in the vertex functions have the largest contributions from the n = l + 1 state. However, for B ≫ B cr , cyclotron transitions to the ground Landau state dominate (Sokolov, Zhukovskii & Nikitina 1973, White 1974, Harding & Preece 1987, so that cyclotron decay rates for n → 0 transitions treated in this paper should be good approximations to the widths of excited states, a circumstance pertinent to astrophysical models of magnetars.…”

Section: Introductionmentioning

confidence: 99%

Spin‐dependent Cyclotron Decay Rates in Strong Magnetic Fields

Baring

Gonthier

Harding

2005

ApJ

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Cyclotron decay and absorption rates have been well studied in the literature, focusing primarily on spectral, angular and polarization dependence. Astrophysical applications usually do not require retention of information on the electron spin state, and these are normally averaged in obtaining the requisite rates. In magnetic fields, higher order quantum processes such as Compton scattering become resonant at the cyclotron frequency and its harmonics, with the resonances being formally divergent. Such divergences are usually eliminated by accounting for the finite lifetimes of excited Landau states. This practice requires the use of spin-dependent cyclotron rates in order to obtain accurate determinations of process rates very near cyclotronic resonances, the phase space domain most relevant for certain applications to pulsar models. This paper develops previous results in the literature to obtain compact analytic expressions for cyclotron decay rates/widths in terms of a series of Legendre functions of the second kind; these expressions can be expediently used in astrophysical models. The rates are derived using two popular eigenstate formalisms, namely that due to Sokolov and Ternov, and that due to Johnson and Lippmann. These constitute two sets of eigenfunctions of the Dirac equation that diagonalize different operators, and accordingly yield different spin-dependent cyclotron rates. This paper illustrates the attractive Lorentz transformation characteristics of the Sokolov and Ternov formulation, which is another reason why it is preferable when electron spin information must be explicitly retained.

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“…Its theory developed already in the middle of the last century is in perfect agreement with experiment [1][2][3]. The very well-known properties of SR have found a great deal of theoretical and technical applications both in studying optical properties of materials and in high-energy physics, as well as in astrophysics, where superstrong magnetic fields of the order of the Schwinger value H Sch = 4.41 × 10 13 G are expected [4,5] to exist. An outstanding phenomenon called "Sokolov-Ternov effect" [6] have found numerous applications in the high-energy physics.…”

Section: Introductionmentioning

confidence: 63%

Bound Electron Transitions under the Influence of Electromagnetic Wave in Constant Magnetic Field

Zhukovsky

2020

Symmetry

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Motion and radiative transitions of an electron in a magnetic field under the influence of an external electromagnetic wave are studied for various confining conditions in semiconductor, graphene, in quantum wells, and relativistic generalization in terms of the Klein–Gordon equation are considered. In particular, the following problems are discussed. The so-called cyclotron resonance, which may appear in graphene, is studied with indication for appearance of the so-called frequency-halving. The problem is solved for two-dimensional massless charged particle, whose gapless nature is protected by sublattice symmetry. The exact classical calculation of this effect is undertaken in the framework of a 2D classical equation for a zero-mass electron. We also find an exact solution of the Schrödinger equation for charge carriers in semiconductors under the influence of an external magnetic field and in the field of electromagnetic wave with an account for their radiative transitions. Solutions of the relativistic Klein–Gordon equation in this configuration of electromagnetic fields are found as a certain generalization of the results obtained for the non-relativistic case. These results may serve as a first step for further efforts to find exact solutions of wave equations for quasiparticles in solid state structures in external fields.

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Quantum transitions of relativistic electrons in a superstrong magnetic field

Cited by 24 publications

References 0 publications

Radiative spin polarization of electrons in an ultrastrong magnetic field

Radiative spin polarization of electrons in an ultrastrong magnetic field

Spin‐dependent Cyclotron Decay Rates in Strong Magnetic Fields

Bound Electron Transitions under the Influence of Electromagnetic Wave in Constant Magnetic Field

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