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2014

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100th anniversary of the birth of Ya.B. Zeldovich


Hydrogen atom in a strong magnetic field

 a,  b
a Russian Federation State Scientific Center A.I. Alikhanov Institute ofTheoretical and Experimental Physics, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation
b National Research Nuclear University MEPhI, Kashirskoe shosse 31, Moscow, 115409, Russian Federation

The paper examines the energy spectrum of atomic hydrogen in strong (B > Ba ∼ 109 G) and ultra-strong (B ≳ Bcr ∼ 1014 G) magnetic fields, in which the hydrogen electron starts to move relativistically and quantum electrodynamics effects become important. Using the adiabatic approximation, highly accurate energy level values are obtained analytically for B > 1011 G, which are then compared with asymptotic and numerical results available in the literature. A characteristic feature noted in electron motion in a strong magnetic field is that for B ≳ Bcr, the transverse motion becomes relativistic while the longitudinal motion (along B) can be described by nonrelativistic theory and is amenable to the adiabatic approximation. Topics discussed include: the qualitative difference in the way odd and even levels change with magnetic field (for B >> Ba); the removal of degeneracy between odd and even atomic states; spectral scaling relations for different quantum numbers (n, nρ, m) and different field strengths; the shape, size, and quadruple moment of the atom at B >> Ba; radiative transitions np → 1s in a strong magnetic field; relativistic QED effects, including: the effects of vacuum polarization and of the electron’s anomalous magnetic moment on the energy level positions; Coulomb potential screening and energy level freezing at B → ∞; the possibility of the Zeldovich effect in the hydrogen spectrum in a strong magnetic field. The critical nuclear charge problem is briefly discussed. Simple asymptotic formulas for Zcr, valid for low-lying levels, are proposed. Some of the available information on extreme magnetic field produced in the laboratory and occurring in space is given. The Coulomb renormalization of the scattering length is considered for the resonance situation with a shallow level in the spectrum.

Text can be downloaded in Russian. English translation is available here.
PACS: 03.65.Ge, 03.65.Pm, 32.30.−r (all)
DOI: 10.3367/UFNe.0184.201403e.0273
URL: https://ufn.ru/en/articles/2014/3/e/
Citation: Popov V S, Karnakov B M "Hydrogen atom in a strong magnetic field" Phys. Usp. 57 257–279 (2014)
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Received: 6th, July 2013, 21st, August 2013

:   ,    «   » 184 273–296 (2014); DOI: 10.3367/UFNr.0184.201403e.0273

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