The paper examines the energy spectrum of atomic hydrogen in strong (B > B_a ∼ 10⁹ G) and ultra-strong (B ≳ B_cr ∼ 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 ≳ B_cr, 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 >> B_a); the removal of degeneracy between odd and even atomic states; spectral scaling relations for different quantum numbers (n, n_ρ, m) and different field strengths; the shape, size, and quadruple moment of the atom at B >> B_a; 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 Z_cr, 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.

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/f/ 000337360600005 2-s2.0-84902168261 2014PhyU...57..257P Citation: Popov V S, Karnakov B M "Hydrogen atom in a strong magnetic field" Phys. Usp. 57 257–279 (2014) BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks PT Journal Article TI Hydrogen atom in a strong magnetic field AU Popov V S FAU Popov VS AU Karnakov B M FAU Karnakov BM DP 10 Mar, 2014 TA Phys. Usp. VI 57 IP 3 PG 257-279 RX 10.3367/UFNe.0184.201403e.0273 URL https://ufn.ru/en/articles/2014/3/f/ SO Phys. Usp. 2014 Mar 10;57(3):257-279 Received: 6th, July 2013, accepted: 21st, August 2013 Оригинал: Попов В С, Карнаков Б М «Атом водорода в сильном магнитном поле» УФН 184 273–296 (2014); DOI: 10.3367/UFNr.0184.201403e.0273