A hydrogen atom in a superstrong magnetic field and the Zeldovich effect

We consider the problem of a hydrogen atom in a superstrong magnetic field, B? B _a =2.35×10⁹ G. The analytical formulas that describe the energy spectrum of this atom are derived for states with various quantum numbers n_ρ and m. A comparison with available calculations shows their high accuracy for B?B _a . We note that the derived formulas point to a manifestation of the Zeldovich effect, i.e., a rearrangement of the atomic spectrum under the influence of strong short-range Coulomb potential distortion. We discuss the relativistic corrections to level energies, which increase in importance with magnetic field and become significant for B?10¹⁴ G. We suggest the parameters in terms of which the Zeldovich effect has the simplest form. Analysis of our precision numerical calculations of the energy spectrum for a hydrogen atom in a constant magnetic field indicates that the Zeldovich effect is observed in the spectrum of atomic levels for superstrong fields, B?5×10¹¹ G. Magnetic fields of such strength exist in neutron stars and, possibly, in magnetic white dwarfs. We set lower limits for the fields B_min required for the manifestation of this effect. We discuss some of the properties of atomic states in a superstrong magnetic field, including their mean radii and quadrupole moments. We calculated the probabilities of electric dipole transitions between odd atomic levels and a deep ground level.     

The spectrum of a hydrogen atom in a superstrong magnetic field and the Zeldovich effect in the short-range Coulomb problem

We derive formulas that describe the energy spectrum of a hydrogen atom in a superstrong magnetic field for states with various magnetic quantum numbers. Comparison with available numerical calculations of the spectrum indicates that the results obtained are highly accurate. These results can be interpreted as a manifestation of the Zeldovich effect regarding the rearrangement of the hydrogen atomic spectrum under the influence of strong Coulomb potential distortion at short distances in the problem under consideration.     

The hydrogen atom in a superstrong magnetic field

A new method for energy-level calculations of the H-atom in a superstrong magnetic field is proposed. The method is based on perturbation theory. The finite-difference technique is used to solve the resulting equations.     

Nonlinear electrodynamics in a superstrong magnetic field

Using a Feynman technique in a two-dimensional space we have calculated an electron propagator and a photon polarization tensor in a superstrong magnetic field $\text{B ? B}{}_{\mathrm{<mtext>0</mtext>}}\text{=}\text{m}{}^{\mathrm{<mtext>2</mtext>}}\text{e}\text{=}\text{4.41 × 10}{}^{13}$ G. Some applications are briefly discussed.     

Quantum transitions of relativistic electrons in a superstrong magnetic field

The probability of emission of a hard γ-quantum in relativistic electron transitions to the ground (or near it) level in a magnetic field H ～ H₀ = m²c³/e₀? = 4.41 × 10¹³G is obtained. For the inverse transitions from these levels the cross-section of electron photoexitation is calculated.     

Relativistic theory of a hydrogen atom in a superstrong magnetic field

The Dirac equation for a hydrogen atom in a static, uniform magnetic field is transformed by a modified FWT transformation into a mixed form; relativistic for perpendicular motion and semi-relativistic for parallel motion. In this way the adiabatic approximation can easily be obtained.     

Spatial structure of the modified Coulomb potential in a superstrong magnetic field

The modification of the Coulomb potential due to the enhancement of loop corrections in a superstrong magnetic field is studied numerically. We calculate the modified potential with high precision and obtain the pattern of equipotential lines. The results confirm the general features known from previous studies, but we emphasize some differences in potential structure that can be important for problems with spatially distributed charges.     

Two-loop corrections to the potential of a pointlike charge in a superstrong magnetic field

The potential of the pointlike charge in a superstrong homogeneous magnetic field B ? m _e ² /e ³ ≈ 6 × 10¹⁵ G is considered. It is well known that Coulomb potential is significantly modified by taking into account vacuum polarization (calculated in one loop approximation). We consider electron selfenergy and correction to the vertex function at one loop, and show that these diagrams are not enhanced by magnetic field like eB.We calculate two-loop corrections to the vacuum polarization and find that these contributions are small.     

Increase in the probability of forbidden electron beta decays in a superstrong magnetic field

Form factors for unique forbidden electron beta decays in a superstrong constant uniform external magnetic field are considered. The probability of forbidden and allowed electron beta decays increases in a superstrong magnetic field owing to the increase in the density of vacant electron bound states at the nucleus involved. It is shown that, because of the growth of the form factors, the relative increase in the probability of forbidden electron beta decays in a magnetic field exceeds the relative increase in the probability of allowed decays (at identical decay endpoint energies).     

Increase in the probability of allowed electron beta decays in a superstrong magnetic field

The effect of a superstrong constant uniform magnetic field, H ? H ₀ = cm _e ² e ³/?³, on the probability of allowed electron beta decays is considered. It is shown that, for an atom whose nucleus is β ^?-active and which is placed in a superstrong magnetic field, the β ^?-decay probability increases owing to the enhancement of β ^? decay to a bound state of the electron. The effect is operative both for the nucleus of a fully ionized atom and for the nucleus of a neutral atom.     

Hydrogen-like atom in a superstrong magnetic field: Photon emission and relativistic energy level shift

Following our previous work, additional arguments are presented that in superstrong magnetic fields B ? (Zα)² B ₀, B ₀ = m ² c ³/e? ≈ 4.41 × 10¹³ G, the Dirac equation and the Schrödinger equation for an electron in the nucleus field following from it become spatially one-dimensional with the only z coordinate along the magnetic field, “Dirac” spinors become two-component, while the 2 × 2 matrices operate in the {0; 3} subspace. Based on the obtained solution of the Dirac equation and the known solution of the “onedimensional” Schrödinger equation by ordinary QED methods extrapolated to the {0; 3} subspace, the probability of photon emission by a “one-dimensional” hydrogen-like atom is calculated, which, for example, for the Lyman-alpha line differs almost twice from the probability in the “three-dimensional” case. Similarly, despite the coincidence of nonrelativistic energy levels, the calculated relativistic corrections of the order of (Zα)⁴ substantially differ from corrections in the absence of a magnetic field. A conclusion is made that, by analyzing the hydrogen emission spectrum and emission spectra at all, we can judge in principle about the presence or absence of superstrong magnetic fields in the vicinity of magnetars (neutron stars and probably brown dwarfs). Possible prospects of applying the proposed method for calculations of multielectron atoms are pointed out and the possibility of a more reliable determination of the presence of superstrong magnetic fields in magnetars by this method is considered.     

Energy losses of a neutron star due to inverse muon decay in the superstrong magnetic field

The emission of a pair of neutrinos by a charged lepton under the influence of a strong magnetic field is examined. The expression found in general form for the probability of the process l l'vV in the strong magnetic field of a neutron star is used to evaluate the contribution of inverse muon decaye vV to the energy losses of the neutron star. The conditions under which this contribution to the energy losses of a neutron star may compete with that due to neutrino pair emission in the processe evV are discussed.Lomonosov State University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 39–44, July, 1995.     

磁场微重力效应的研究

将导电的液体置于磁场中,使导电液体中浮力驱动的自然对流减弱甚至消失,在导电液体中制造出了二级微重力效应,将这种情况称为磁场微重力效应.通过研究导电液体自然对流驱动力的无量纲Grashof数的变化,发现微重力效应的水平可以用公式g_m＝（β₀/β_m）（ν₀ /ν_m）²g₀ 计算,如果略去一次项,则可用g_m＝（ν₀ /ν_m）²g₀来估算.测量研究了不同磁场条件下硅熔体的磁黏度,估算不同磁场强度对应的磁场微重力水平后,发现估算结果与实验结果基本符合. 关键词： 磁场 二级微重力效应 Grashof数 微重力水平     

Processes of associated production of the Higgs boson with the Z boson in a superstrong magnetic field

We compute probabilities for the processes ee+Z+H, and e⁺+e^–Z+H in a superstrong magnetic field. It is shown that the magnetobremsstrahlung of the Higgs boson with the Z boson in the magnetic field Bs>B₀=m²/e=4.41·10¹³ G may be a relatively probable process, and that the superstrong magnetic field significantly influences the process e⁺+e^–Z+H, which is possible even in the absence of the field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 104–108, January, 1991.The author thanks V. Ch. Zhukovskii and A. V. Borisov for discussions on the results of this work.     

Radiative corrections to the Coulomb energy levels and emission of a hydrogen-like atom in a superstrong magnetic field

The probability and intensity of hydrogen-like atom emission in strong magnetic field В >> Z ^2α2 B ₀, α = e ²/cħ = 1/137, and B ₀ = m ² c ³ /eħ = 4.41⋅10¹³ G is calculated. The role of electron-positron vacuum polarization is discussed.     

Righi-Leduc effect in a quantizing magnetic field

The Righi-Leduc effect in semiconductors with a Kane dispersion law in the presence of strong, quantizing, magnetic fields is studied theoretically. The explicit form of the dependence on the magnetic field, temperature, and concentration in arbitrary quantizing magnetic fields is established for semiconductors with a nondegenerate electron gas in the approximation of small nonparabolicity. A simple formula that is applicable for all strong magnetic fields, including quantizing fields, is derived for the Righi-Leduc coefficient in the case of strongly degenerate semiconductors with an arbitrary nonparabolic band. It is shown that in order to determine the photon part of the thermal conductivity ,ph directly from experiment it is best to employ samples with a nondegenerate electron gas in strong, but nonquantizing, magnetic fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 102–107, July, 1988.