The Zeldovich effect in a superstrong magnetic field

It follows from the analysis of the precision numerical calculations of the energy spectrum of a hydrogen atom in a static magnetic field that the Zeldovich effect (rearrangement of the atomic spectrum) in the spectrum of atomic levels is observed at superstrong magnetic fields B≥5×10₁₁ G. Magnetic fields of such strengths are reached in neutron stars and magnetic white dwarfs. We established a lower bound B_min for the fields required for this effect to occur.     

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.     

On the Energy of a “One-Dimensional” Two-Electron Atom

Based on the perturbation theory and variational method long known for a “three-dimensional” atom, the ground and first excited state energies are calculated for a “one-dimensional” two-electron atom in the “one-dimensional ortho-helium” configuration, which can be obtained experimentally in principle, as has been already done for a Na Bose condensate, or produced in a super strong magnetic field B ? (2α)²B₀ (B₀ = m²c³/e? ≈ 4.41 × 10¹³ G). The “screening constant” σ for this atom in the ground and excited states was about 0.20 and 0.17, 0.18, respectively, depending on the relative parity PP' of the electronic states, which is somewhat smaller than in “two-dimensional” and “three-dimensional” variants (in these cases, this constant in the ground state is almost the same and about 0.3). The frequencies of the main spectral lines of a “onedimensional” He atom representing a doublet split over the relative parity PP' are found. The presence of the close lines of this doublet in the emission spectrum of magnetars at frequencies ω_{1, 2} ≈ {1.15; 1.17}α²(c/λC) (α = e²/?c, λ_C =?/mc) corresponding to the “one-dimensional ortho-helium” would suggest the existence of a superstrong magnetic field in such astrophysical objects.     

Bestimmung der Kernmomente des Ho165 aus der Hyperfeinstruktur des Grundzustandes im Ho I-Spektrum

In an atomic beam magnetic resonance experiment, the hyperfine interaction constantsA andB of the⁴ I _2/15-groundstate of Ho¹⁶⁵ were found to beA=800,58389 (50) MHz,B=?1667,997 (50) MHz. Using an effective value for 〈r ^?3〉, the magnetic moment of the Ho¹⁶⁵ nucleus was calculated to beμ=4·1(4)μ _n . The quadrupolement was determined by use of the 〈r ^?3〉 given byWatson andFreeman. The result isQ=2·4·10^?24 cm².     

Magnetoresistance of a highly correlated electron liquid

The behavior in a magnetic field of a highly correlated electron liquid approaching the fermion condensation quantum phase transition from the disordered phase is considered. We show that, at sufficiently high temperatures T≥T*(x), the effective mass starts to depend on T, M* ∝T^?1/2. This T^?1/2 dependence of the effective mass at elevated temperatures leads to the non-Fermi liquid behavior of the resistivity, σ(T) ∝ T and at higher temperatures σ(T) ∝ T^3/2. The application of a magnetic field B restores the common T² behavior of the resistivity. The effective mass depends on the magnetic field, M*(B) ∝ B^?2/3, being approximately independent of the temperature at T≤T*(B) ∝ B^4/3. At T≥T*(B), the T^?1/2 dependence of the effective mass is reestablished. We demonstrate that this B-T phase diagram has a strong impact on the magnetoresistance (MR) of the highly correlated electron liquid. The MR as a function of the temperature exhibits a transition from negative values of MR at T→0 to positive values at T ∝ B^4/3. Thus, at T≥T*(B), MR as a function of the temperature possesses a node at T ∝ B^4/3.     

Equilibrium and stability of the charged particles’ fluxes drifting crosswise to the strong magnetic field at the expense of the Hall charge separation

The current equilibrium is investigated, where the generation of the Hall electric field on the magnetic Debye radius r _B = B ₀/(4πen _e) is considered by the drifting of the relativistic electrons crosswise to the strong magnetic field. In this case, the electron propagation is possible at the distance d that is essentially larger than the electron radius of the backward reflection in the magnetic field r ₀ ? m _e v _z c/(eB ₀). The instability of the joint drift motion of ions and electrons is investigated for the frequency oscillation w much higher than the ion cyclotron frequency w _Bi and by 4π n _i m _i c ² ? B ₀ ² and (k · B ₀) = 0. It is shown that the resonance effects by the ion beam’s plasma frequency w ? kv ₀ = w _pi leads to the generation of the nonpotential perturbations with the characteristic increment Imw ～ 10^?1 ÷ 10^{? 2} w _pi. Estimates show that the instability, associated with the propagation of the high-energy ion beam through the strong magnetic field, can essentially be like the edge-localized mode in tokamaks.     

Untersuchung ferromagnetischen Materials mit polarisierter γ-Strahlung

Circularly polarized Co⁶⁰ γ-ray quanta have been used to measure the polarization-dependent part of the Compton effect on an iron-cobalt alloy. The asymmetryδ=(N ₊?N _?)/(N ₊+N _?) observed by inversion of the magnetic field direction was investigated as a function of the mean induction¯B between 1 and 23kI ^?. The experimental values of δ do not nearly drop as fast as¯B when going down from saturation to zero.     

Resolvent Expansion and Time Decay of the Wave Functions for Two-Dimensional Magnetic Schrödinger Operators

We consider two-dimensional Schrödinger operators H(B, V) given by Eq. (1.1) below. We prove that, under certain regularity and decay assumptions on B and V, the character of the expansion for the resolvent (H(B, V) ? λ)^?1 as λ → 0 is determined by the flux of the magnetic field B through \({\mathbb{R}^2}\) . Subsequently, we derive the leading term of the asymptotic expansion of the unitary group e ^{?i t H(B, V)} as t → ∞ and show how the magnetic field improves its decay in t with respect to the decay of the unitary group e ^{?i t H(0, V)}.     

Selective Reflection of Potassium Vapor Nanolayers in a Magnetic Field

The selective reflection of laser radiation from the interface between a dielectric window and the atomic vapors confined in a nanocell of thickness L ≈ 350 nm is used to develop effective Doppler-broadening- free spectroscopy of potassium atoms. A small atomic line width and a relation between the signal intensity and the transition probability allowed us to resolve four lines of atomic transitions responsible for the D1 lines of the ³⁹K and ⁴¹K isotopes. Two groups containing four atomic transitions form in an applied magnetic field upon pumping by radiation with circular polarization σ⁺ or σ^–. Different intensities (probabilities) of transitions for the σ⁺ and σ^– excitations are detected in magnetic field B₀ ≈ A _hfs /μ_B ≈ 165 G (A _hfs is the magnetic dipole constant for the ground state and μ_B is the Bohr magneton). A substantially different situation is observed at B ? B₀, since high symmetry appears for the two groups formed by radiation with circular polarization σ⁺ or σ^–. Each group is the mirror image of the other group with respect to the frequency of the 4²S_1/2–4²P_1/2 transition, which additionally proves the occurrence of the complete Paschen–Back regime of the hyperfine structure at B ≈ 2.5 kG. A developed theoretical model well reproduces the experimental results. Possible practical applications are described. The results obtained can also be applied to the D₁ lines of ⁸⁷Rb and ²³Na.     

Investigation of the field-tuned quantum critical point in CeCoIn<Subscript>5</Subscript>

The main properties and the type of the field-tuned quantum critical point in the heavy-fermion metal CeCoIn₅ that arise upon application of magnetic fields B are considered within a scenario based on fermion condensation quantum phase transition. We analyze the behavior of the effective mass, resistivity, specific heat, charge, and heat transport as functions of applied magnetic fields B and show that, in the Landau Fermi liquid regime, these quantities demonstrate critical behavior, which is scaled by the critical behavior of the effective mass. We show that, in the high-field non-Fermi liquid regime, the effective mass exhibits very specific behavior, M*～ T^{? 2/3}, and the resistivity demonstrates T^2/3 dependence. Finally, at elevated temperatures, it changes to M*～T^?1/2, while the resistivity becomes linear in T. In zero magnetic field, the effective mass is controlled by temperature T and the resistivity is also linear in T. The obtained results are in good agreement with recent experimental facts.     

Hyperfine-structure measurements on Dy161 and Dy163

In an atomic beam magnetic resonance experiment the hyperfine interaction constantsA andB of the⁵ I ₈ groundstate of Dy¹⁶¹ and Dy¹⁶³ were found to be Dy¹⁶¹:A=?(115.8±1)MHz, Dy¹⁶³:A=(162.9±0.6)MHz,B=(1102±15)MHz,B=(1150±20)MHz. Using an effective value for 〈r^?3〉, the magnetic moments and electric quadrupole moments of the Dy¹⁶¹ and Dy¹⁶³ nuclei were calculated to be Dy¹⁶¹:μ _I=?(0.47±0.09) n.m., Dy¹⁶³:μ _I=(0.66±0.13)n.m.,Q=(2.36±0.4)barns,Q=(2.46±0.4)barns.     

Resistive sensor of weak magnetic fields on the basis of a thick HTSC film

The following parameters have been obtained for a thick (thickness t ～50 μm) film of high-temperature superconducting ceramics of the Bi-2223 system have been implemented: magnetosensitivity S _u ～ 29 V T^?1 and resolutions δB ～ 3 nT and δ? ～ 4?₀ in magnetic field and magnetic flux, respectively. It is shown that the film magnetosensitivity can be significantly increased due to the size effect. The expected characteristics, estimated with allowance for the size effect, are S _u ≥ 1000 V T^?1, δB ～ 0.01 nT, δ? ～ 0.01 ?₀, and the range of dynamic measurement ≥150 dB.     

A free convective boundary layer in a conducting fluid in the presence of a transverse magnetic field

The properties of free convection in a conducting fluid in laminar regime near a hot solid vertical w all in the presence of a transverse magnetic field are theoretically analyzed. The existence of two regimes of heat transfer from the wall to the fluid are established. In the first regime, at small heights x?x* where the magnetic field effect can be disregarded, heat transfer is described by the well-known results for a free convective boundary layer in a nonconducting fluid with the Nusselt number Nu_x∝x^3/4. In the second regime, at x? x* where the magnetic field plays a crucial role, the dependence of heat transfer on the height and field strength is \(Nu_x \propto {{\sqrt x } \mathord{\left/ {\vphantom {{\sqrt x } B}} \right. \kern-\nulldelimiterspace} B}\). The location of the boundary between these regimes strongly depends on the magnetic field, x*∝ B^?4.     

Exotic molecular states in a strong magnetic field: H<Stack><Subscript>3</Subscript><Superscript>(2+)</Superscript></Stack> ion

The existence of the molecular ion H ₃ ⁽²⁺⁾ in a magnetic field in a triangular and a linear configuration is discussed. A variational method (with an optimization of the form of the vector potential) is used. It is shown that, in the range of magnetic fields 10⁸<B<10¹¹ G, the system (pppe), with the protons forming an equilateral triangle perpendicular to the magnetic line, has a well-pronounced minimum in the total energy. Also, for B?10¹⁰ G, if the protons are situated along a magnetic line (linear configuration), a well-pronounced minimum in the total energy appears. Both configurations are unstable under the decays H(atom) + p + p and H ₂ ⁽⁺⁾ + p. A possible connection between the H ₃ ⁽²⁺⁾ molecular ion and a recently discovered absorption feature in a neutron-star atmosphere is discussed.     

Self-similar distribution in “giant” magnetic flux creep

The problem of magnetic field penetration into the half-space is considered in parallel geometry in an external magnetic field increasing with time in accordance with the law B(0, t, τ₀ = B _{c 1} (1 + t/τ₀) ^m , m ≥ 0, t ≥ 0 (τ ₀ is the time of magnetic flux redistribution and B _{c 1} is the lower critical field). It is assumed that the flow of vortices is thermally activated in the “giant” creep mode (i.e., for weak pinning creep and high temperatures). A model equation is derived for describing the magnetic flux evolution. Analytic formulas are obtained for the depth and velocity of magnetic field penetration. It is shown that the giant creep regime is stable for 0 ≤ m ≤ 1/2.     

Level-crossing-Untersuchung der Hyperfeinstruktur des 3d 10 4p 2 P 3/2-Terms von Cu63 und Cu65

The level-crossing technic has been used to investigate the hyperfinestructur of the 3d ¹⁰ 4p ² P _3/2-term in Copper I by scattering the resonance line λ=3248 Å on an atomic beam of separated isotop Cu⁶³ respectively Cu⁶⁵ in an external magnetic field. From the level-crossing signals values for the magnetic dipol interaction constantsA and for the electric quadrupol interaction constantsB are deduced to beeA(Cu⁶³)=(194,72±0,15) Mc/secB(Cu⁶³)=?(28,8±0,6) Mc/secA(Cu⁶⁵)=(208,57±0,15) Mc/secB(Cu⁶⁵)=?(25,9±0,6) Mc/sec. With theA-value of the 3d ¹⁰ 4p²P_1/2-term from optical measurements the ratioA(² P _3/2)∶A(² P _1/2)≈0,4 is about twice greater than for an unperturbetalkali-like²P-term. From the width of the level-crossing signals a mean lifetime of the 3d¹⁰ 4p²P_3/2-term τ=(7,0±0,2) · 10^?9 sec is deduced.     

Photon propagation in a supercritical magnetic field

We show that, for the asymptotically strong (super-Schwinger) magnetic field B exceeding the critical value B_cr=m²c³/eh=4.4×10¹³G, the vacuum polarization effects become important not only in the γ-range, but also for softer electromagnetic quanta, including X-rays and optical photons, and for electromagnetic waves of radio frequencies. This is a consequence of the linearly growing term ?B/B_cr present in the vacuum polarization in an asymptotically strong magnetic field. The results may be essential in studying reflection, refraction, and splitting of X-rays, light and radio waves by magnetic fields of magnetars, and in considering emission of such waves by charged particles.     

Temperature Dependence of the Thermal Conductivity of a Trapped Dipolar Bose-Condensed Gas

The thermal conductivity of a trapped dipolar Bose condensed gas is calculated as a function of temperature in the framework of linear response theory. The contributions of the interactions between condensed and noncondensed atoms and between noncondensed atoms in the presence of both contact and dipole-dipole interactions are taken into account to the thermal relaxation time, by evaluating the self-energies of the system in the Beliaev approximation. We will show that above the Bose-Einstein condensation temperature (T?>?T _BEC ) in the absence of dipole-dipole interaction, the temperature dependence of the thermal conductivity reduces to that of an ideal Bose gas. In a trapped Bose-condensed gas for temperature interval k _B T?<<?n ₀ g _B , E _p ?<<?k _B T (n ₀ is the condensed density and g _B is the strength of the contact interaction), the relaxation rates due to dipolar and contact interactions between condensed and noncondensed atoms change as \( {\tau}_{dd12}^{-1}\propto {e}^{-E/{k}_BT} \) and τ _c12?∝?T ^?5, respectively, and the contact interaction plays the dominant role in the temperature dependence of the thermal conductivity, which leads to the T ^?3 behavior of the thermal conductivity. In the low-temperature limit, k _B T?<<?n ₀ g _B , E _p ?>>?k _B T, since the relaxation rate \( {\tau}_{c12}^{-1} \) is independent of temperature and the relaxation rate due to dipolar interaction goes to zero exponentially, the T ² temperature behavior for the thermal conductivity comes from the thermal mean velocity of the particles. We will also show that in the high-temperature limit (k _B T?>?n ₀ g _B ) and low momenta, the relaxation rates \( {\tau}_{c12}^{-1} \) and \( {\tau}_{dd12}^{-1} \) change linearly with temperature for both dipolar and contact interactions and the thermal conductivity scales linearly with temperature.