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.     

Emission of axions by a hydrogen-like atom in an ultrastrong magnetic field

The resonance effect of emission of axions by a hydrogen-like atom in an ultrastrong magnetic field B ≫ B ₀ = m ²/e = 4.41 × 10¹³ Gs, which is induced by polarization of electron-positron vacuum, is considered. The emission probability and the radiation intensity are on the order of (B/B ₀) × 10⁻¹² of electromagnetic radiation characteristics, which exceeds the conventional ratio by many orders of magnitude. It is shown that, at the temperature of early Universe ≲(Zα)² m, the contribution from the resonance mechanism prevails. However, the relation between the concentrations of relic photons and axions cannot explain the origin of cold dark matter. The axion energy density in “our epoch” is 10⁻⁴(B/B ₀) eV/cm³.     

Three-particle recombination coefficient of a weakly nonideal ultracold plasma in a high magnetic field

An expression for the recombination coefficient α _B in a weakly nonideal ultracold plasma in a high magnetic field has been proposed. According to this expression, α _B ∼ T _e ^−1.5 B ⁻², where T _e is the temperature of electrons and B is the strength of the magnetic field. Comparison of calculated values with experimental data including the results of the recent experiments on recombination in antihydrogen confirms the theoretical dependence.     

e + e − pair production in ultrarelativistic heavy-ion collisions at intermediate impact parameters

Using the semiclassical Green’s function in the Coulomb field, we analyze the probabilities of single and multiple e ⁺ e ⁻ pair production at a fixed impact parameter b between colliding ultrarelativistic heavy nuclei. We perform calculations in the Born approximation with respect to the parameter Z _Bα and exactly in Z _Aα, where Z _A and Z _B are the charge numbers of the corresponding nuclei. We also obtain the approximate formulas for the probabilities valid for Z _Aα, Z _Bα ≲ 1. The text was submitted by the authors in English.     

On the spectrum of the hydrogen atom in an ultrastrong magnetic field

Various approaches to computing the energies of the ground state and excited levels of the hydrogen atom in an ultrastrong magnetic field B that considerably exceeds the field B _a = m _e ² e ³ c/ħ ³ ∼ 10⁹ G are considered. The effects of polarization of vacuum and anomalous magnetic moment of the electron on the position of the atomic levels are discussed. The vacuum polarization effects are negligibly weak for B < 10¹⁵ G but become significant in fields B ≫ 10¹⁶ G, in which these effects qualitatively modify the atomic spectrum in this range. The difference in the behaviors of the even and odd energy levels for B ≫ B _a is analyzed and the formulas for the energies of odd levels as a function of field B are refined.     

Parity violation effects in hydrogen atom in forbidden magnetic-dipole transitions

General expressions for the probability of all strongly forbidden magnetic-dipole transitions between states njl and n′jl in the hydrogen atom and light hydrogen-like ions are derived in the lowest order in the parameter (αZ) in the form W _n′jl;njl ^(Ml) = D _n′n ^lj αm _e (αZ)¹⁰ (in relativistic units), where m _e is the electron mass, α is the fine-structure constant, Z is the nuclear charge, and the constants D _n′n ^lj are presented in an analytical form. Using these expressions, the dependence of the degree of parity violation on the principal quantum numbers n and n′ of the lower and upper states in the ns _1/2-n′s _1/2 and np _1/2-n′p _1/2 M1 transitions is systematically analyzed. The results obtained can be used in designing experiments on parity violation in the hydrogen atom.     

Coulomb excitation of 72 30Zn42

The reduced transition probability B(E2: 0₁ ⁺→ 2⁺) of ⁷²Zn has been measured for the first time by Coulomb excitation at intermediate energy. The result B(E2: 0₁ ⁺→ 2⁺) = 1740±210 e²fm⁴, corresponds to the deformation parameter β₂ of 0.23, in close agreement with expectations derived from the neighboring nucleus ⁷³Zn. A discussion of the evolution of the N = 40 sub-shell closure as a function of Z is presented. Received: 19 December 2001 / Accepted: 14 March 2002     

Hyperfine structure of the ground state muonic <Superscript>3</Superscript>He atom

On the basis of the perturbation theory in the fine structure constant α and the ratio of the electron to muon masses we calculate one-loop vacuum polarisation and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of the muonic helium atom (μ e ³ ₂He). We obtain total results for the ground state hyperfine splitting Δ ν ^hfs = 4166.648 MHz which improves the previous calculation of Lakdawala and Mohr due to new corrections of orders α ⁵ and α ⁶. The remaining differences between our theoretical result and experimental value of the hyperfine splitting lie in the range of theoretical and experimental errors and require the subsequent investigation of higher order corrections.     

Total electron scattering cross-sections for O atoms: O2 and O3 molecules

Total (elastic+inelastic) cross sections fore ⁻-O,e ⁻-O₂ ande ⁻-O₃ scattering have been calculated at sample energies between 100 and 1000eV. The basice ⁻-O atom scattering amplitudes are obtained from the partial wave analysis with a complex optical potential. Thee ⁻-O₂ ande ⁻-O₃ cross-sections are obtained through the independent atom model. Oure ⁻-O₂ cross-sections reproduce the experimental data quite well. Adequate comparisons are made in all the three cases.     

Plasma parameters in the upgraded Trimyx-M Galathea

Results are presented from measurements of the plasma parameters in the upgraded Trimyx-M Galathea. After the barrier magnetic field and the energy of the injected hydrogen plasma bunch were increased to B _bar ∼ 0.1 T and W ₀ ≈ 200 J, respectively, the following plasma parameters were achieved: the density n ∼ 5 × 10¹³ cm⁻³, the plasma confinement time τ* = 800–900 μs, the elergy of the confined plasma W ₁ ∼ 100 J, the ratio of the plasma pressure to the barrier magnetic pressure β ₀ ∼ 0.2, the electron temperature T _e ∼ 20 eV, and the ion temperature T _i ∼ 2T _e . The maximum time during which the plasma density decreased e-fold, τ _p , was found to be 300 μs at B _bar = 0.1 T, which agrees with the classical transport model.     

New analysis of the Douglas-Herzberg system (A1Π- X1Σ+) in the CH+ ion radical

Three bands of the A¹Π- X¹Σ⁺ system in the ¹²CH⁺ ion radical have been rephotographed under high resolution as an emission spectra using a Geissler-type discharge tube. The conventional technique of spectroscopy has been implemented. Using the Th lines as a standards, as well as an interferometric comparator equipped with a photoelectric scanning device, the 0-0 , 0-1 and 2-1 bands have been reanalyzed. By means of much longer bands (J_max = 17 in the Q(J) branch of the 0-0 band; J_max = 16 in the R(J) branch of the 0-1 band; J_max = 14 in the P(J) and Q(J) branches of the 2-1 band), than have been observed so far, as well as the merged calculations, using another five bands given by Carrington et al. [A. Carrington, D.A. Ramsay, Phys. Scripta 25, 272 (1982)] additionally, more accurate molecular constants for the X¹Σ⁺ state, the improved reduced band system origin T_e = 24118.726 (14) cm^-1 as well as for the first time the equilibrium molecular constants with their one standard deviation for the A¹Π state in the CH⁺ molecule have been computed: ω_e'=1864.402(22), ω_ex_e'=115.832(14), ω_ey_e'= 2.6301(24), B_e'=11.88677(72), α_e'= 0.9163(18), γ_e'= -2.29(12)×10^-2, ε_e'= 4.95(20)×10^-3, D_e'=1.92960(31)×10^-3, β_e'= 1.0733(50)×10^-4, δ_e'= -1.312(16)×10^-5, , α_qe'= -3.14(16)×10^-3, and q_De'= -2.20(14)×10^-5 cm^-1. Only in our research the addition to the zero-point energy Y'₀₀=-1.9430 cm^-1 and cm^-1 have been calculated. The equilibrium bond lengths of r'_e=1.235053(37) ? and ? for the A¹Π and X¹Σ⁺ states, respectively have been computed. Full quantum-mechanics characteristic of the A-X bands system in the ¹²CH⁺ molecule, i.e. RKR turning points, the Franck-Condon factors and r-centroids have been obtained. Dissociation energies D_e^{X1 Σ+}=(38470± 3503) cm^-1 and D_e^{A1 Π}= (14415 ±3509) cm^-1 for the molecule under consideration have been estimated.     

Influence of elastic strain onμ + SR in α-iron single crystalsSR in α-iron single crystals

The spin-precession frequencies and the transverse spin relaxation rates of positive mouns (μ ⁺) have been measured on two elastically strained α-Fe single crystal platelets as well as on an unstrained reference α-Fe crystal at temperatures down to 2.7 K in applied magnetic field 0≤B _appl≤3 T. The drastic effects of the strains may be qualitatively understood in terms of their influence on both the magnetic domain structure and theμ ⁺ energies at the various interstitial sites. This leads to the conclusion that at low temperaturesμ ⁺ in α-Fe occupy configurations related to octahedral interstitials with dipolar fieldB _dip=0.70 T.     

Oscillations of the magnetoresistance in an inclined magnetic field for MIS structures on (100) silicon with a high electron density

At electron densities N _S>6×10⁻² cm⁻²² a second series of oscillations, which are tentatively attributed to population of the second energy subband, is observed in addition to the main series of Shubnikov-de Haas oscillations. A change in phase of the oscillations of the second series is observed at some angle of inclination α_e of the field. The measured value of α_e is used to calculate the ratio of the cyclotron mass to the effective g factor. The maximum possible cyclotron mass is also determined as m _H< 0.32m _e. On this basis it is concluded that the second series of oscillations is due to electrons which have an in-plane effective mass m*≈0.2m _e and which belong to the same valleys of the Fermi surface as in the case of the main oscillations. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 136–140 (25 January 1998)     

Atomic levels in superstrong magnetic fields and <Emphasis Type="Italic">D</Emphasis> = 2 QED of massive electrons: Screening

The photon polarization operator in superstrong magnetic fields induces the dynamical photon “mass” which leads to screening of Coulomb potential at small distances z ≪ 1/m, m is the mass of an electron. We demonstrate that this behavior is qualitatively different from the case of D = 2 QED, where the same formula for a polarization operator leads to screening at large distances as well. Because of screening the ground state energy of the hydrogen atom at the magnetic fields B ≫ m ²/e ³ has the finite value E ⁰ = −me ⁴/2 ln²(1/e ⁶).     

Energy and angular distributions of backscattered electrons from collisions of 5 keV electrons with thick Al,Ti, Ag,W and Pt targets

The energy and angular distributions of backscattered electrons produced under the impact of 5 keV electrons with thick Al, Ti, Ag, W and Pt targets are measured. The energy range of backscattered electrons is considered between E _B = 50 eV and 5000 eV. The angle of incidence α and take-off angle θ are chosen to have values α = 0 and 10 and θ = 100, 110 and 120 respectively. The measured energy spectra are compared with the available theoretical models for α = 0 and 10. The elastic peak intensity of backscattered electrons is found to be a function of angle of incidence, take-off angle and atomic number of the target material. The considered theories are reasonably in good agreement with experiment for the energy spectra of the backscattered electrons having their reduced energies ∈ (= E _B/E ₀) in the range of 0.20 to 1.00.      

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Comment on: “Universal relation between spectroscopic constants”

Kaur and Mahajan [1] have claimed to derive a universal relation InG = 1.91578(±0.09727) + 0.97111(±0.03809) In Δ between the Sutherland parameter Δ(=ω _er _e ² /2D_e) and the dimensionless parameterG(= 8ω _ex_e/B_e) for the ground as well as excited electronic states of diatomic molecules. Validity of this relation is checked and we find that the relation is not correct. Next, we checked the validity of the relation Δ = 2.2r_e for the alkali group diatomic molecules. This relation is also found not to be correct.     

Revisiting generalized Chaplygin gas as a unified dark matter and dark energy model

In this paper, we revisit the generalized Chaplygin gas (GCG) model as a unified dark matter and dark energy model. The energy density of GCG model is given as ρ _GCG/ρ _GCG0=[B _s +(1−B _s )a ^−3(1+α)]^1/(1+α), where α and B _s are two model parameters which will be constrained by type Ia supernova as standard candles, baryon acoustic oscillation as standard rulers and the seventh year full WMAP data points. In this paper, we will not separate GCG into dark matter and dark energy parts any more as adopted in the literature. By using the Markov Chain Monte Carlo method, we find the results a = 0.00126_{-0.00126- 0.00126}^{+ 0.000970+ 0.00268}\alpha=0.00126_{-0.00126- 0.00126}^{+ 0.000970+ 0.00268} and B_s = 0.775_{-0.0161- 0.0338}^{+ 0.0161+ 0.0307}B_{s}= 0.775_{-0.0161- 0.0338}^{+ 0.0161+ 0.0307}.     

First measurement of J/ ψ azimuthal anisotropy in PHENIX at forward rapidity in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

In this paper, we calculate the decay rates of the D ⁺→D ⁰ e ⁺ ν, D _S ⁺→D ⁰ e ⁺ ν, , D _S ⁺→D ⁺ e ⁻ e ⁺ and B _S ⁰→B ⁰ e ⁻ e ⁺ semileptonic decay processes, in which only the light quarks decay, while the heavy flavors remain unchanged. The branching ratios of these decay processes are calculated with the flavor SU(3) symmetry. The uncertainties are estimated by considering the SU(3) breaking effect. We find that the decay rates are very tiny in the framework of the standard model. We also estimate the sensitivities of the measurements of these rare decays at future experiments, such as BES-III, super-B and LHC-b.