Integrated Cross Sections of High-Energy <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>–</Superscript> Pair Electroproduction by an Electron in an Atomic Field

The integrated cross sections of e⁺e^– pair electroproduction by an ultrarelativistic electron in an atomic field are studied. The importance of various contributions to the integrated cross sections is discussed. The Coulomb corrections have turned out to make a large contribution to both differential and integrated cross sections even at moderate values of the nuclear charge number. The interaction of the electron emitting a virtual photon with the atomic field is shown to contribute significantly to the cross sections differential with respect to the electron transverse momentum. However, this interaction affects only slightly the cross section differential only with respect to the positron transverse momentum.     

One-loop electro-weak corrections to three-jet observables of <Emphasis Type="Italic">b</Emphasis>-quarks <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilations

We compute the full one-loop EW contributions of \({\mathcal{O}}(\alpha_{\mathrm{S}}\alpha_{\mathrm{EM}}^{3})\) entering the electron–positron into two b-quarks and one gluon cross section at the Z peak and LC energies. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of W ^± and Z bosons. Their importance for the measurement of α _S from jet rates and shape variables is explained qualitatively and illustrated quantitatively. Their impact on the forward–backward asymmetry is also analysed.     

Coulomb deexcitation of muonic hydrogen within the quantum close-coupling method

The Coulomb deexcitation of muonic hydrogen in collisions with the hydrogen atom has been studied in the framework of the fully quantum-mechanical close-coupling method for the first time. The calculations of the l-averaged cross sections of the Coulomb deexcitation are performed for (μp)_n and (μd)_n atoms in the initial states with the principal quantum number n = 3–9 and at relative energies E = 0.1–100 eV. The obtained results for the n and E dependences of the Coulomb deexcitation cross sections drastically differ from the semiclassical results. An important contribution of the transitions with Δn > 1 to the total Coulomb deexcitation cross sections (up to ～37%) is predicted.     

Verhältnis des differentiellen (e,N)- zum totalen (γ,N)-Wirkungsquerschnitt

The ratio of the differential cross section for the (e, N)-process to the total (γ,N) -cross section is derived with the use of the relativistic Coulomb Eigenfunctions for the continuous spectrum. For electric and magnetic dipole transitions the Born approximation, the Coulomb correction, the effect of screening and that of finite nuclear size are calculated. In this angular distribution there should be no interference of electron waves scattered by different multipoles, where the inelastically scattered electrons are detected. Numerical calculations have been done for nuclei withZ=6, 29, and 82 and scattering anglesθ=1Ω, 132Ω, 160Ω and 180Ω of the electron. The result of this theory is compared with the experiments of W.C.Barber et al.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Coulomb-Korrekturen bei der inneren Bremsstrahlung

Coulomb corrections to the internal Bremsstrahlung associated with allowedβ-decay have been calculated. The Coulomb field is taken into account through the electron wave function. The corrections to the contributions of the intermediate states to the spectrum are evaluated. These corrections do not cancel out when the spectrum is normalized to the emission of oneβ-particle. Hence the corrections to the normalized spectrum are no longer small. The polarization is practically not affected by these Coulomb corrections. Numerical values for P³², S³⁵ and Y⁹⁰ are compared with experimental results. Especially in the high energy part of the spectrum the former discrepancies between theory and experimental yield are removed.     

Data on photoneutron reactions from various experiments for <Superscript>133</Superscript>Cs, <Superscript>138</Superscript>Ba and <Superscript>209</Superscript>Bi nuclei

Basic methods for determining cross sections for photoneutron partial reactions are examined. They are obtained directly in experiments with quasimonoeneregetic annihilation photons or from the cross section for the (γ, xn) = (γ, 1n) + 2(γ, 2n) + 3(γ, 3n) +... neutron-yield reaction in experiments with bremsstrahlung photons by introducing corrections based on statistical nuclear-reaction theory. The difference in the conditions of these experiments, which leads to discrepancies between their results because of sizable systematic errors, is analyzed. Physical criteria are used to study the reliability of data on the photodisintegration of ¹³³Cs, ¹³⁸Ba, and ²⁰⁹Bi nuclei. The cross sections for partial and total reactions satisfying the reliability criteria are evaluated within the experimental–theoretical method (σ^eval(γ, in) = F_i^theor × σ^expt(γ, xn)) on the basis of the experimental cross sections σ^expt(γ, xn) and the results of the calculations within the combined model of photonuclear reactions.     

Die Intensität der Bremsstrahlung und der charakteristischenK-Röntgenstrahlung dünner Anoden

The intensities of bremsstrahlung and characteristicK X-rays of thin Al, Mn, Cu, Se, Ag and Sn targets were measured with a scintillation counter. The angle between the 50 keV electrons and the direction of emission was 90°. — The spectral intensity of bremsstrahlung for 20 keV quantum energy was determined in agreement with the theory ofKirkpatrick andWiedmann. The result obtained isi _v=(2.7) · 10^?53.Z ^{2, 0} ergs per steradian, unit frequency interval, bombarding electron and atomper-cm². The cross section ofK-ionisation by electron impact has been found out by measuring the characteristicKX-ray intensity in agreement with known theoretical and experimental values. The result of this work isσ _K=(7.0) · 10^?16 ·Z ^?4,3 cm².     

Photoionization of the Bound Systems at High Energies

We consider photoionization of a system bound by the central potential V(r). We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann–Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the analytic properties of the potential V(r). We show that the energy dependence of the asymptotics of photoionization cross sections of fullerenes is to large extent model-dependent. We demonstrate that if the fullerene field V(r) is approximated by the function with singularities in the complex plane, the power drop of the asymptotics is reached at the energies which are so high that the cross section becomes unobservably small. The preasymptotic behavior with a faster decrease of the cross sections becomes important in these cases.     

Electronic transport through a Majorana bound state coupled to a T-shaped quantum-dot system with Coulomb interaction

Using the Green’s function technique, we respectively investigate the electron transport properties of two spin components through the system of a T-shaped double quantum dot structure coupled to a Majorana bound state, in which only one quantum dot is connected with two metallic leads. We explore the interplay between the Fano effect and the MBSs for different dot-MBS coupling strength λ, dot-dot coupling strength t, and MBS-MBS coupling strength ε_M in the noninteracting case. Then the Coulomb interaction and magnetic field effect on the conductance spectra are investigated. Our results indicate that G_↓(ω) is not affected by the Majorana bound states, but a “0.5” conductance signature occurs in the vicinities of Fermi level of G_↑(ω). This robust property persists for a wide range of dot-dot coupling strength and dot-MBS coupling strength, but it can be destroyed by Coulomb interaction in quantum dots. By adjusting the size and direction of magnetic field around the quantum dots, the “0.5” conductance signature damaged by U can be restored. At last, the spin magnetic moments of two dots by applying external magnetic field are also predicted.     

Interaction of dirac particle AMM with Coulomb field of a superheavy nucleus: Perturbative and nonperturbative aspects

The interaction ΔU_AMM of the Dirac particle anomalous magnetic moment (AMM) with the Coulomb field of a nucleus and its effect on the low-lying atomic levels are studied for Zα > 1 using both perturbative and essentially nonperturbative approaches. The Zα dependence of particle wavefunctions (WFs) is fully taken into account from the beginning. In deriving the ΔU_AMM contribution, the nucleus is viewed either as a uniformly charged extended Coulomb source or as a distributed system formed by pointlike u and d quarks. When estimated nonperturbatively, the ΔU_AMM-induced effects in the Dirac equation framework prove to be identical for these two cases. At the same time, the ΔU_AMM-induced effect is specific in that its perturbative and nonperturbative estimates are very different for Δg ? const and practically identical as soon as the dynamical screening of AMM at short distances is taken into account in the Dirac equation.     

Physical criteria for the reliability of data on the photodisintegration of the <Superscript>89</Superscript>Y nucleus

Experimental photonuclear reaction cross sections obtained in experiments using quasimonoenergetic annihilation, monoenergetic tagged photons, and bremsstrahlung γ-radiation are analyzed using physical criteria for the reliability of data on the ⁸⁹Y nucleus. It is found that the reliability of data on the cross sections of partial reactions (γ, 1n) and (γ, 2n), obtained by means of photoneutron multiplicity sorting, is highly doubtful. Reliable cross sections of reactions (γ, 1n) and (γ, 2n) are obtained using the experimental–theoretical method (ETM) for evaluating using both experimental cross sections of neutron yield reaction σ^exp(γ, xn) that are free of neutron multiplicity problems, and theoretically calculated F _i ^theor ratios of the cross sections of definite (i) partial reactions to cross section σ^theor(γ, xn). It is shown that the evaluated cross sections differ noticeably from the experimental data.     

Inelastische Positronenstreuung am Atomkern

The ratio of the total and differential cross section for the inelastic positron-nucleus scattering (ē, N)-process to the total (γ, N) -cross section is derived in Born approximation for electric and magnetic dipole transitions. The result agrees with that obtained for the (e, N)-processes. Using the relativistic Coulomb Eigenfunctions for the continuous spectrum of the positrons, the Coulomb correction, the effect of screening and that of finite nuclear size agree with the (e, N)-process, when the annihilation of positrons with atomic electrons is neglected, and for positron energiesE _1,2 ⁺ >10 MeV. The effect of finite nuclear size is only calculated in Born approximation. ForE _1,2 ⁺ ≦2 MeV only the Coulomb correction differs from that obtained for the (e, N)-process. In the angular distribution for the (ē, N)-process there should be no interference of positron waves scattered by different multipoles, where the inelastic scattered positrons are detected. Numerical calculations have been carried out for nuclei withZ=6.29 and 82 and scattering angles ?=1°, 132°, 160° and 180° of the positron. This theory can be compared with the experiments in progress by W.C.Barber et al. using positrons for the inelastic scattering process at nuclei. The two-and three-virtual quanta-exchange effect in the (ē, N)-cross section is below 1.3% for positron energies between 10≦E ₁ ⁺ ≦300 MeV, and decreases rapidly for higher energies. This theory is also valied for inelastic scattering processes with positiveμ-mesons at nuclei; one has only to change the mass in the following equations.     

Über das Verhältnis der Wirkungsquerschnitte für den (e,n)- und (γ,n)-Prozeß

The ratio of the cross sections for the (e, n)-and (γ, n)-process is derived with the use of the relativistic Coulomb Eigenfunctions for the continuous spectrum, used bySommerfeld-Maue andBethe-Maximon. Only the electric and magnetic dipole transition are considered. For this transitions the Coulomb correction to the Born approximation is calculated. The result of an estimation of the electric quadrupole transition is given. The effect of screening and that of finite nuclear size is estimated. With the ratio thus obtained one is able to calculate the cross sections for the (e, n)- and (γ, n)-process using the experimental values of only one of this quantities.     

Ionization-Excitation of helium-like ions by high-energy electrons

The differential and total cross sections are calculated for the ionization of helium-like ions that is accompanied by the excitation of residual ions to ns states owing to an electron impact. Nonrelativistic perturbation theory in electron–electron interaction with Coulomb functions used for a zero-order approximation underlies these calculations. The expressions obtained in this way have a universal character. They are applicable at moderate values of the target charge number Z and high energies of incident electrons. A comparison with total cross sections calculated for the helium atom within various theoretical approaches is performed.     

Merging of X-Ray photons in the field of a light atomic ion

The process of merging of three X-ray photons into one photon in the field of a light atomic ion is theoretically studied. A pronounced resonance structure and a strong angular anisotropy of the differential cross section for merging are predicted in the region of the incident photon energy ?ω ? I _1s /2 (I _1s is the threshold energy of ionization of the -shell of the ion). The magnitude of the observed merging cross section is estimated.     

The 3–3–1 Model with RH Neutrinos and Associated ZH Production at High-Energy ${\bf \textit{e}}^{+}{\bf \textit{e}}^{-}$ Collider

In the context of SU(3) _C ?? SU(3) _L ?? U(1) _X (3–3–1) model with right-handed neutrinos, we study the Higgsstrahlung process e ^?+? e ^???→ZH and calculate the cross section of this process at leading order. Our numerical results showed that the production cross sections for this process can be significantly large as \(M_{Z'}\approx \sqrt{s}\). With reasonable values of the Z′ mass M _Z′, Z′ exchange can generate large corrections to the cross sections of this process, which might be detected in the future high-energy linear e ^?+? e ^??? collider experiments.     

Zener Tunneling between the Landau Levels in a Two-Dimensional Electron System with One-Dimensional Periodic Modulation

Nonlinear magnetotransport in a two-dimensional electron gas in one-dimensional lateral lattices fabricated from a selectively doped GaAs/AlAs heterostructure is investigated. One-dimensional potential modulation is imposed on the two-dimensional electron gas by means of a set of metal strips formed on the planar surface of Hall bars. The dependences of the differential resistance r_xx on the magnetic field B < 0.5 T are studied at a temperature T = 1.6 K in lattices with a period of a ≈ 200nm. It is shown that periodic oscillations in r_xx(1/B) occur in such lattices under the action of a current-induced Hall field due to Zener tunneling between Landau levels. Interference is found between Zener oscillations and commensurability oscillations of r_xx in two-dimensional electron systems with one-dimensional periodic modulation. The experimental results are qualitatively explained by the role of Landau bands in nonlinear transport at large filling factors.     

The effect of high pressure on the structure and on the magnetic and electronic properties of nickel monoxide

A diamond anvil cell is used to investigate the effect of high pressure (up to 37.5 GPa) on the optical absorption spectra of a single crystal of nickel oxide (NiO). In addition, strain-gage measurements are used to experimentally investigate the V(P) equation of state at a hydrostatic pressure of up to 8.5 GPa in a high-pressure chamber of the “toroid” type. Measurements are performed at room temperature. Absorption bands are observed, which correspond to optical d-d transitions of Ni²⁺ ion in the crystal field of ligands ³A_2g → ³T_2g, ³A_2g → {au1}E_1g, ³A_2g → ³T_1g(F), and ³A_2g → ¹T_2g. The values of energy of these transitions increase linearly with pressure, and their pressure coefficients are 7.3 ± 0.2, 2.87 ± 0.9, 9.7 ± 0.5, and 8.9 ± 0.3 meV/GPa, respectively. The pressure derivative of the crystal field parameter 10Dq corresponding to the ³A_2g → ³T_2g transition gives the pressure dependence of the magnitude of exchange integral J in the Anderson hybridization model. It is found that, in the pressure range from zero to 37.5 GPa, the behavior of the exchange integral J is largely defined by the hybridization parameter b = (10Dq/3). At the same time, the Coulomb interaction parameter U_eff is independent of pressure and, therefore, has no effect on the variation of J. The Coulomb interaction U_eff ≈ 7.47 ± 0.005 eV is determined. The experimental data on the equation of state are used to derive the \(J \propto V^\varepsilon \) correlation, where ε = ?2.99 ± 0.15, which is in good agreement with the predictions of Bloch’s theory (ε = ?10/3).     

Dynamical screening of AMM and QED effects for large-<Emphasis Type="Italic">Z</Emphasis> hydrogen-like atoms

The effective interaction ΔU_AMM of the anomalous magnetic moment (AMM) of an electron with the Coulomb field of an extended nucleus is analyzed. As soon as the q² dependence of the electron formfactor F₂(q²)is taken into account from the beginning, the AMM is found to be dynamically screened at small distances of r ? 1/m. The ΔU_AMM effects on the low-lying electronic levels of a superheavy extended nucleus with Zα > 1are analyzed using the nonperturbative approach. The growth rate of the ΔU_AMM contribution with increasing Z is shown to be essentially nonmonotonic. At the same time, the energy shifts of electronic levels in the vicinity of the threshold of the lower continuum monotonically decrease in the region Z ?Z_cr,1s. The latter result is generalized to the whole self-energy contribution to energy shifts of electronic levels, thus also referring to the possible behavior of QED radiative effects with virtual-photon exchange, considered beyond the framework of the perturbative expansion in Zα.