Nonlinear supersymmetry at HERA-energies

Some consequences of a model whereN=1 supersymmetry is realized nonlinearly are worked out forep-collisions at HERA-energies. The model contains in addition to the standard particles one Goldstone-fermion λ, a neutrino-like Majoranaparticle. The existence of such a particle would be signalled by events with large missing energy and momentum. We present detailed predictions for the following special kinematic regions: (1) events with a tagged small angle electron and a largeE _T jet, (2) events with a large angle electron and a small angle tagged exclusive proton, (3) events with a tagged small angle electron and a tagged small angle exclusive proton. We indicate the region in coupling constant and mass of the Goldstone-fermion which can be explored at HERA and compare with the limits obtainable from existing data one ⁺ e ^? and \(p\bar p\) collisions at high energies.     

Measurement of azimuthal magnetic fields in a Z-pinch gas discharge using the faraday rotation of a probe beam

The Faraday rotation of the plane of polarisation of a probe beam by azimuthal magnetic fields in the presence of beam deflection caused by refractive index gradients is discussed for a plasma carrying an axial current. A method for calculation of the magnetic field profile from experimental data is described. Bθ can be found by Abel inversion if the electron density is known and if deflected rays can be collected by an optical system and focussed onto a detector. Typical Faraday rotations calculated for the Bennett pinch assuming small beam deflection are found to be proportional to the plasma current and to the angle of deflection. If the probe beam wavelength is chosen to satisfy the approximate relation N₀λ² ≈ 3.5 × 10¹³ m^-1, where N₀ is the electron density on the axis, measurement of Bθ with beam deflections less than 2 × 10^-2 radians should be possible in cases where small rotations can be detected in the mid-to-far infra-red part of the spectrum.     

Application of obliquely interfering TE10 modes for electron energy gain

Two fundamental TE₁₀ modes are considered to interfere at a small angle θ and then propagate along the z-axis in an evacuated rectangular waveguide. The electron trajectory in the resultant field and the expressions for energy gain and the acceleration gradient are obtained, when the electron is injected along the z-axis. A 50 keV electron gains 718 keV energy in a 4.0 cm × 2.5 cm waveguide, when the microwave with intensity of 1 × 10¹⁰ W/cm² and frequency 5.577 GHz is used and the modes superpose at an angle of 10°; here the maximum acceleration gradient is obtained as 251 MeV/m. The energy gain and acceleration gradient are decreased with increasing width of the waveguide and microwave frequency. Higher gradient and larger energy gain are obtained for the higher microwave intensity, smaller angle of superposition and also when the electron is injected with larger initial energy.     

On the influence of elastic scattering on asymmetric xp-signal distribution

In the standard equation for the strength of photoelectron signals the angular dependence of emitted photoelectrons is represented by the asymmetry parameter. As the geometry has a number of characteristic angles, γ, for example due to a finite solid angle of electron detection, one expects an effective asymmetry parameter β* instead of the theoretical β. But elastic electron scattering causes much more of a spread from the characteristic angle γ to a spectrum of possible γ-values. This paper aims to obtain quantitative results allowing a quantification of the influence of elastic scattering on the theoretical asymmetry parameter β. For photoelectrons with kinetic energies within 1–1.5 keV and elements up to Z = 46 the result is β* = (1.0688 ?0.0235Z+0.000188Z²)β     

Charge-density oscillations at (1 1 1) noble metal surfaces

Induced charge-density oscillations at noble metal surfaces caused by an external static impurity are studied within linear response theory. The calculation takes into account such properties of realistic surface electronic structure as an energy gap for three-dimensional (3D) bulk electrons and a s − p_z surface state that forms two-dimensional (2D) electron system. It is demonstrated that the coexistence of these 2D and 3D electron systems has profound impact on the induced charge-density in the surface region. Thus, the oscillations with the 1/R² decay as a function of lateral distance, R, are established in both electron systems with characteristic chess-board-like structure. Additionally, the charge-density penetrates into the solid at a finite angle with respect to the surface normal in contrast to that in jellium model. The origin of both these findings is investigated.     

Isotope effect in electron capture by protons into the 2S-state of hydrogen

We have investigated the isotope effect for electron capture into the 2S-state of hydrogen in close collisions for the processes H⁺ in H₂ and H⁺ in D₂. The differential cross sections and transition probabilities P_2S obtained for capture into H(2S) as a function of energy at a fixed angle of θ = 1° exhibit distinctive features, but no apparent isotope effects are detected.     

Coupling to the elastic channel in electron impact spectroscopy: A simple second born model and its application to excitation of the 61P1 state of mercury and to the excitation of molecules

The matrix element in the infinite channel close coupling approximation responsible for coupling to the elastic channel in electron impact inelastic encounters is investigated. The contribution from the imaginary part of the energy denominator in the elastic coupling matrix element for dipole allowed transitions is shown to yield large angle differential cross sections in good agreement with experiment. This coupling mechanism predicts that the shape of the inelastic differential cross section will be dominated by the shape of the elastic cross section in the large angle high energy limit. In fact the coupling matrix element exhibits a dependence on incident energy, k², and momentum transfer, K, of the form 1/kK² which is in agreement with the theoretical predictions of Huo and means that in the limit of high incident energy the non-first-Born elastic coupling will dominate the angular dependence of the inelastic differential cross section at large scattering angles. In the case of molecular electron impact spectra it is shown that the analog of the Massey—Moore coherence features depending on the symmetry of the states involved in the excitation process will also occur in the coupling contribution. It is suggested that this new mechanism for producing coherent features in inelastic differential cross sections may be the explanation of the coherent features observed experimentally by Karle and Swick.It can be concluded on the basis of the results obtained here that the coupling to the elastic cross section provided by the imaginary contribution from the second Born energy denominator is sufficient to explain presently available experimental data on the large angle differential cross section and spin polarization. The simple coupling model was found to be inadequate to explain the small angle differential cross section in the range 10° < θ < 30° even at incident energies as high as 400 eV. The calculations also showed significant differences between first and second Born calculations at zero scattering angle. No conclusion can be drawn about this observation as all the omitted terms should make significant contributions in the small angle region. It is important to again emphasize that the large angle scattering even in the limit of high incident electron energy will be completely dominated by the coupling to the elastic channel^{7, 11}. On the basis of this work it appears that the coherent structure in the large angle inelastic differential cross section observed by Swick and Karle^{12, 13} at incident electron energies in the keV region may well be due to coupling to the elastic channel.     

Absorption of electromagnetic energy by slow electrons under scattering from Coulomb centers

Simple analytical expressions are obtained for the rate of the inverse stimulated bremsstrahlung absorption under electron scattering from a Coulomb center with charge Z in the presence of the electromagnetic field. The initial and final values of electron energy are assumed to be small compared to the Rydberg energy Z ² (atomic units are used throughout). Single-photon processes of absorption and induced radiation of photon by electron are treated. It is assumed that the electromagnetic field frequency ω is rather low, so that the condition Zω/p ³ ? 1, where p is the electron momentum, and the condition ?ω ? p ² are valid. However, this frequency is assumed to be fairly high compared to the electron-Coulomb center collision frequency: ω ? v _nei. The dependences of the rates of photon absorption and induced radiation on the angle θ between the direction of incident electron and the electromagnetic field polarization vector (assumed to be linearly polarized) are obtained. It is demonstrated that, for any angles θ, the rate of photon absorption is higher than the rate of induced radiation and, therefore, the Marcuse effect for slow electrons (electromagnetic field amplification) is absent. It is further demonstrated that a slow electron on the average absorbs double ponderomotive energy per collision with an ion (Coulomb center) in Maxwellian plasma. This agrees both with the known results calculation for fast electrons and with the known results of the calculation based on the classical Boltzmann kinetic equation for plasma.     

Matrix formulation of the beam quality of the Hermite-Gaussian beam

Based on the M ²-parameter of Hermite-Gaussian beam, we deduced the matrix formulation of the beam quality for nonsymmetric two-dimensional Hermite-Gaussian beam, which at an arbitrary azimyth angle α. And coupled beam radius square, coupled M ²-parameter also have been introduced. The beam radius versus azimuth angle α at different positions has been presented by numerical simulation; and the track of M ²-parameter versus azimuth angle α has been given. The M ²-parameter matrix is universal and available both in the theoretical analysis and the practical measurement of the beam quality for a arbitrary two-dimensional nonsymmetric higher-order Gaussian beam.     

A measurement of the azimuthal angle dependence of the process ep → enπ+ near threshold

The azimuthal angle dependence of the process ep → enπ⁺ has been measured by detecting the electron and neutron in coincidence. Data are presented for momentum transfers (?k²) between 0.08 and 0.32 $\text{(}\text{GeV}\text{c}\text{)}{}^2$ and at energies close to threshold. Fixed-t dispersion relation models give predictionsin good qualitative agreement with the data.     

The Qweak: Precision Measurement of the Proton’s Weak Charge by Parity Violating Experiment

The Qweak experiment at the Thomas Jefferson National Accelerator Facility measures the parity violating asymmetry in longitudinally polarized electron scattering from the proton at very low momentum transfer, Q ² = 0.026 (GeV/c)², at an incident electron beam energy of 1.16 GeV. With this measurement and the earlier results of the parity violating elastic scattering experiments, the Qweak experiment determines the weak charge of the proton, ${Q^p_{\rm W}}$ , with a 4% combined statistical and systematic error. This measurement will be used to determine the weak mixing angle, ${\sin^2\theta_{\rm W}}$ , that is predicted by the Standard Model from the Z ⁰ pole down to lower energies. Qweak will determine ${\sin^2\theta_{\rm W}}$ to a 0.3% relative precision, providing a competitive measurement of the running of this quantity. Moreover, if there is a significant deviation of the weak mixing angle from the Standard Model prediction, then the Qweak experiment will give a glimpse of possible extensions of the Standard Model.     

The reaction e− + p → Λ + ν and the contributions of the individual form factors to the differential cross section

We calculate the differential cross section for the weak, strangeness changing, electron scattering process, e⁻ + p → Λ + ν, for incoming electron energies of 0.5, 1.0, 2.0, 4.0, and 6.0 GeV. We obtain as well contributions of the individual form factors to the differential cross sections. We find that the differential cross sections peak as the maximal scattering angle for the Λ is approached and that the peak height increases as the electron energy is increased. The behavior of the differential cross section near the maximal angle is discussed as is the possibility of observing this reaction in a facility such as TJNAF.     

Simultaneous solution of Kompaneets equation and radiative transfer equation in the photon energy range 1-125 keV

Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 keV photon energy range. Diffuse radiation field are calculated using time-independent radiative transfer equation in plane parallel geometry, which is developed using discrete space theory (DST) of radiative transfer in a homogeneous medium for different optical depths. We assumed free-free emission and absorption and emission due to electron gas to be operating in the medium. The three terms n, n² and (∂n/∂x_k) where n is photon phase density and x_k=(hν/kT_e), in Kompaneets equation and those due to free-free emission are utilized to calculate the change in the photon phase density in a hot electron gas. Two types of incident radiation are considered: (1) isotropic radiation with the modified black body radiation I^MB[1] and (2) anisotropic radiation which is angle dependent. The emergent radiation at τ=0 and reflected radiation τ=τ_max are calculated by using the diffuse radiation from the medium. The emergent and reflected radiation contain the free-free emission and emission from the hot electron gas. Kompaneets equation gives the changes in photon phase densities in different types of media. Although the initial spectrum is angle dependent, the Kompaneets equation gives a spectrum which is angle independent after several Compton scattering times.     

N@C60 and P@C60 as quantum bits

Due to their long electron spin relaxation times, the endohedral fullerenes N@C₆₀ and P@C₆₀ are good candidates for the implementation of qubits in an electron spin quantum computer. A central operation in this context is the rotation of the spin direction by an arbitrary angle. In the present experiment, this nutation behavior was studied in pulsed electron spin resonance measurements. We show that, even at room temperature, about 50 Rabi oscillations (about 100 qubit operations) can be performed without refocusing the spin system, although inhomogeneities are present. A special feature of the group V endohedral fullerenes is the electron spinS=3/2, which complicates the nutation behavior. The zero-field splitting at low temperature gives rise to different nutation frequencies for the (1/2,?1/2) transition and the (±3/2, ±1/2) transitions. The frequency ratio is 2/3^1/2.     

Dissociative recombination of electrons and O 2 + molecular ions in the field of intense visible laser radiation

We analyze the low-temperature dissociative recombination reaction e ^?+O ₂ ⁺ → O(¹ D)+O(³ P) in the field of visible monochromatic laser radiation. The analysis is performed in terms of the multichannel quantum defect theory using the stationary formalism of the radiative collision matrix. We calculate the dependences of the reaction cross section on the incident electron energy, the external electromagnetic field strength and frequency, and also the angle between the directions of the electron beam and the electric vector for linearly polarized radiation. The cross section is shown to increase by several orders of magnitude for a certain choice of these parameters, suggesting the possible laser stimulation of this reaction.     

Resonances at slow electron collisions with zinc atoms and ions

The optical excitation functions of four spectral lines corresponding to the transitions from the 4¹ D ₂, 5³ S ₁, 4³ D _j, and 6¹ S ₀ levels of atomic Zn were investigated with an electron spectrometer of a new construction. For the first time, elastic scattering of slow electrons from the Zn ions at an angle close to 180° was studied. In the energy range under investigation (0–7 eV), both the optical excitation functions of atomic spectral lines and the differential cross section of elastic scattering manifested the resonant structure caused by the contribution of autoionization states of the atom.     

Magnetic contributions to high energy inverse bremsstrahlung process

Magnetic contribution to inverse bremsstrahlung is estimated at high energies. It begins to dominate over the Coulomb contribution in the ratioCE ₂ ² tan² (θ ₂/2) (1+sin² (θ ₂/2)) whereE ₂ andθ ₂ denote the energy and angle of the accelerated electron andC is essentially a nuclear constant.     

Messung der Energie- und Winkelabhängigkeit der Asymmetrie der äußeren Bremsstrahlung

In order to obtain an azimuthal dependence of the external bremsstrahlung produced by electrons, the electron beam has to be transversely polarized. In first-order Born approximation the differential cross section does not depend on the azimuthal angle φ¹, but the second-order approximation includes the spin vector of the electrons^2,3 and yields, consequently, a φ-dependence. This paper deals with a measurement of the bremsstrahlung asymmetry as function of the photon energy and the emission angle Θ. The transversely polarized electron beam was produced by momentum deflection of longitudinally polarizedβ-decay electrons emitted from a⁹⁰Sr source. With a kinetic energy of 300±10 keV and a degree of transverse polarization of 74% the electrons hit a Pb target. Because of the high γ-background it was necessary to detect the emitted bremsstrahlung in coincidence with the incident electrons. We found effects of about 3% in contrast to considerably larger values (13%) published in an earlier paper. The asymmetry was numerically calculated according to Johnson and Rozics. Since at an electron energy of 300 keV the Born approximation gives not yet good results, theory and measurement agree only in order of magnitude, particularly at highγ-energies.     

Total cross section for inclusive electron scattering in the lowQ 2 region

Absolute cross sections for inclusive electron scattering on H, D, Be, Al, and Si have been measured in the kinematical region 0.08 (GeV/c)²<Q ²<1.0 (GeV/c)² and 0.3 GeV<v<6.5 GeV. The measurements have been performed at incident energies of 3, 5, 6, and 7 GeV and at the fixed scattering angle of 10°. A careful treatment of radiative corrections due to elastic electron nucleus scattering, quasielastic and inelastic scattering on the bound nucleons has been applied to the measured cross sections. The comparison of the nuclear cross sections with the elementary ones leads to a value ofA _eff<A with a rapid onset of this effect at small values of the scaling variablex′.     

Electroproduction of neutral pions at energies above the resonance region

The reaction e p→e'pπ⁰ has been measured at W=2.55 GeV a fixed electron scattering angle of 10.3°. Two magnetic spectrometers and a lead glass hodoscope were used to detect all four final state particles. Electroproduction cross sections in the t range ?0.15 to ?1.4 (GeV/c)² at q² = ?0.22, ?0.55 and ?0.85 (GeV/c)² are presented. Above |t|=0.6 (GeV/c)² the cross sections are considerably smaller than those for photoproduction.