Scattering of Fermions by a Magnetic Dipole Field

In this paper we study the problem of fermions scattering by the field of a magnetic dipole in Minkowski space-time. The amplitude and differential cross section for scattering of massive fermions are obtained using the exact solution of the Dirac equation written in the helicity basis. We found that the most probable transitions are those that scatter the fermions perpendicular to the direction of the magnetic field and we consider only the transverse momenta in our analysis. The differential cross section behavior in terms of scattering angle and energy is graphically analysed and we perform a comparative study with the Coulomb scattering.

Infrared Effects

It is shown that the presence of zero mass particles makes the elements of the S-matrix divergent. We explain the physical origin of such divergences. We argue that they are due to the long range of the interactions which violate the assumptions we made when we derived the asymptotic conditions for scattering. We study these divergences in the particular case of QED at tree, as well as one-loop level and present the Bloch–Nordsieck solution. We show that the cancellation of infrared divergences among virtual exchanged and real emitted soft photons is true to all orders in the perturbation expansion and we obtain the Sudakov double logarithm formula for Coulomb scattering.

Exploring the Properties of the Electron Strahl at 1 AU as an Indicator of the Quality of the Magnetic Connection Between the Earth and the Sun

In this report some properties of the electron strahl at 1 AU are examined to assess the strahl at 272 eV as an indicator of the quality of the magnetic connection of the near-Earth solar wind to the Sun. The absence of a strahl has been taken to represent either a lack of magnetic connection to the corona or the strahl not surviving to 1 AU owing to scattering. Solar-energetic-electron (SEE) events can be used as indicators of good magnetic connection: examination of 216 impulsive SEE events finds that they are all characterized by strong strahls. The strahl intensity at 1 AU is statistically examined for various types of solar-wind plasma: it is found that the strahl is characteristically weak in sector-reversal-region plasma. In sector-reversal-region plasma and other slow wind, temporal changes in the strahl intensity at 1 AU are examined with 64 s resolution measurements and the statistical relationships of strahl changes to simultaneous plasma-property changes are established. The strahl-intensity changes are co-located with current sheets (directional discontinuities) with strong changes in the magnetic-field direction. The strahl-intensity changes at 1 AU are positively correlated with changes in the proton specific entropy, the proton temperature, and the magnetic-field strength; the strahl-intensity changes are anti-correlated with changes in the proton number density, the angle of the magnetic field with respect to the Parker-spiral direction, and the alpha-to-proton number-density ratio. Reductions in the strahl intensity are not consistent with expectations for a simple model of whistler-turbulence scattering. Reductions in the strahl intensity are mildly consistent with expectations for Coulomb scattering, however the strongest-observed plasma-change correlations are unrelated to Coulomb scattering and whistler scattering. The implications of the strahl-intensity-change analysis are that the change in the magnetic-field direction at a strahl change represents a change in the magnetic connection to the corona, resulting in a different strahl intensity and different plasma properties. An outstanding question is: Does an absence of an electron strahl represent a magnetic disconnection from the Sun or a poor strahl source in some region of the corona?

Track Models

The chapter shows how the equations of motion for charged particles in a homogeneous or inhomogeneous magnetic field are solved. Various types of parametrizations are presented, and formulas for track propagation and error propagation are derived. As the effects of the detector material on the trajectory have to be taken into account, the statistical properties of multiple Coulomb scattering, energy loss by ionization, and energy loss by bremsstrahlung are discussed; then it is shown how the effects can be treated in the track reconstruction. As multiple scattering in thin layers and energy loss by bremsstrahlung have distinctive non-Gaussian features, an approximation by normal mixtures is presented.

Major scattering processes

This chapter discusses major scattering processes found in semiconductors, including phonon scattering (deformation scattering, piezoelectric scattering, polar scattering and non-polar scattering), scattering arising from impurities (charged, so a Coulomb scattering, and charge neutral) and scattering arising in compositional randomness, from carrier-carrier events and due to coupled-particle interactions. The discussion starts by making connections between the classical scattering cross-section and its quantum-mechanical origins through the matrix elements for scattering. The ability to write the matrix element is employed for describing scattering by phonons in its various forms, for impurities and their various levels of accuracy of the description. Umklapp processes are described. When multiple scattering processes are present, the resulting transport manifests the processes’ independence and dependence. With an understanding of the scattering, observed behavior in semiconductors of interest is summarized to show their relative importance. The chapter concludes by discussing frequency and high field behavior manifested by electron ensembles.