Relativistic Differential Cross Sections Research Articles

Coulomb effect on elastic electron scattering by hydrogen atom and hydrogen-like ions in their metastable 2s state in the 511–770 KeV energy range

This paper reports on a study investigating the elastic scattering of hydrogen atoms in their metastable state (2S-2S) when subjected to electron impact, with a focus on the Coulomb effect within an energy range spanning from 511 keV to 770 keV . The analysis employs semi-relativistic wave functions to depict the hydrogen states. The validity of using Darwin wave functions is confirmed by ensuring that the condition Zα << 1 is met, where α represents the structure constant. Both incident and scattered free electrons are described using Dirac spinors. Notably, the semi-relativistic calculations converge with those of the non-relativistic case at low electron velocities. Additionally, in the presence of the Coulomb effect, the electron wave function is approximated by a Dirac function modulated by the confluent hypergeometric function. The paper presents the relativistic differential cross-section (RDCS) as a function of the final scattering angle for various energies of the incident electron, revealing intriguing insights into diffusion probabilities in specific directions. Moreover, the impact of the atomic number Z on the elastic scattering of hydrogen atoms and hydrogen-like ions by electron impact under the influence of the Coulomb effect is thoroughly examined.

Coulomb and anomalous magnetic moment effects on laser-assisted electron scattering by atomic nucleus

In the framework of the first Born approximation, we investigate, in the presence of a circularly polarized electromagnetic laser field, the double effect of Coulomb and anomalous magnetic moment (AMM) on the scattering of electron by a fixed atomic nucleus. In this approximation, the initial and final states of the electron are described by the relativistic Coulomb Dirac–Volkov wave functions with AMM effect. For convenience, we choose the origin of the Laboratory coordinate system at the centre of the fixed nucleus presenting a classical Coulomb potential. Both AMM and Coulomb effects on the incident and scattered electrons have affected the relativistic differential cross section. At high energies of the incident electron, our explored numerical results give the predominance of the AMM effect over that of Coulomb. The behavior of the differential cross section, as a function of the electric field strength as well as the laser frequency, is presented.

On the Coulomb effect in laser-assisted proton scattering by a stationary atomic nucleus

In the framework of the first Born approximation, we investigate the scenario where in addition to a laser field, a nuclear Coulomb field is also present to affect a proton. We work in the approximation in which the proton is considered to be a structureless spin 1/2 Dirac particle with a mass mp. Furthermore, in the laboratory system, the fixed nucleus is treated as a point-like Coulomb potential. In the presence of a laser field, and taking into account the Coulomb effect, the proton will be described by distorted Dirac–Volkov wave functions. The introduction of the Coulomb effect to both the incident and scattered proton will enhance the relativistic differential cross sections (RDCSs). Regarding the physical picture, it is found that for the various kinetic energies of the incident proton, the Coulomb effect can be neglected at high kinetic energies in this particular geometry. Therefore, Dirac–Volkov states are largely sufficient to describe the laser-dressed protons. The behavior of the various RDCSs versus the atomic number Z is also presented.

Electron impact excitation of hydrogen atom with anomalous magnetic moment effects

In framework of first Born approximation, Salamin wave states have been used to calculate the differential cross section for laser assisted semirelativistic 1s–2s excitation of hydrogen atom by electron impact with anomalous magnetic moment effects fully included. The obtained results have been compared with laser assisted relativistic differential cross section without such effects. It is found that the electron’s anomalous magnetic moment effects in laser assisted 1s–2s excitation is very important particularly with increase of intensity. Good agreement with laser assisted differential cross section without anomalous magnetic moment effects is obtained when electron’s anomaly \(\kappa=4a_{e^-}=2(g-2)\) is taken to be zero.

Three-dimensional time and frequency-domain theory of femtosecond x-ray pulse generation through Thomson scattering

The generation of high intensity, ultrashort x-ray pulses enables exciting new experimental capabilities, such as femtosecond pump-probe experiments used to temporally resolve material structural dynamics on atomic time scales. Thomson backscattering of a high intensity laser pulse with a bright relativistic electron bunch is a promising method for producing such high-brightness x-ray pulses in the 10--100 keV range within a compact facility. While a variety of methods for producing subpicosecond x-ray bursts by Thomson scattering exist, including compression of the electron bunch to subpicosecond bunch lengths and/or colliding a subpicosecond laser pulse in a side-on geometry to minimize the interaction time, a promising alternative approach to achieving this goal while maintaining ultrahigh brightness is the production of a time-correlated (or chirped) x-ray pulse in conjunction with pulse slicing or compression. We present the results of a complete analysis of this process using a recently developed 3D time and frequency-domain code for analyzing the spatial, temporal, and spectral properties an x-ray beam produced by relativistic Thomson scattering. Based on the relativistic differential cross section, this code has the capability to calculate time and space dependent spectra of the x-ray photons produced from linear Thomson scattering for both bandwidth-limited and chirped incident laser pulses. Spectral broadening of the scattered x-ray pulse resulting from the incident laser bandwidth, laser focus, and the transverse and longitudinal phase space of the electron beam were examined. Simulations of chirped x-ray pulse production using both a chirped electron beam and a chirped laser pulse are presented. Required electron beam and laser parameters are summarized by investigating the effects of beam emittance, energy spread, and laser bandwidth on the scattered x-ray spectrum. It is shown that sufficient temporal correlation in the scattered x-ray spectrum to produce sub-100 fs temporal slice resolution can be produced from state-of-the-art, high-brightness electron beams without the need to perform longitudinal compression on the electron bunch.

Experimental characterization of an ultrafast Thomson scattering x-ray source with three-dimensional time and frequency-domain analysis

We present a detailed comparison of the measured characteristics of Thomson backscattered x rays produced at the Picosecond Laser-Electron Interaction for the Dynamic Evaluation of Structures facility at Lawrence Livermore National Laboratory to predicted results from a newly developed, fully three-dimensional time and frequency-domain code. Based on the relativistic differential cross section, this code has the capability to calculate time and space dependent spectra of the x-ray photons produced from linear Thomson scattering for both bandwidth-limited and chirped incident laser pulses. Spectral broadening of the scattered x-ray pulse resulting from the incident laser bandwidth, perpendicular wave vector components in the laser focus, and the transverse and longitudinal phase spaces of the electron beam are included. Electron beam energy, energy spread, and transverse phase space measurements of the electron beam at the interaction point are presented, and the corresponding predicted x-ray characteristics are determined. In addition, time-integrated measurements of the x rays produced from the interaction are presented and shown to agree well with the simulations.

Pair annihilation in superstrong magnetic fields

view Abstract Citations (58) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Pair annihilation in superstrong magnetic fields Daugherty, J. K. ; Bussard, R. W. Abstract The kinematical and dynamical aspects of the annihilation processes in superstrong magnetic fields are studied. The feasibility and potential significance of detecting from magnetic neutron stars are discussed. The discussion proceeds from the derivation of the fully relativistic differential cross sections and annihilation rates for both one- and two-photon emission from a ground-state gas of electrons and positrons in a static, uniform magnetic field. Publication: The Astrophysical Journal Pub Date: May 1980 DOI: 10.1086/157985 Bibcode: 1980ApJ...238..296D Keywords: Neutron Stars; Particle Interactions; Positron Annihilation; Stellar Magnetic Fields; Astrodynamics; Field Strength; Magnetic Effects; Pair Production; Pulsars; Nuclear and High-Energy Physics full text sources ADS |

Relativistic Compton scattering from a relativistic maxwellian distribution of electrons

Using an earlier developed relativistic differential cross section formula for Compton scattering of photons from a given momentum distribution of electrons, an expression for the differential cross section is derived for the case of a relativistic Boltzmann distribution.

Incoherent scattering of gamma rays by bound electrons: a comparison with relativistic theories

The experimental differential cross sections for the incoherent scattering of 662 keV gamma rays from the K-shell electrons of bismuth (Z=83), reported earlier, are compared with the relativistic values computed by Whittingham (1971) and by Talukdar et al. (1971) for lead (Z=82) using the same energy. Good agreement is found between the experimental values on the one hand and the exact relativistic differential cross sections of Whittingham and the values of the relativistic incoherent scattering function (SK) of Talukdar et al. on the other.

Classical equivalent of Klein-Nishina formula for laser-electron scattering

A classical formula of relativistic differential cross section is suggested for the scattering of a coherent radiation by a free electron. The angular behaviour of this formula is shown quite similar to that of Klein-Nishina for incoherent radiation.

Incoherent scattering of gamma rays in heavy atoms

Exact relativistic differential cross sections for the incoherent scattering of gamma rays by the inner shell electrons of heavy atoms are developed from the second order S matrix element for the electron-photon interaction in the Furry (1951) picture. Electron binding is accounted for completely by using the bound electron propagator and Dirac eigenfunctions for the initial and final electron states. A pure Coulomb potential is used to calculate the energy spectrum and the differential cross section for 662 keV gamma rays scattered by the K electrons of lead. In contrast with the results of Di Lazzaro and Missoni (1966) the energy spectrum maximum is displaced by 10% from the Compton energy towards higher photon energies, and there is no increase in the spectrum at the low-energy end. The relativistic results for the ratio of the bound electron to feed electron cross sections are larger than the incoherent scattering function calculations and exceed unity for scattering angles above 52 degrees .