First Born Approximation Research Articles

Charged-particle scattering in the presence of a magnetic and a laser field and multiphoton emissions

Charged-particle scattering by a static potential V(r) in the simultaneous presence of a magnetic and a laser field, both directed along the z axis, is studied within the Green's function formalism and the first Born approximation (FBA). For three types of scattering potential (screened Coulomb, pure Coulomb and exponential) the first-order matrix elements and the cross sections are calculated exactly and given in analytic closed form. The optical theorem is derived, with the result that the total scattering cross section is found to be expressed not through the imaginary part of the forward elastic scattering amplitude as is usually the case, but through the real part. The analytic structure of the cross sections in the presence of the two external fields is found to resemble the cross sections of collision processes involving particles with discrete internal structure. The analysis shows that the magnetic field assisted potential scattering is one of the physical processes where a beam of free electrons is found to amplify coherent radiation, especially in the low-frequency regions (infrared or less).

Elastic scattering of electrons and positrons from H and Ar in the second-order eikonal approximation

Wallace's (WSOEA) second-order eikonal approximation is used to calculate elastic differential cross sections for e-or+-H and e-or+-Ar scattering at 100 and 500 eV in the angular range 0-20 degrees . The predictions of the WSOEA are compared with those of the partial-wave calculation (PWC), in addition to the results obtained in the first Born approximation (FBA) and Glauber's first-order eikonal approximation (FOEA). The WOSEA shows a definite improvement upon the FBA and the FOEA and yields cross sections in good agreement with the PWC results.

Comparison of the Born and Glauber generalized oscillator strengths for the2s→3ptransition of atomic hydrogen

Minima and maxima of the generalized oscillator strength for the $2s\ensuremath{\rightarrow}3p$ transition of atomic hydrogen are found using the Glauber approximation. In contrast to the first-Born approximation, the number of extrema and their positions are found to vary with the energy of the incident particle, and the values at the minima do not vanish. There is qualitative agreement in the behavior of the first minimum with known experimental data on the resonance transitions of rare gases and mercury. For large incident energy, the transition amplitude in the Glauber approximation falls off with large momentum transfer more rapidly than predicted by a previous calculation based on the second-Born approximation.

Total Born-approximation cross sections for single-electron loss by atoms and ions colliding with atoms

The first Born approximation (FBA) is applied to the calculation of single-electron-loss cross sections for various ions and atoms containing from one to seven electrons. Screened hydrogenic wave functions are used for the states of the electron ejected from the projectile, and Hartree-Fock elastic and incoherent scattering factors are used to describe the target. The effect of the target atom on the scaling of projectile ionization cross sections with repect to the projectile nuclear charge is explored in the case of hydrogenlike ions. Also examined is the scaling of the cross section with respect to the target nuclear charge for electron loss by ${\mathrm{Fe}}^{+25}$ in collision with neutral atoms ranging from H to Fe. These results are compared to those of the binary-encounter approximation (BEA) and to the FBA for the case of ionization by completely stripped target ions. Electron-loss cross sections are also calculated for the ions ${\mathrm{O}}^{+i}(i=3\ensuremath{-}7)$ and ${\mathrm{N}}^{+i}(i=0\ensuremath{-}6)$ in collision with He targets in the energy range of \ensuremath{\sim}0.1 to 100 MeV/nucleon. These results are found to be in excellent agreement with the available data near the peak of the ionization cross section.

Excitation of the autoionizing level in Zn I and Cd. I

Electron impact differential and integrated cross sections for the excitation of the autoionizing level in zinc (3d to 4p) and cadmium (4d to 5p) are calculated using the first Born approximation (FBA) and the modified first Born approximation (MFBA). The orbital approximation has been employed. The ground-state orbital (nd, n=3 for Zn and n=4 for Cd) is represented by analytical SCF orbitals as obtained by Clementi (1967). The excited orbitals (4p and 5p) have been approximated by hydrogenic orbitals with appropriate effective Z.

Elastic first Born matrix elements and systems containing large numbers of electrons

It is argued that the more electrons a target atom or molecule has, the higher one has to go in energy before the first Born approximation (FBA) to elastic electron scattering can be relied upon. For excitation processes, on the other hand, the FBA should be useful in roughly the same kind of energy range for a system containing a large number of electrons as for a system containing a small number of electrons, provided that the excitation processes considered are similar. Ramifications of these two results in the theory of heavy particle collisions are pointed out. Electron loss by hydrogen atoms passing through Ar is taken as an example. It is shown how the presently existing discrepancy between the Dmitriev and Nikolaev (1963) free scattering approximation to this process and the available experimental data can be corrected. Large differences between FBA calculations of heavy particle collision processes involving targets containing large numbers of electrons and experimental data are also explained and a solution proposed.

Frequency effects of electromagnetic scattering from underdense turbulent plasmas

Generalized relations are presented for the first and second moments of the scattered power spectrum function, for underdense turbulent plasmas, in terms of the spatial distribution of electron density and velocity fluctuations, and of mean velocity. The scattering model is based on the far-field and first-Born approximations; retarded potential effects are neglected through use of a time-smoothed autocorrelation function of the received electric field signal. A form of the space-time autocorrelation function for electron density fluctuations is derived that accounts for unequal velocity fluctuation components and electron molecular diffusivity to first order. Specific application of the theory is made to axisymmetric, near-wake flows, for which the molecular diffusivity effect on the spectrum function is negligible. In particular, the case of backscattering at small aspect angles is considered. Radial profiles of rms electron density and logitudinal velocity fluctuations, as well as mean velocity, are used that are based on available experimental data. Under the assumption that the spatial electron density spectrum function is constant throughout the scattering volume, relatively simple analytic expressions are arrived at for the first and second moments of the scattered power spectrum function. Numerical results are presented for these moments, interpreted as range rate (or Doppler mean wake velocity) and velocity standard deviation (or Doppler velocity spread). For conditions supported by available data, it is found that, to a first approximation, 1) range rate is equal to the difference between body velocity and mean wake velocity averaged over a wake cross section, Ua9 and 2) velocity standard deviation is equal to the difference between the wake front velocity and t/0.

Matter-field correlations and first Born photon statistics

It is shown that the final form of quantum statistics evolving via a first-Born approximation interaction depends critically on the dynamic inclusion of matter-field correlations. It is pointed out that these matter-field correlations are directly measured in photon statistic experiments.