Electron projectile

On the other hand. Fig. 1 demonstrates the power of classical collision theory. In view of the complexity of a complete quantal treatment of the stopping of a point charge in a many-electron target, or even a many-electron projectile in a many-electron target, utilizing the power of classical collision theory whereever justified, and knowing its limitations, is nothing less than a necessity from a practical point of view. 

The target molecule can be considered in terms of the isolated electron involved in the transition, charge q, and a charge, q", determined by the dipole moment of the molecule, Pq, and its orientation with respect to the electron projectile. The effective charge in the collision is given by = q + where. 

In summary, preliminary experiments have demonstrated that the efficiency and outcome of electron ionization is influenced by molecular orientation. That is, the magnitude of the electron impact ionization cross section depends on the spatial orientation of the molecule widi respect to the electron projectile. The ionization efficiency is lowest for electron impact on the negative end of the molecular dipole. In addition, the mass spectrum is orientation-dependent for example, in the ionization of CH3CI the ratio CHjCriCHj depends on the molecular orientation. There are both similarities in and differences between the effect of orientation on electron transfer (as an elementary step in the harpoon mechanism) and electron impact ionization, but there is a substantial effect in both cases. It seems likely that other types of particle interactions, for example, free-radical chemistry and ion-molecule chemistry, may also exhibit a dependence on relative spatial orientation. The information emerging from these studies should contribute one more perspective to our view of particle interactions and eventually to a deeper understanding of complex chemical and biological reaction mechanisms. 

Recently Schulz et aland Fischer et al have had some difficulty in applying the CDW-EIS theory successfully for fully differential cross sections in fast ion-atom collisions at large perturbations. These ionization cross sections are expected to be sensitive to the quality of the target wave function and therefore accurate wave functions are needed to calculate these cross sections. Thus one purpose of this paper is to address this problem theoretically by re-examining the CDW-EIS model and the assumptions on which it is based. We will explore this by employing different potentials to represent the interaction between the ionized electron, projectile ion and residual target ion. For other recent work carried out on fully differential cross sections see and references therein. This discussion is presented in section 4. 

The experimental situation is that times characteristic of an experiment are of the order 10 s, while the time characteristic of an atomic collision is, for example, the time it takes an electron projectile to traverse an atom. This is of the order 10 s. It is therefore physically reasonable to consider the limit t —> oo or e —> 0+. Experiments involving time resolution have been devised with resonant states whose lifetimes are greater than 10 s. Such experiments must be described by explicit wave packets rather than the formalism of the present section. An example is given in section 4.6. 

Ej is the orbital energy associated with the target wave function Here Vpg is an effective potential seen hy the active electron, which contains the screening effect produced by other electrons from the medium. For bare incident ions, the active-electron projectile interaction Vpg is just the Coulomb potential. However, in the case where the projectile carries electrons, we use a screened potential made up of the Coulomb part due to the projectile-nuclear charge and the static potential produced by the target electrons that screen the projectile-nuclear charge... 

In the SCA rectilinear trajectory picture, the cross sections depend on the velocity of the projectile, not its mass. The rectilinear assumption is inaccurate for electron projectiles unless is much greater than that of the target electron it becomes inaccurate for any projectile if the energy of excitation is comparable with the initial energy of the projectile, For velocities in this region the wave picture should be used. Cross sections now depend on the mass of the projectile. The expression for the scattering amplitude is... 

McDaniei E W 1989 Atomic Collisions Electron and Photon Projectiles (New York Wiiey)... 

Theoretically, the asymptotic fonn of die solution for the electron wave fiinction is the same for low-energy projectiles as it is at high energy however, one must account for the protracted period of interaction between projectile and target at the intennediate stages of the process. The usual procedure is to separate the incident-electron wave fiinction into partial waves... 

The partial wave decomposition of the incident-electron wave provides the basis of an especially appealing picture of strong, low-energy resonant scattering wherein the projectile electron spends a sufficient period of time in the vicinity... 

Figure Bl.24.4. Energy loss components for a projectile that scatters from depth t. The particle loses energy A E- via inelastic collisions with electrons along the inward path. There is energy loss A E in the elastic scattering process at depth t. There is energy lost to melastic collisions A along the outward path. For an incident energy Eq the energy of tlie exiting particle is = q - A iv - AE - A E. ...

An electron or atomic beam of (projectile or test) particles A with density N, of particles per cm travels with speed V and energy E tln-ongh an infinitesimal thickness dv of (target or fielc0 gas particles B at rest with... 

The END trajectories for the simultaneous dynamics of classical nuclei and quantum electrons will yield deflection functions. For collision processes with nonspherical targets and projectiles, one obtains one deflection function per orientation, which in turn yields the semiclassical phase shift and thus the scattering amplitude and the semiclassical differential cross-section... 

Shock-wave loading of solids is normally accomplished by either projectile impact, such as produced by guns or by explosives. The shock heating and compression of solids covers a wide range of temperatures and densities. For example, the temperature may be as high as a few electron volts (1 eV =... 

Deviations from Rutherford cross-sections are also found for heavy projectiles at lower impact energies, when the projectile can bind inner shell electrons which screen the nuclear charge. These deviations are usually small and can easily be taken into account by use of a theoretical correction [3.160]. 

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