Differential Ionization Cross Sections
Ionization cross sections play such an important role in so many branches of physical science that a considerable amount of effort has been devoted both to the theoretical and experimental determinations of these cross sections.
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Differential Ionization Cross Sections P. J. 0. Teubner Institute for Atomic Studies, School of Physical Sciences, The Flinders University of South Australia, Bedford Park, South Australia
4.1 Introduction Ionization cross sections play such an important role in so many branches of physical science that a considerable amount of effort has been devoted both to the theoretical and experimental determinations of these cross sections. The theoretical problem can be summarised by the observation that the final state of the system consists of at least three bodies all of which interact through the long range Coulomb force. Thus a description of the ionization mechanism requires a solution to the many body problem. It is not surprising that there has been only limited success in providing even total cross sections at energies less than those at which the Born approximation is valid. The most complete description of an ionization event is provided by determining the energy and momentum of all particles involved in the collision. The triple differential cross section thus defined is given by (Ehrhardt eta/. (1972a))
d3 (J
dEdQAdQB
f3(Eo,EA,()A,8B,c/Jn).
(4-1)
Where the scattering angles are defined in Fig. 4-1, E0 is the incident energy and E A the energy of one of the electrons. The energy of the other electron E8 is determined by the conservation of energy which also allows for the separation energy or ionization potential of the electron in the target. This cross section depends on five variables and therefore is sometimes referred to as the five-fold differential cross section. More recently the term (e, 2 e) cross section has been used to describe these processes. The measurement of this cross section requires the coincident detection of both post collision electrons. The cross section depends not only on a description of the ionization mechanism but also on the structure of the target and the ion. In certain regions of phase space the ionization mechanism can be described accurately, thus the (e, 2 e) cross section can be used to provide structural information. Such is the case for certain symmetric T. D. Märk et al. (eds.), Electron Impact Ionization © Springer-Verlag Wien 1985
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collision geometries and the differential cross section has been used to probe the momentum space wavefunctions of valence electrons in atoms and molecules (McCarthy and Weigold (1976)). The other limiting case concerns ionizing events in which the ion core plays a significant role in the collision. This class of events provides a very sensitive test of the details ofthe ionization mechanism and it is here that most theoretical studies have been singularly unsuccessful. Triple differential or (e, 2 e) cross sections will be discussed in Section 4.2. The double differential cross section is obtained by measuring the intensity distribution of one of the electrons as a function of energy and angle. This is equivalent to integrating the (e, 2 e) cross section over the solid angle of the unobserved electron with a con
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