SOME ASPECTS OF ELECTRON IMPACT IONIZATION OF ATOMS AND IONS

Abstract

The study of electron impact ionization of atoms and ions has evoked quite an interest in recent years. The scattering cross sections for electron/positron impact ionization of hydrogen and helium atoms is of particular interest because a study of these systems enables test of the theories which hopefully would have applicability to other more complicated systems. The complication in the analysis of this process arises due to the involvement of at least a three-particle contin-uum state. Let a particle (electron) of energy (momenta) Eo('o) impinge on an atom. If Eo is greater than the ionization potential for single ionizatign, then two electrons of energies E (momenta ka) and Eb (momenta 1b) emerge in the final state with the scattering angles 8a and 8b with respect to the incident particle direction. The probability of such an events is given by the triple differential cross--section (TDCS), which may be expressed d~ d3 E = f3 (Eo,E 8 ,8 a b a a s b' this cross scction depends on five variables and is there-fore sometimes referred to as five-fold differential cross- sections. The double differential cross-section is obtained lil by measuring the intensity distribution of one of the electrons as a function of its energy and angle. This is equivalent to integrating TDCS over the solid angle of the other electron. Further integration over the angle yield's the single differential cross-section. It represents the energy distribution of the scattered and ejected electrons. The integral over Ea gives twice the total cross section for the impact energy Eo. Those integration steps have an averaging effect and almost always involve mathematical and physical approximations, with a consequent loss of information. The maximum information about the ionization process is given by TDCS. In this thesis we shall consider only triple differential cross sections. The TDCS are generally measured in two types of arrangements (i) Symmetric geometry : It can be further classified into two types of kinematical arrangements (a) Coplanar symmetric geometry in which Ea = Eb,ea = eb and ~ -- ~e = 1800. The vectors kto, ka and ktb are in the same piano. (b) Non-coplanar symmetric geometry where tcb is out of (Lo, ita) piano. The experiments in the symmetric regime, in particular those employing non-coplanar symmetric kinematics yield target bound state information in the form of the probability distri-butions and separation energy spectra. (ii) Asymmetric coplanar geometry : In this typo of geometry for a fast iv incident electron of energy Eo a fast (scattered) electron of energy Ea close to the incident energy Eo is detected in the differential element dSLa in coinci-dence with a slow (ejected) electron of energy Eb in the differential element dJ1 b. The momenta k~o, k and I b are in the same plane so •that tea = 0 and ~,'= 0 or it. This type of geometry is very sensitive to the ionization mechanism. In this thesis we shall concent-rate mainly on this type of geometry. Extensive experiments in the later geometry have been-performed by Ehrhardt at al. For low impact energies and close to the ionization threshold the triple differ-ential cross sections vary very rapidly with the kinematic parametters, because of the interference of the scattering amplitudes f and g where f stands for the direct scatter-ing amplitude g for the exchange amplitude. For high impact energies and asymmetric geometry the amplitude g does not contribute 'much. At these energies a double peaked strong angular correlation is found betwcon the scattered and the ejected electrons : One peak (called the binary peak) which is mostly due to the binary collision between the ' incident electron and the atomic electron, near the direction of linear momentum transfer and the other one (called the recoil peak) which corresponds to a largo momentum transfer to the ion, in a direction nearly v opposite to that of the binary peak. The size of the binary peak increases with the increase in the energy Eo of the incident electron. For a fixed Eo the ratio of the binary to the recoil peak increases as the scatt-ering anglo 9 increases or as the ejected electron energy Eb increases. For large Aa and large Eb the recoil peak is very small compared to the binary peak. Since the kinematic parameters E0,Ea,Eb,0a and Ab can be varied in measurement of the triple differen-tial cross sections for a given target, it is quite important to investigate the structure of the triple differential cross sections in terms of some suitably defined structure parameters such as the angular positions of the intensity maximum of the binary and recoil peaks, half width of the binary and recoil peak. The deviation of the binary and recoil peak maxima from the momentum transfer direction, and the ratio of the binary to recoil peak.