TRIPLE DIFFERENTIAL CROSS SECTIONS FOR THE ELECTRON IMPACT IONIZATION OF HYDROGEN AND HELIUM AT INTERMEDIATE AND HIGH ENERGIES

Abstract

In the present study we have undertaken the investigation of, the ionization of atomic targets (hydrogen and helium) by the electron impact at intermediate and high energies. A lot of theoretical and experimental work has been done on the ionization of atoms by the impact of charged particles. Most of this is related to the total ionization cross sections. For most applications a fairly reliable estimate of the total cross sections is all that is needed, and a good theoretical description is generally possible for it. However in the process of obtaining total cross sections various interesting features of the differential cross sections are masked during summing and averaging over kinematical parameters of the ejected acid -scattered electrons. •The result is that the theories which are able to lead to a good agreement with measured total cross sections fail to do so when applied to explain differential cross sections. A more stringent test of a theoretical model is, therefore, provided by the cross sections that are differential in nature with respect to one or more parameters. The quantity having the most detailed information about a (e , 2e) reaction is the triple differen-tial cross , section (TDCS) since all kinematic parameters are determined, namely the energy of the incident electron Eo , the energies Ea and Eb and directions (8a , (~a) and (8b ' Ob) 0 of the two outgoing electrons, the initial state of the target and the final state of the residual ion. We have concentra-ted our attention to calculating TDCS for the electron impact ionization of atomic hydrogen and helium. The first experimental measurement of TDCS (e--He) was reported by Ehrhardt and co-workers in 1969. Several measure-merits were carried out thereafter on various systems using different type of geometries. Weigold and co-workers at the Flinder' s University, South Australia have used symmetric geometry in which both the outgoing electrons are detected with about the same energy and at same angles with respect to the incident direction, At high energies such a geometry is very useful in obtaining the momentum distribution of the initially bound target electrons. Ehrhardt and co-workers at Kaiserslautern, West Germany have pioneered a more interesting geometry called the coplanar asymmetric geometry. Here, one. of the electrons (scattered) is detected at relatively, small scattering angle with energy close to the incident one, and the cross section is measured as a function of the scattering angle of the other (slow, ejected) electron. This type of geometry provides a particularly sensitive test for a theory describing the dynamics of the collision process. Martino and co-workers at Rome, Lahmam-Bennani and co-workers at Orsay, Paris and Popov and co-workers at Moscow State University have (iv) followed the Ehrhardt-type geometry. For any given energy of ejection Eb and scattering angle 9 ; the angular distri-bution of ejected electrons shows a strong (binary) peak close to the direction of momentum transfer K and a subsidiary (recoil) peak in a direction close to -K. These two peaks are not centred about a common axis, Most of the ionizing collisions at high Eo are such that ejected electron energy Eb and scattering angle 8a are small giving rise to a rocuil peak of substantial size. We will mainly be concerned with this type of geometry