New geometry for the quasi-binary incident electron-centre of mass collision in (e, 3e) process on He

We present in this paper the results of our calculation of five-fold differential cross sections (FDCS) in a new geometrical arrangement (constant theta-12-phi-12 mode) for the study of the quasi-binary incident electron-centre of mass collision in the (e, 3e) process on He in a better way. In this geometrical arrangement, we restrict the momentum of the centre of mass of the ejected electrons to lie in the scattering plane, defined by the momenta of the incident and scattered electrons, even though the momenta of the ejected electrons are not in the scattering plane. This geometrical mode has a greater potential to study the quasi-binary collision than the earlier study of FDCS (Choubisa et al 2003a Pramana J. Phys. 60 1187, 2003b J. Phys. B: At. Mol. Opt. Phys. 36 1731, Lahmam-Bennani et al 2002 J. Phys. B: At. Mol. Opt. Phys. 35 L215) in the coplanar constant theta-12 mode which has a limited application due to the restriction on the momenta of all the outgoing electrons to lie in the scattering plane whereas the new geometrical mode can be used for any direction of ejected electrons as long as the momentum of the centre of mass is in the scattering plane. We present our first and second Born results in the 3 C wave approach and compare our results with the available experimental data and the first Born CCC theory to check the consistency of our theoretical model and it is found to be satisfactory qualitatively. The results of our calculation of FDCS in the first as well as the second Born approximation on the He atom in the proposed geometrical mode reveal some interesting features about the quasi-binary incident electron-centre of mass collision, its dependence on the geometrical arrangement of the momenta of the ejected electrons as well as on the first-and the second-order projectile-target interaction. We are of the opinion that this geometrical arrangement may serve as a useful guideline for future (e, 3e) experimentations.