On the relativistic electron impact K-shell (e, (3-1)e) differential cross sections for atoms

In this paper, we present the results of our calculation of four-fold differential cross section (4DCS) for the K-shell electron impact double ionization (DI) on various atoms in the relativistic energy regime. The 4DCS is computed from the five-fold differential cross sections (5DCS) by integrating 5DCS over either the angles of one of the ejected electrons or the scattered electron (this process is referred as an (e, (3-1)e) process). Hence, it requires, possibly feasible double coincidence techniques to supplement our findings experimentally instead of the difficult triple coincidence technique, which is required for the complete description of the DI process. The angular profile of 5DCS is scanned with the angles of one of the ejected electrons for both the (e, (3-1)e) cases. A dominant peak in the momentum transfer direction is found when the scattered and one of the ejected electrons are detected in coincidence. The effects of nucleus (Z), energies of the ejected electrons, and the scattering angle on the 4DCS have been discussed. The angular correlation of the ejected electrons has also been discussed when only the ejected electrons are detected. We consider the spin aspects by scanning the singlet and triplet contributions in the angular profile of 4DCS. We also find that the interference term of the longitudinal and transverse interaction is responsible for the strengthening of the secondary peak. We observe a clear manifestation of the effect of nucleus on the spin asymmetry for behavior targets.