On the spin interplay of the ejected electrons in the relativistic electron impact K-shell double ionization of atoms

Abstract

A detailed analysis on the spin aspects of the ejected electrons is presented for the electron impact K-shell double ionization of Ca, Mo and Xe atoms. The five-fold differential cross sections have been seperated in terms of singlet–singlet and singlet–triplet transitions during the double ionization of the K-shell electrons of atoms. This type of study has led us to unravel the interesting spin interplay of the ejected electrons and their higher degree of dependence with their kinematical arrangements in the continuum state. Various geometrical arrangements are identified wherein the important relative contributions of the singlet and triplet terms are found. The singlet contribution for the back-to-back emission of the ejected electrons is found to be smaller for the Ca atom, however, on the other hand, it becomes the dominating term for the Xe atom and is isotropic in nature. We also observe that the parallel spin orientation of the ejected electrons is more favourable for the perpendicular emission of the ejected electrons (i.e., when θ1 = θq and θ2 = θq − 90°) and it remains the dominant term regardless of the energy sharing ratio of the ejected electrons. All of the singlet and triplet transitions depend on the emission direction of the ejected electrons as well as on their energies.

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

“…There are two-fold advantages for the experimentalist; the first one is the double coincidence detection of the electrons, and the other one is the larger coincidence rates for the coincidence detection. Recently, we have calculated 5DCS and spin asymmetry in 5DCS for various atoms for the (e, 3e) processes in the relativistic energy regime [13,14]. We found that the absolute value of 5DCS is very small, which, prima facie, seems to hinder its further development in the very near future, especially in the experimental side.…”

“…As explained in [13,14], we describe the ejected electrons wave function (ψ r r ( , ) f 1 2 ) by the 2-Coulomb wave function with Gamow factor, multiplied by the 4-components Dirac spinors. The antisymmetrization of the ejected electrons is done by considering the singlet and triplet states as discussed in our earlier papers [13,14]. We will not write their explicit forms here.…”

“…In addition to this, as mentioned earlier, we have a larger coincidence differential cross section (here, four-fold differential cross section (4DCS)) as compared to the 5DCS of the (e, 3e) process. The purpose of this paper is to calculate 4DCS from the 5DCS calculated from our previous theoretical formalism [13,14]. We present 4DCS for various atoms for two cases: one in which one of the ejected electrons is not detected and the other one in which the scattered electron is not detected (see figure 1).…”

Double ionization of helium by twisted electron beam

“…where, b is the vector that describes the transverse orientation of the incident twsited electron beam with repect to the He atom [35] beam contary to the plane wave [32]. We can get equation ( 16) by just substituting b = 0 in equation (22). As we did for b = 0 case to get the T tw fi (refer to equation ( 21)), we can get the twisted wave transition amplitude T tw fi in terms of plane wave transition amplitude as;…”

“…Since then, the differential cross-section calculations were performed for many atomic targets in the non-relativistic energy regime, like for He [14][15][16][17][18], lithium [19], noble gases like Ne, Ar, Kr and Xe [20]. Further, there have been a few (e,3e) studies in literature reported for the relativistic energy regime [21,22]. To the best of our knowledge, the collision studies in the (e,3e) process have been done for the plane wave incident electron case (not possessing any orbital angular momentum).…”