## Schematic diagram for the constant θ<sub>12</sub> mode in the coplanar geometry

2013-09-05T00:00:00Z (GMT) by
<p><strong>Figure 1.</strong> Schematic diagram for the constant θ<sub>12</sub> mode in the coplanar geometry. The angles of the ejected electrons are varied in such a manner that their mutual angle θ<sub>12</sub> = θ<sub>2</sub> − θ<sub>1</sub> is fixed. The FDCS is plotted as a function of the bisecting angle (i.e., θ) of θ<sub>12</sub> (i.e., θ = (θ<sub>1</sub> + θ<sub>2</sub>)/2). The scattered electron is detected at a fixed angle (θ<sub><em>s</em></sub> = −15° in the present paper). The bisecting angle will point in the direction of the collective momentum of the ejected electrons (i.e., \vec{K_c}=\vec{k_1}+\vec{k_2}) when <em>E</em><sub>1</sub> = <em>E</em><sub>2</sub>. The arrows over the \vec{k_1} and \vec{k_2} show the rotating direction of \vec{k_1} and \vec{k_2} in the scattering plane. The arrow over the hypothetical momentum \vec{K_c}, which is not related to any participating electron in the (<em>e</em>, 3<em>e</em>) process, is just for figurative purpose to remind us that the vector \vec{K_c} is also rotating in the scattering plane.</p> <p><strong>Abstract</strong></p> <p>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 θ<sub>1</sub> = θ<sub><em>q</em></sub> and θ<sub>2</sub> = θ<sub><em>q</em></sub> − 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.</p>