## FDCS in *mb*/*sr*^{3}(keV)^{2} for the singlet (*S*, refer to equation (4)), triplet 1 (*T*1, refer to equation (5)) and triplet 2 (*T*2, refer to equations (6) and (7)) contributions are plotted as a function of the bisecting angle θ (in degrees) of the ejected electrons for the Ca atom for (a) 30°, (b) 90°, (c) 120° and (d) 180°

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**Figure 2.** FDCS in *mb*/*sr*^{3}(keV)^{2} for the singlet (*S*, refer to equation (4)), triplet 1 (*T*1, refer to equation (5)) and triplet 2 (*T*2, refer to equations (6) and (7)) contributions are plotted as a function of the bisecting angle θ (in degrees) of the ejected electrons for the Ca atom for (a) 30°, (b) 90°, (c) 120° and (d) 180°. The kinematics used here are *E _{i}* = 540 keV, fixed scattering angle (θ

_{s}) = −15°,

*E*

_{1}=

*E*

_{2}= 16.1 keV. The energy of the scattered electron can be found from the energy conservation. Dotted, dashed and dash–dotted curves represent the

*S*,

*T*1 and

*T*2 contributions of FDCS respectively. The arrow in each frame indicates the momentum transfer direction.

**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 θ_{1} = θ_{q} and θ_{2} = θ_{q} − 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.