Specificity of exchange and correlation in elastic electron scattering off semifilled shell atoms

Atoms with multielectron semifilled shells in their ground states possess the highest spin multiplicity among other atoms. The current understanding of electron scattering off such atoms is rudimentary. Choosing e$^{-}+$Mn($3d^{5}$$4s^{2}$, $^{6}S$) elastic scattering as a case study, we scrutinize scattering phase shifts, partial, and total scattering cross sections versus the energy and spin polarization of a scattered electron. A drastic dependence of a correlation impact on electron scattering versus the spin-orientation of a scattered electron is unraveled. This, in turn, is found to be due to a specific impact of exchange interaction on correlation in the e$^{-}+$ atom system. The findings are argued to be inherent features of electron scattering off any multielectron semifilled shell atom. They result in significant differences between scattering of oppositely spin-polarized electrons off the atom. In particular, the existence of a narrow resonant maximum in the total scattering cross section of spin-down electrons near $\epsilon \approx 8$ eV but the absence of such in the cross section of spin-up electrons elastically scattered off the Mn atom is predicted. A ``spin-polarized'' Hartree-Fock approximation in combination with the Dyson equation for the self-energy part of the Green function of a scattered electron are employed in the study.