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.