  We theoretically study the positron elastic scattering by an atom with a
multielectron semifilled subshell in its structure. The positron scattering by
the Mn($...3d^{5}4s^{2}$,$^{6}S)$ atom with a $3d^{5}$ semifilled subshell
($e^{+}+Mn$ scattering) is chosen as a case study. We account for both the
electron correlation and the formation of a $e^{+}+e^{-}$ virtual positronium
(Ps) in the intermediate states of the $e^{+}+Mn$ system. Electron correlation
is taken into account in the framework of the self-energy part of the
scattering positron Green function generalized for the application to
semifilled-shell atoms. The influence of the virtual Ps formation on $e^{+}+Mn$
scattering is taken into account by the reduction of the energy of the virtual
\textit{positron plus atomic-excited-configuration} states by the Ps-binding
energy, to a reasonable approximation. We unravel the importance and
specificity of the influence of both the virtual Ps and electron correlation on
$e^{+}+Mn$ elastic scattering. We demonstrate spectacular differences between
the electron and positron scattering processes.
