  The pairing mechanism and gap structure in Ba122 pnictides have been hotly
discussed for long time as one of the central issues in Fe-based
superconductors. Here, we attack this problem by taking account of the vertex
corrections (VCs) for the Coulomb interaction $U$ ($U$-VCs), which are totally
dropped in conventional Migdal-Eliashberg formalism. The $U$-VC in the charge
susceptibility induces strong orbital fluctuations, and the $U$-VC also
enlarges the orbital-fluctuation-mediated attractive interaction. By analyzing
the effective multiorbital Hubbard model for Ba122 pnictides, we find that the
orbital fluctuations develop in all four $d$-orbitals ($t_{2g}$- and
$z^2$-orbitals), by which the FSs are composed. For this reason, nearly
isotropic gap function appears on all the hole-type FSs, including the outer
hole-FS around Z-point composed of $z^2$-orbital. In contrast, nodal gap
structure appears on the electron-type FSs for wide parameter range. The
obtained nodal $s$-wave state changes to fully-gapped $s$-wave state without
sign-reversal ($s_{++}$-wave state) by introducing small amount of impurities,
accompanied by small reduction in $T_c$. The present microscopic theory
naturally explains the important characteristics of the gap structure of both
hole- and electron-FSs in Ba122 pnictides, without introducing any
phenomenological pairing interaction.
