Raman selection rules for electronic and magnetic excitations in BaFe2As2 were theoretically investigated and applied them to the separate detection of the nodal and anti-nodal gap excitations at the spin density wave (SDW) transition and the separate detection of the nearest and the next nearest neighbor exchange interaction energies. The SDW gap has Dirac nodes, because many orbitals participate in the electronic states near the Fermi energy. Using a two-orbital band model the electronic excitations near the Dirac node and the anti-node are found to have different symmetries. Applying the symmetry difference to Raman scattering the nodal and anti-nodal electronic excitations are separately obtained. The low-energy spectra from the anti-nodal region have critical fluctuation just above TSDW and change into the gap structure by the first order transition at TSDW, while those from the nodal region gradually change into the SDW state. The selection rule for two-magnon scattering from the stripe spin structure was obtained. Applying it to the two-magnon Raman spectra it is found that the magnetic exchange interaction energies are not presented by the short-range superexchange model, but the second derivative of the total energy of the stripe spin structure with respect to the moment directions. The selection rule and the peak energy are expressed by the two-magnon scattering process in an insulator, but the large spectral weight above twice the maximum spin wave energy is difficult to explain by the decayed spin wave. It may be explained by the electronic scattering of itinerant carriers with the magnetic self-energy in the localized spin picture or the particle-hole excitation model in the itinerant spin picture. The magnetic scattering spectra are compared to the insulating and metallic cuprate superconductors whose spins are believed to be localized.
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