Journal of the Physical Society of Japan FULL PAPERSRaman selection rules for electronic and magnetic excitations in BaFe 2 As 2 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.Raman spectra are composed of magnetic excitations with gradually decreasing intensity toward far above the SDW transition temperature (T SDW ) and electronic excitations induced by the Brillouin zone folding below T SDW . The SDW gap has Dirac nodes, be- and change into the gap structure by the first order transition at T SDW , while those from the nodal region gradually change into the SDW state. Magnetic excitations are observed as a very broad peak in all polarization configurations. 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.