A detailed study of inelastic x-ray scattering from the ground state to the 3 AE g ð3 À1 g 3s 1 g Þ state of the O 2 molecule is presented. The observed angular anisotropy shows that the vibrational excitations within this final state are strongly dependent on the polarization of the incident radiation. The analysis demonstrates that this is a manifestation of interference between resonant and direct nonresonant inelastic x-ray scattering. This interference provides a new tool to monitor nuclear dynamics by relative rotation of the polarization vectors of the incident and scattered photons. DOI: 10.1103/PhysRevLett.110.223001 PACS numbers: 33.20.Rm, 32.80.Aa, 33.20.Fb, 33.80.Gj The nonresonant scattering channel has so far been neglected when considering resonant inelastic scattering (RIXS) in the sub-keV range. On the other hand, the direct nonresonant (Thomson) scattering channel significantly contributes to resonant elastic scattering [1][2][3][4][5]. Nonresonant inelastic x-ray scattering (NIXS) is prominent in the hard x-ray range, and is exploited in well-established materials science methods [6][7][8][9]. To the best of our knowledge, however, a demonstration of the influence of the nonresonant channel on resonant inelastic scattering phenomena is lacking also for hard x rays.Here we show that NIXS influences scattering deep in the soft x-ray range, in the spectrum of the O 2 molecule excited at the 1s ! Ã resonance [10][11][12]. NIXS interference with the RIXS channel is reflected in the polarization dependence of vibrational excitations within a welldefined electronic final state. This phenomenology is an indication of NIXS-RIXS interference because the NIXS and RIXS channels have different polarization dependence and induce different nuclear dynamics. The observed angular anisotropy is pronounced, demonstrating that NIXS-RIXS interference is important in this case and suggesting that NIXS should be considered when analyzing state-ofthe-art resonant x-ray scattering spectra in general.The observed polarization dependence of the vibrational excitations is a consequence of NIXS-RIXS interference and does not indicate that the Born-Oppenheimer approximation is violated. In spite of the formal analogy with the interference between the resonant channel and the channel of nonresonant direct ionization in resonant Auger scattering, there is a qualitative difference between the two processes. The interference between the resonant channel and the channel of direct ionization is a typical non-BornOppenheimer effect [13][14][15][16]. Here the final state wave function cannot be written as a product of electronic and nuclear wave functions due to the mixing between the degenerate autoionizing core-excited state and the continuum state in which it is embedded. The picture is qualitatively different for x-ray Raman scattering where the energy spacing between the final and the core-excited state is very large (% 524 eV). In the absence of external fields, the nuclear motion in the gerade final state is independent...