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Resonant elastic soft x-ray scattering in oxygen-ordered YBa_2Cu_3O_{6+delta}

Static charge-density wave (CDW) and spin-density wave (SDW) order has been convincingly observed in La-based cuprates for some time. However, more recently it has been suggested by quantum oscillation, transport and thermodynamic measurements that density wave order is generic to underdoped cuprates and plays a significant role in YBa_2Cu_3O_{6+delta} (YBCO). We use resonant soft x-ray scattering at the Cu L and O K edges to search for evidence of density wave order in Ortho-II and Ortho-VIII oxygen-ordered YBCO. We report a null result -- no evidence for static CDW order -- in both Ortho-II and Ortho-VIII ordered YBCO. While this does not rule out static CDW order in the CuO_2 planes of YBCO, these measurements place limits on the parameter space (temperature, magnetic field, scattering vector) in which static CDW order may exist. In addition, we present a detailed analysis of the energy and polarization dependence of the Ortho-II superstructure Bragg reflection [0.5 0 0] at the Cu L edge. The intensity of this peak, which is due to the valence modulations of Cu in the chain layer, is compared with calculations using atomic scattering form factors deduced from x-ray absorption measurements. The calculated energy and polarization dependence of the scattering intensity is shown to agree very well with the measurement, validating the approach and providing a framework for analyzing future resonant soft x-ray scattering measurements.