  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.
