Isolated photons with high transverse energy have been studied in deep inelastic ep scattering with the ZEUS detector at HERA, using an integrated luminosity of 326 pb−1 in the range of exchanged-photon virtuality 10-350 GeV2. Outgoing isolated photons with transverse energy 4 ≺ E T γ ≺ 15 GeV and pseudorapidity − 0.7 ≺ η γ ≺ 0.9 were measured with accompanying jets having transverse energy and pseudorapidity 2.5≺ E T jet ≺ 35 GeV and −1.5 ≺ ηjet ≺ 1.8, respectively. Differential cross sections are presented for the following variables: the fraction of the incoming photon energy and momentum that is transferred to the outgoing photon and the leading jet; the fraction of the incoming proton energy transferred to the photon and leading jet; the differences in azimuthal angle and pseudorapidity between the outgoing photon and the leading jet and between the outgoing photon and the scattered electron. Comparisons are made with theoretical predictions: a leading-logarithm Monte Carlo simulation, a next-to-leading-order QCD prediction, and a prediction using the k T -factorisation approach
