We present XMM-Newton imaging spectroscopy of ten weak emission-line quasars (WLQs) at $0.928leq z leq 3.767$, six of which are radio quiet and four which are radio intermediate. The new X-ray data enabled us to measure the power-law photon index, at rest-frame energies $>2$ keV, in each source with relatively high accuracy. These measurements allowed us to confirm previous reports that WLQs have steeper X-ray spectra, suggesting higher accretion rates with respect to typical quasars. A comparison between the photon indices of our radio-quiet WLQs and those of a control sample of 85 sources shows that the first are significantly higher, at the >~$3sigma$ level. Collectively, the four radio-intermediate WLQs have lower photon indices with respect to the six radio-quiet WLQs, as may be expected if the spectra of the first group are contaminated by X-ray emission from a jet. Therefore, in the absence of significant jet emission along our line of sight, these results are in agreement with the idea that WLQs constitute the extreme high end of the accretion rate distribution in quasars. We detect soft excess emission in our lowest-redshift radio-quiet WLQ, in agreement with previous findings suggesting that the prominence of this feature is associated with a high accretion rate. We have not detected signatures of Compton reflection, Fe K$alpha$ lines, or strong variability between two X-ray epochs in any of our WLQs, which can be attributed to their relatively high luminosity.
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