Scintillation and ionisation yields for nuclear recoils in liquid xenon above 10 keVnr (nuclear recoil energy) are deduced from data acquired using broadband Am-Be neutron sources. The nuclear recoil data from several exposures to two sources were compared to detailed simulations. Energy-dependent scintillation and ionisation yields giving acceptable fits to the data were derived. Efficiency and resolution effects are treated using a light collection Monte Carlo, measured photomultiplier response profiles and hardware trigger studies. A gradual fall in scintillation yield below ~40 keVnr is found, together with a rising ionisation yield; both are in good agreement with the latest independent measurements. The analysis method is applied to both the most recent ZEPLIN-III data, acquired with a significantly upgraded detector and a precision-calibrated Am-Be source, as well as to the earlier data from the first run in 2008. A new method for deriving the recoil scintillation yield, which includes sub-threshold S1 events, is also presented which confirms the main analysis.
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