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The DEAP-1 low-background liquid argon detector was used to measurescintillation pulse shapes of electron and nuclear recoil events and todemonstrate the feasibility of pulse-shape discrimination (PSD) down to anelectron-equivalent energy of 20 keV.  In the surface dataset using a triple-coincidence tag we found the fractionof beta events that are misidentified as nuclear recoils to be $<1.4\times10^{-7}$ (90% C.L.) for energies between 43-86 keVee and for a nuclear recoilacceptance of at least 90%, with 4% systematic uncertainty on the absoluteenergy scale. The discrimination measurement on surface was limited by nuclearrecoils induced by cosmic-ray generated neutrons. This was improved by movingthe detector to the SNOLAB underground laboratory, where the reduced backgroundrate allowed the same measurement with only a double-coincidence tag.  The combined data set contains $1.23\times10^8$ events. One of those, in theunderground data set, is in the nuclear-recoil region of interest. Taking intoaccount the expected background of 0.48 events coming from random pileup, theresulting upper limit on the electronic recoil contamination is$<2.7\times10^{-8}$ (90% C.L.) between 44-89 keVee and for a nuclear recoilacceptance of at least 90%, with 6% systematic uncertainty on the absoluteenergy scale.  We developed a general mathematical framework to describe PSD parameterdistributions and used it to build an analytical model of the distributionsobserved in DEAP-1. Using this model, we project a misidentification fractionof approx. $10^{-10}$ for an electron-equivalent energy threshold of 15 keV fora detector with 8 PE/keVee light yield. This reduction enables a search forspin-independent scattering of WIMPs from 1000 kg of liquid argon with aWIMP-nucleon cross-section sensitivity of $10^{-46}$ cm$^2$, assumingnegligible contribution from nuclear recoil backgrounds.

Measurement of the scintillation time spectra and pulse-shape discrimination of low-energy beta and nuclear recoils in liquid argon with DEAP-1