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