Understanding internal backgrounds of NaI(Tl) crystals toward a 200~kg
  array for the KIMS-NaI experiment
  The Korea Invisible Mass Search (KIMS) collaboration has developed
low-background NaI(Tl) crystals that are suitable for the direct detection of
WIMP dark matter. With experience built on the KIMS-CsI programs, the KIMS-NaI
experiment will consist of a 200~kg NaI(Tl) crystal array surrounded by layers
of shielding structures and will be operated at the Yangyang underground
laboratory. The goal is to provide an unambiguous test of the DAMA/LIBRA's
annual modulation signature. Measurements of six prototype crystals show
progress in the reduction of internal contaminations of radioisotopes. Based on
our understanding of these measurements, we expect to achieve a background
level in the final detector configuration that is less than 1~count/day/keV/kg
for recoil energies around 2~keV. The annual modulation sensitivity for the
KIMS-NaI experiment shows that an unambiguous 7$\sigma$ test of the DAMA/LIBRA
signature would be possible with a 600~kg$\cdot$year exposure with this system.
