Development of low radioactivity photomultiplier tubes for the XMASS-I
  detector
  XMASS-I is a single-phase liquid xenon detector whose purpose is direct
detection of dark matter. To achieve the low background requirements necessary
in the detector, a new model of photomultiplier tubes (PMTs), R10789, with a
hexagonal window was developed based on the R8778 PMT used in the XMASS
prototype detector. We screened the numerous component materials for their
radioactivity. During development, the largest contributions to the reduction
of radioactivity came from the stem and the dynode support. The glass stem was
exchanged to the Kovar alloy one and the ceramic support were changed to the
quartz one. R10789 is the first model of Hamamatsu Photonics K. K. that adopted
these materials for low background purposes and provided a groundbreaking step
for further reductions of radioactivity in PMTs. Measurements with germanium
detectors showed 1.2$\pm$0.3 mBq/PMT of $^{226}$Ra, less than 0.78 mBq/PMT of
$^{228}$Ra, 9.1$\pm$2.2 mBq/PMT of $^{40}$K, and 2.8$\pm$0.2 mBq/PMT of
$^{60}$Co. In this paper, the radioactive details of the developed R10789 are
described together with our screening methods and the components of the PMT.
