  We successfully developed a new photomultiplier tube (PMT) with a three-inch
diameter, convex-shaped photocathode, R13111. Its prominent features include
good performance and ultra-low radioactivity. The convex-shaped photocathode
realized a large photon acceptance and good timing resolution. Low
radioactivity was achieved by three factors: (1) the glass material was
synthesized using low-radioactive-contamination material; (2) the photocathode
was produced with $^{39}$K-enriched potassium; and (3) the purest grade of
aluminum material was used for the vacuum seal. As a result each R13111 PMT
contains only about 0.4 mBq of $^{226}$Ra, less than 2 mBq of $^{238}$U, 0.3
mBq of $^{228}$Ra, 2 mBq of $^{40}$K and 0.2 mBq of $^{60}$Co. We also examined
and resolved the intrinsic leakage of Xe gas into PMTs that was observed in
several older models. We thus succeeded in developing a PMT that has low
background, large angular acceptance with high collection efficiency, good
timing resolution, and long-term stable operation. These features are highly
desirable for experiments searching for rare events beyond the standard model,
such as dark matter particle interactions and neutrinoless double beta decay
events.
