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.
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