  We have developed an accurate simulation model of the large 9 inch
photomultiplier tubes (PMT) used in water-Cherenkov detectors of cosmic-ray
induced extensive air-showers. This work was carried out as part of the
development of the Offline simulation software for the Pierre Auger Observatory
surface array, but our findings may be relevant also for other astrophysics
experiments that employ similar large PMTs.
  The implementation is realistic in terms of geometrical dimensions, optical
processes at various surfaces, thin-film treatment of the photocathode, and
photon reflections on the inner structure of the PMT. With the quantum
efficiency obtained for this advanced model we have calibrated a much simpler
and a more rudimentary model of the PMT which is more practical for massive
simulation productions. We show that the quantum efficiency declared by
manufactures of the PMTs is usually determined under conditions substantially
different from those relevant for the particular experiment and thus requires
careful (re)interpretation when applied to the experimental data or when used
in simulations. In principle, the effective quantum efficiency could vary
depending on the optical characteristics of individual events.
