The Bielefeld-Brookhaven collaboration began in 1989 and was originall
y scheduled for a duration of three and then six years and has recentl
y been extended for about one more year. It will end in 1996 for reaso
ns of manpower and funding. The goal of this collaboration was to meas
ure integral and differential e(+)-H cross sections by employing the h
igh-intensity positron beam (HIP) of the Brookhaven National Laborator
y, anticipated to provide an electrostatically guided beam of 10(9) mo
derated positrons s(-1). This goal has not yet been reached. Over all
these years, the HIP operation has been suffering from a variety of te
chnical difficulties, despite the great efforts of all parties involve
d. Nevertheless, since the HIP situation is improving, we will continu
e this collaboration and try to reach the goal within the remaining ti
me. Our experimental results obtained with low-current positron beams
thus far are discussed together with related experimental and theoreti
cal work of other groups. Particular attention is given to open questi
ons. The present experimental setup at the Brookhaven National Laborat
ory is described in detail. The planned measurements are outlined in o
rder of their priority.