The luminosity independent method [46] is the best way to
measure the total cross section using the FPD, since it does not require
very low |t| acceptance. This method combines the definition of the total
cross section (Eq. 11)
with the optical theorem
and the relation to obtain
where is the extrapolated number of elastic events,
is the number of inelastic events, B is the slope of the elastic |t|
distribution,
and
is the ratio of the real to imaginary
part of the elastic scattering amplitude.
In a low luminosity special run with extra beam scraping, it will be
possible to obtain a GeV
.
CDF and E710 are in very
good agreement for the elastic slope
in the region |t|<0.15 GeV
(
), with a virtually
identical central value yielding a world average measurement of
GeV
.
For a 50,000 event special run, the largest
error in the measurement should be about 1.5%
from the extrapolation to t=0.
The contribution of the
error
to the cross section is small, and the Level Ø counters will be
used to accurately measure
. The slope in the region
0.15<|t|<0.6 GeV
(
) is flatter than
,
and is measured to be
GeV
[46]. This
3% error could be reduced to about 0.5% during this run.
The elastic cross section is roughly 20 mb, and about 8%
of the events have |t|>0.15 GeV, giving an effective cross
section of 1.6 mb. Assuming a
acceptance of 20% and a
luminosity of
cm
gives a rate of 3 Hz.
A five hour run will thus give 50,000 elastic events.
Note that this will be a one-time run which could be done after
all of the properties of the
FPD are well-understood, and would consequently not require any
dedicated setup time.
With a data sample of 50,000 good elastic events
it should be possible to measure the total
cross section to an accuracy of about 2%.