Particles entering the detector far from the vertex have
incident angles nearly parallel (
7
)
to the surface of the vertex
detector. Consequently, a single particle
will pass through many strips if the strips are oriented perpendicular to the
beam axis. The number of hit strips
as a function of z is
,
where z is the distance from the vertex and R is the radius of the barrel. At
the ends of the detector, about 25 strips are
hit in the inner barrel, for
discriminator thresholds at
, as in E789 at Fermilab6. This threshold represents
the highest threshold for full efficiency for normally incident
particles;
Landau fluctuations allow the energy loss in 300
of Si to be as small
as 1/2 of the average energy loss. If this signal is split equally between
two strips, then the signal in each will be 1/4 of the mean.
Particles incident nearly parallel to the
surface would give about 1/3 of the signal (
) expected
from a particle at normal incidence (
).
So all 25 strips could register hits, drastically increasing the apparent
occupancy. Realistically,
considering Landau fluctuations in the energy loss in a thin layer, a threshold
at , compared to a signal of about 
would
probably give some strips which would be "on" and some which would be
"off". This situation would make accurate measurements of the
multiplicity and 
extremely difficult.
One solution to this problem is to turn the strips parallel to the beam
direction. In this case, a particle at a nearly parallel incidence angle would
give a large signal (
), essentially all in one
strip. This eases the measurements of and
multiplicity, but increases the dynamic range needed in the electronics.