Segment Angles of the GSI-Clover Detector
A.) Transformation of a polar coordinate system from the target
position to a flat detector
Figure: Left: polar coordinate system in target or source position
(y-axis points out of plane); center: coordinate system moved in detector
position (d=distance between detector and target, 
);
right: coordinate system rotated around the y-axis ( )
to measure events from the target.
1.) Polar coordinate system with its origin in target position
(y-axis points upwards)
2.) The origin of the coordinate system is shifted to detector surface
(d = distance from detector surface to target position,
-angle is negative for the displayed example in fig.1)
3.) The coordinate system is rotated around y-axis
( -angle is negative for the displayed example in fig.1)
Boundary condition: z'' = 0 for flat detector surface
One obtains the following relation for a point (x'',y'') on the detector
surface and the polar angle 
and azimuthal angle 
:
B.) Calculation of the GSI-clover segment angles
The GSI-clover detector has 16 position segments which are displayed in Fig.2.
Figure: The centriods (x'',y'') of the 16 position segments of the
GSI-clover detector are given in cm. The central contacts are black and
blue (upper half from left to right) and green and red (lower half from
left to right).
Table: Polar- ( ) and azimuthal ( ) angles of
the GSI-clover segments for 
and d=11.4 cm
Table: Polar ( ) angles of the GSI-clover segments
for different central contacts ( , d=11.4 cm)
Table: Azimuthal ( ) angles of the GSI-clover segments
for different central contacts ( , d=11.4 cm)
Figure: The centriods 
of the 16 position segments
of the GSI-clover detector in degree ( , d=11.4 cm).
The central contacts are black and
blue (upper half from left to right) and green and red (lower half from
left to right).
Table: Polar- ( ) and azimuthal ( ) angles of
the GSI-clover segments for and d=11.4 cm
Table: Polar ( ) angles of the GSI-clover segments
for different central contacts ( , d=11.4 cm)
Table: Azimuthal ( ) angles of the GSI-clover segments
for different central contacts ( , d=11.4 cm)
Figure: The centriods of the 16 position segments
of the GSI-clover detector in degree ( , d=11.4 cm).
The central contacts are black and
blue (upper half from left to right) and green and red (lower half from
left to right).