Annual Report 2009/2010 - JUWEL - Forschungszentrum Jülich

2
2 2
d0
R
ds
d0
dw
la(
)
d
i(
)
d0
(3)
where R is the drum radius, d s the mean thickness of the passive matrix and a parameter
calculated as following:
d pi
cos( i)
d ( )
0
i
(4).
The mean distance covered by the -ray in the passive matrix is given by:
l ( )
d ( )
d
s
i
0
2 2 2
d0
R d0
la(
)
dw
The mean distance covered by the -ray in the collimator (cylindrical) of the -ray detector is
given by:
l () 0
c for di(
) d
col
L
R
l col col
c(
)
for 2 di(
) d
col
1
where L col is the collimator length, R col the collimator radius and d col calculated as:
R
col
d 1
col
d
i(
)
L
(7).
col
2
The density of the active waste matrix a in a drum segment may be expressed as:
(6)
(5).
a
s
V
V
a
m
s
(8)
where m is the apparent drum waste density determined by weighing; s is the density of the
passive matrix and V and V a are the volumes of the drum segment and of the active matrix
seen by the collimated -ray detector, respectively. V is expressed for a cylindrical collimator
by:
V
2
R
2
2
2
R
d
3
d R
d
col
w 0
w
3 L
(9)
col
and V a by:
V
a
2 2
R
col
s w
s w
3 L
2
0
col
2 2
R
d d
3
d R d
d R d
d
2
The volume of the passive matrix V s is calculated as the difference between V and V a .
The above equations enable to simulate the angular dependent count rate distributions for
various point source configurations and different properties of the active and passive matrix
and a given counting geometry. For the localization of the ‘hot spots’ within a drum segment
and the determination of the gamma attenuation properties of the drum segment, the
simulated count rates Z () are fitted to the measured count rates T () using the following 2
minimization:
s
w
(10).
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