GammaVision
®
v7 (A66-BW) 783620H / 1013
6.13. EBAR — Average Energy
The average energy calculation (EBAR) represents the sum of the average beta-gamma emission energy per disintegration for the identified radionuclides in the sample. The nuclides must be in the analysis library and the EBAR table (i.e., the
.EBR
file). The weighting factors of the activity of each isotope are usually defined by the plant chemistry procedures or can be calculated based on data found in radioactive-decay tabulations such as DOE/TIC-11026
35
or ORNL/NUREG/
TM-102.
36
The EBAR formula is:
(138)
where:
EBAR = the sum of the average beta and gamma energies in keV/disintegration
E i
A i n
= , the average energy/disintegration for an individual nuclide
= the activity for nuclide i
= the number of nuclides
The average energy for a given nuclide is the sum of the product of the energy of the gamma ray and the abundance of that ray, plus the product of the energies of the electrons (1/3 the maximum for beta decay), plus the abundance of that ray.
As an example, consider the decay scheme for
133
Xe–
133
Cs in Fig. 254.
The maximum beta energy is given as 346 keV, which gives 267 keV and 45 keV for the energies of the transitions to the 160 keV and 382 keV states in
133
Cs. In addition to beta-decay electrons, the internal conversion electrons must also be included. The K-conversion electron has an energy of 45 keV and an abundance of 54%; the L electron has an energy of 75 keV and an abundance of 7%.
35
DOE/TIC-11026, United States Department of Energy, Office of Scientific and Technical Information, Oak
Ridge, Tennessee.
36
Technical Manual TM-102, Nuclear Regulatory Commission Guide, Oak Ridge National Laboratory, Oak
Ridge, Tennessee.
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783620H / 1013 6. ANALYSIS METHODS
Fig. 254. Decay Scheme.
Thus, for the betas, the energy is:
346 × 0.993 × 1/3
+ 45 × 0.09
= 114.5
+ 267 × 0.007 × 1/3 =
+ 45 × 6.0×10
-5
× 1/3 =
+ 45 × 0.534
1.9
0
= 24.1
0.6
= 6.8
146.0
For the gamma rays, each gamma energy is multiplied by its abundance. In addition, the x-ray fluorescence from the internal conversion must also be included. For the two electrons (K and L), the x-ray energies are 36 keV and 6 keV, respectively. The same abundances as above are used.
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