PLUTONIUM ISOTOPIC ANALYSIS WITH FRAM V4 IN THE LOW ENERGY REGION. Page: 4 of 10
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A. New Relative Efficiency Curve Option
All versions 3.x and earlier FRANM used an empirical relative efficiency curve first proposed by
Fleissner. [2]
ln(Area/BR) = c, + c,/E, + c3(InE) + c4(InE)2 + c5(lnE)3 + c, + c;/E,
where E is the energy in MeV; ci is associated with additional isotopes beyond the first one, and
each c; is associated with an efficiency function beyond the first one.
This empirical relative-efficiency curve has been very successful for many measurement
situations. However, its empirical nature and polynomial structure make it behave unphysically in
some situations, notably when extrapolated outside its range of definition or when used with very
weak data.
In FRAM v4, we added new efficiency curve formalism based on the physical properties of the
analyzed material and surrounding materials. The new efficiency curve is constructed as
Area/BR ] * [e 11 e~2.2 e-3 *[I* [ec / E] * [Det eff] * [Correction factor]
PPu xPu
where the term inside the first square bracket associates with the U/Pu attenuation; the term inside
the second square bracket associates with the attenuation due to the absorbers (up to three
different absorbers can be used); Ii is associated with the activity of the isotope i; c associates
with an efficiency function beyond the first one; "Det eff' is a generic detector efficiency
parameterized in the software; and "Correction factor" is to correct for the detector efficiency and
the attenuation of the measured materials and the absorbers.
This formula is very much the same as the one in the widely used MGA. (The MGA code was the
first to use a physics-based model for the relative efficiency). The factor that makes this different
from the MGA is the "correction factor," where in the MGA is expressed as a quadratic (1 + bE +
cE2). In our formula we use the modified Hoerl formula (El * c"/) where E is the peak energy and
b and c are some variables.
The advantage of using the Hoerl equation for the correction factor is that all the individual
deviations can be corrected and all those corrections can be combined together and still retain the
Hoerl form
(EbcIVE) (Eb c/ E)= F(+b')(cic 1/E = Ebc/,
where the leftmost side of the equation shows the individual corrections (such as detector
efficiency and self-attenuation in the solution, etc.), and the rightmost side of the equation shows
the combined correction where3
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Vo, Duc T. & Li, T. K. (Tien K.). PLUTONIUM ISOTOPIC ANALYSIS WITH FRAM V4 IN THE LOW ENERGY REGION., article, January 1, 2001; United States. (https://digital.library.unt.edu/ark:/67531/metadc932526/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.