Use of the Known-M Method for NDA of Plutonium Scrap Page: 3 of 10
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po = fD vs2 / (2 vs1),
K = vi2vsi / [vs2 (vsi - 1) ] ~ 2.17,
e is the neutron counter efficiency,
fD is the doubles gate fraction, and
vij, vsj are the jth moments of the induced and
spontaneous fission neutron multiplicities, respectively.
(m240)eff= S / [473.5 E vsi M ( c + 1)] (3)
For any neutron-based measurement, the isotopic composition of the items to be assayed must be
known. In this case, the equations are given in terms of the effective 239Pu and 24OPu masses to more
accurately account for induced fission (equation (4) below) and spontaneous fission (equation (5)
below) effects. These are generally defined as follows':
(m239)eff = mN [ f239 + 0.786 f238 + 0.515 f24o + 1.414 f24~ + 0.545 fAm241 ] (4)
(m240)eff = mN [ 2.52 f238 + f24o + 1.68 f24 ] (5)
where mNu is the calculated plutonium elemental mass, and
fn is the isotopic mass fraction of "u or 241Am.
Except for equation (1), the above equations are the same as the equations for a neutron multiplicity
calculations. For a multiplicity calculation, the first equation is a cubic equation in the parameters used
above in equations (2) and (3), plus the Triples count rate and Triples gate fraction. The cubic equation
is solved for M, and then in succession equations (2) and (3) are solved, and, using the known isotopic
fractions, the plutonium mass is thereby obtained. But neutron multiplicity counting was not suitable
for SS&C material and the available neutron counter. First, the SS&C material produces a large number
of (a, n) neutrons, manifest in a relatively large value of a, ranging from about 5 to about 35. (The two
uses of a here may be momentarily confusing: (a, n) refers to interactions of a-particles emitted from
plutonium and other radioisotopes with low-A nuclei, and symbol a defined in equation (2) is the ratio
of the number of (a, n) neutrons to the number of spontaneous fission neutrons.) Material generally
assayed by multiplicity counting has a ~ 1. Second, the efficiency for counting Triples events is E3, and
the relatively low efficiency of the available neutron counter ( e ~17% ) makes counting Triples very
inefficient. As a result of these two conditions (large a and small e), a multiplicity measurement using
the available neutron counter requires count times of 12 hours or more to obtain satisfactory statistical
accuracy.
The Known-M method is applicable if the material to be assayed is consistent enough in composition
and geometry to allow expression of the multiplication M as in equation (1). The Triples count rate and
its uncertainty are not needed. In this case, the plutonium mass, the result of the overall calculation, is
needed in equation (1), the very start of the calculation. In fact, the Known-M equations must be solved
by iteration. Fortunately, the convergence behavior of the series of equations is such that the iteration
function of the Microsoft Excel TM spreadsheet can be used. To avoid the divergence that occurred in
many cases, an algorithm to "encourage" convergence was devised, and the cell formula for that
purpose is discussed below.
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Thompson, R.S. Use of the Known-M Method for NDA of Plutonium Scrap, article, July 22, 1999; South Carolina. (https://digital.library.unt.edu/ark:/67531/metadc793604/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.