We have carried out a search for neon and argon isotopes produced in ternary fission of $^{235}\mathrm{U}$, using high-sensitivity mass spectrometry. The following upper limits - expressed in atoms per binary fission - were obtained: $^{20}\mathrm{Ne}$ 5.8 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}8}$, $^{21}\mathrm{Ne}$ 3.4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$, $^{22}\mathrm{Ne}$ 5.9 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$, $^{36}\mathrm{Ar}$ 2.4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$, $^{37}\mathrm{Ar}$ 2.2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$, $^{38}\mathrm{Ar}$ 2.0 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$, $^{39}\mathrm{Ar}$ 7.8 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$, $^{40}\mathrm{Ar}$ 6.9 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$, $^{42}\mathrm{Ar}$ 2.2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$. Except in the case of $^{40}\mathrm{Ar}$, these limits are lower by 1 to 4 orders of magnitude than indicated from results of triple-coincidence experiments carried out by previous workers. Assuming unique formation of $^{40}\mathrm{Ar}$, the upper limit for this nuclide is a factor of 5 lower than the triple-coincidence frequency.
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