We report the results of an experiment conducted near the High Flux Isotope Reactor of Oak Ridge National Laboratory, designed to address the question of whether a flux of reactor-generated electron antineutrinos can alter the rates of weak nuclear interaction-induced decays for Mn-54, Na-22, and Co-60. This experiment, while quite sensitive, cannot exclude perturbations less than one or two parts in $10^4$ in $beta$ decay (or electron capture) processes, in the presence of an antineutrino flux of $3times 10^{12}$ cm$^{-2}$ s$^{-1}$. The present experimental methods are applicable to a wide range of isotopes. Improved sensitivity in future experiments may be possible if we can understand and reduce the dominant systematic uncertainties.
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