Search for Oscillation of the Electron-Capture Decay Probability of $^{142}$Pm*

We have searched for time modulation of the electron capture decay probability of $^{142}$Pm in an attempt to confirm a claim from a group at the Gesellschaft f\"{u}r Schwerionenforschung (GSI) attributed to neutrino oscillation. We produced $^{142}$Pm via the $^{124}$Sn($^{23}$Na, 5n)$^{142}$Pm reaction at the Berkeley 88-Inch Cyclotron with a short bombardment time. Isotope selection by the Berkeley Gas-filled Separator is followed by implantation and a long period of monitoring the $^{142}$Nd K$_{\alpha}$ x-rays from the daughter. The decay time spectrum of the x-rays is well-described by a simple exponential and our measured half-life is consistent with the accepted value. We observed no decay rate oscillation at the frequency reported by Litvinov {\it et al.} (Phys.~Lett.~B {\bf 664}, 162 (2008)), and no oscillation terms at any frequency were statistically significant. A search for previous experiments that might have been sensitive to the reported modulation uncovered another example in $^{142}$Eu electron-capture decay. A reanalysis of the published data shows no decay rate oscillation.