  We derive Feynman rules for the interactions of a single gravitino with
(s)quarks and gluons/gluinos from an effective supergravity Lagrangian in
non-derivative form and use them to calculate the hadroproduction cross
sections and decay widths of single gravitinos. We confirm the results obtained
previously with a derivative Lagrangian as well as those obtained with the
non-derivative Lagrangian in the high-energy limit and elaborate on the
connection between gauge independence and the presence of quartic vertices. We
perform extensive numerical studies of branching ratios, total cross sections,
and transverse-momentum spectra at the Tevatron and the LHC. From the latest
CDF monojet cross section limit, we derive a new and robust exclusion contour
in the gravitino-squark/gluino mass plane, implying that gravitinos with masses
below $2\cdot10^{-5}$ to $1\cdot10^{-5}$ eV are excluded for
squark/gluino-masses below 200 and 500 GeV, respectively. These limits are
complementary to the one obtained by the CDF collaboration, $1.1\cdot 10^{-5}$
eV, under the assumption of infinitely heavy squarks and gluinos. For the LHC,
we conclude that SUSY scenarios with light gravitinos will lead to a striking
monojet signal very quickly after its startup.
