  The first excited isomeric state of Th-229 has an exceptionally low energy of
only a few eV and could form the gateway to high-precision laser spectroscopy
of nuclei. The excitation energy of the isomeric state has been inferred from
precision gamma spectroscopy, but its uncertainty is still too large to
commence laser spectroscopy. Reducing this uncertainty is one of the most
pressing challenges in the field.
  Here we present an approach to infer the energy of the isomer from
spectroscopy of the electron which is emitted when the isomer de-excites
through internal conversion (IC). The experiment builds on U-233, which decays
to Th-229 and populates the isomeric state with a 2% fraction. A film of U-233
is covered by a stopping layer of few-nm thickness and placed between an alpha
detector and an electron detector, such that the alpha particle and the IC
electron can be detected in coincidence. Retarding field electrodes allow for
an energy measurement. In the present design, the signal of the Th-229m IC
electrons is masked by low-energy electrons emitted from the surface of the
metallic stopping layer. We perform reference measurements with U-232 and U-234
to study systematic effects, and we study various means to reduce the
background of low-energy electrons. Our study gives guidelines to the design of
an experiment that is capable of detecting the IC electrons and measuring the
isomer energy.
