  We propose a simple approach to measure the energy of the few-eV isomeric
state in Th-229. To this end, U-229 nuclei are doped into VUV-transparent
crystals, where they undergo alpha decay into Th-229, and, with a probability
of 2%, populate the isomeric state. These Th-229m nuclei may decay into the
nuclear ground state under emission of the sought-after VUV gamma, whose
wavelength can be determined with a spectrometer. Based on measurements of the
optical transmission of U:CaF2 crystals in the VUV range, we expect a signal at
least 2 orders of magnitude larger compared to current schemes using
surface-implantation of recoil nuclei. The signal background is dominated by
Cherenkov radiation induced by beta decays of the thorium decay chain. We
estimate that, even if the isomer undergoes radiative de-excitation with a
probability of only 0.1%, the VUV gamma can be detected within a reasonable
measurement time.
