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Abstract

The first nuclear excited state of $^{229}$Th offers the unique opportunity
for laser-based optical control of a nucleus. Its exceptional properties allow
for the development of a nuclear optical clock which offers a complementary
technology and is expected to outperform current electronic-shell based atomic
clocks. The development of a nuclear clock was so far impeded by an imprecise
knowledge of the energy of the $^{229}$Th nuclear excited state. In this letter
we report a direct excitation energy measurement of this elusive state and
constrain this to 8.28$\pm$0.17 eV. The energy is determined by spectroscopy of
the internal conversion electrons emitted in-flight during the decay of the
excited nucleus in neutral $^{229}$Th atoms. The nuclear excitation energy is
measured via the valence electronic shell, thereby merging the fields of
nuclear- and atomic physics to advance precision metrology. The transition
energy between ground and excited state corresponds to a wavelength of
149.7$\pm$3.1 nm. These findings set the starting point for high-resolution
nuclear laser spectroscopy and thus the development of a nuclear optical clock
of unprecedented accuracy. A nuclear clock is expected to have a large variety
of applications, ranging from relativistic geodesy over dark matter research to
the observation of potential temporal variation of fundamental constants.