Energy of the 229^{229}Th nuclear clock transition

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

The concept of laser-based conversion electron Mössbauer spectroscopy for a precise energy determination of 229m^{229m}Th

$^{229}$Th is the only nucleus currently under investigation for the development of a nuclear optical clock (NOC) of ultra-high accuracy. The insufficient knowledge of the first nuclear excitation energy of $^{229}$Th has so far hindered direct nuclear laser spectroscopy of thorium ions and thus the development of a NOC. Here, a nuclear laser excitation scheme is detailed, which makes use of thorium atoms instead of ions. This concept, besides potentially leading to the first nuclear laser spectroscopy, would determine the isomeric energy to 40 $\mu$eV resolution, corresponding to 10 GHz, which is a $10^4$ times improvement compared to the current best energy constraint. This would determine the nuclear isomeric energy to a sufficient accuracy to allow for nuclear laser spectroscopy of individual thorium ions in a Paul trap and thus the development of a single-ion nuclear optical clock