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Register a new userEnergy of the $^{229}$Th Nuclear Clock Isomer Determined by Absolute $gamma$-ray Energy Difference
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The low-lying isomeric state of $^{229}$Th provides unique opportunities for high-resolution laser spectroscopy of the atomic nucleus. We determine the energy of this isomeric state by taking the absolute energy difference between the excitation energy required to populate the 29.2-keV state from the ground-state and the energy emitted in its decay to the isomeric excited state. A transition-edge sensor microcalorimeter was used to measure the absolute energy of the 29.2-keV $gamma$-ray. Together with the cross-band transition energy (29.2 keV$to$ground) and the branching ratio of the 29.2-keV state measured in a recent study, the isomer energy was determined to be 8.30$pm$0.92 eV. Our result is in agreement with latest measurements based on different experimental techniques, which further confirms that the isomeric state of $^{229}$Th is in the laser-accessible vacuum ultraviolet range.
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Thorium-229 is a unique case in nuclear physics: it presents a metastable first excited state Th-229m, just a few electronvolts above the nuclear ground state. This so-called isomer is accessible by VUV lasers, which allows transferring the amazing precision of atomic laser spectroscopy to nuclear physics. Being able to manipulate the Th-229 nuclear states at will opens up a multitude of prospects, from studies of the fundamental interactions in physics to applications as a compact and robust nuclear clock. However, direct optical excitation of the isomer or its radiative decay back to the ground state has not yet been observed, and a series of key nuclear structure parameters such as the exact energies and half-lives of the low-lying nuclear levels of Th-229 are yet unknown. Here we present the first active optical pumping into Th-229m. Our scheme employs narrow-band 29 keV synchrotron radiation to resonantly excite the second excited state, which then predominantly decays into the isomer. We determine the resonance energy with 0.07 eV accuracy, measure a half-life of 82.2 ps, an excitation linewidth of 1.70 neV, and extract the branching ratio of the second excited state into the ground and isomeric state respectively. These measurements allow us to re-evaluate gamma spectroscopy data that have been collected over 40~years.
A new approach to observe the radiative decay of the $^{229}$Th nuclear isomer, and to determine its energy and radiative lifetime, is presented. Situated at a uniquely low excitation energy, this nuclear state might be a key ingredient for the development of a nuclear clock, a nuclear laser and the search for time variations of the fundamental constants. The isomers $gamma$ decay towards the ground state will be studied with a high-resolution VUV spectrometer after its production by the $beta$ decay of $^{229}$Ac. The novel production method presents a number of advantages asserting its competitive nature with respect to the commonly used $^{233}$U $alpha$-decay recoil source. In this paper, a feasibility analysis of this new concept, and an experimental investigation of its key ingredients, using a pure $^{229}$Ac ion beam produced at the ISOLDE radioactive beam facility, is reported.
We perform coincidence measurements between $alpha$ particles and $gamma$ rays from a $^{233}$U source to determine the half-lives of the excited state in a $^{229}$Th nucleus. We first prove that the half-lives of 42.43- and 164.53-keV states are consistent with literature values, whereas that of the 97.14-keV state (93(7) ps) deviates from a previously measured value (147(12) ps). The half-lives of 71.83- and 163.25-keV states are determined for the first time. Based on the obtained half-lives and the Alaga rule, we estimate the radiative half-life of the low-energy isomeric state ($^{229m}$Th) to be $5.0(11)times10^{3}$ s, which is one of the key parameters for the frequency standard based on $^{229}$Th.
Electromagnetic properties of the deformed neutron-odd nucleus $^{229}$Th are investigated in the framework of the unified model, with primary emphasis upon the properties of the low-lying isomeric state.
$^{229}$Th is a promising candidate for developing a nuclear optical clock and searching the new physics beyond the standard model. Accurate knowledge of the nuclear properties of $^{229}$Th is very important. In this work, we calculate hyperfine-structure constants for the first four states of $^{229}$Th$^{3+}$ using the relativistic coupled-cluster method based on the Gauss basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with the lowest-order quantum electrodynamics (QED) correction is the starting point, together with all linear and non-linear terms of single and double excitations are included in coupled-cluster calculation. With the measured value of the hyperfine-structure constants [Phys. Rev. Lett. 106. 223001(2011)], we get the magnetic dipole moment, $mu=0.359(9)$, and the electric quadrupole moment, $Q=2.95(7)$, of the $^{229}$Th nucleus. Our magnetic dipole moment is perfectly consistent with the recommended values, $mu=0.360(7)$, from the all-order calculation by Safronova textit{et. al.}[Phys.Rev.A 88, 060501 (2013)], but our electric quadrupole moment is smaller than their recommended value, $Q=3.11(6)$, about 5%. Our results show that the non-linear terms of single and double excitations, which were not included in the all-order calculation by Safronova textit{et. al.}, are very crucial to produce a precise $Q$ value of $^{229}$Th. Additionally, we also present magnetic octupole hyperfine-structure constants and some important non-diagonal hyperfine transition matrix elements, which are required for further extracting the magnetic octupole moment $Omega$ of $^{229}$Th nucleus.
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