A possibility of the two-photon excitation of an isomeric state in a nucleus of thorium-229 has been discussed. The fluorescence intensity of the excitation is demonstrated to be identical for the irradiation of nuclei with either monochromatic light or polychromatic radiation consisting of a sequence of short light pulses of the same intensity. The two-photon excitation of Th^{3+} ion in an electromagnetic trap with a focused laser beam with a wavelength of about 320 nm and power of 100 mW can lead to the absorption saturation, at which the fluorescence emission with the frequency of the transition in a nucleus is maximal. In crystals doped with Th^{4+} to a concentration of about 10^{18} cm^{-3} and irradiated with a laser radiation 10 W in power, the emission of several photons per second with a wavelength of about 160 nm becomes possible.
The thorium nucleus with mass number $A=229$ has attracted much interest because its extremely low lying first excited isomeric state at about $8$eV opens the possibility for the development of a nuclear clock. However, neither the exact energy of this nuclear isomer nor properties, such as nuclear magnetic dipole and electric quadrupole moment are known to a high precision so far. The latter can be determined by investigating the hyperfine structure of thorium atoms or ions. Due to its electronic structure and the long lifetime of the nuclear isomeric state, Th$^{2+}$ is especially suitable f…
We carry out necessary theoretical justifications for the method of recoil nuclei in application to direct observation of the Th-229m isomeric state. We consider Cherenkov radiation, phosphorescence and fluorescence in the crystal plate which is used for collecting of thorium recoil nuclei and discuss the ways to avoid these parasitic signals revealing the Th-229m decay photons.
The impact of coherent light propagation on the excitation and fluorescence of thorium nuclei in a crystal lattice environment is investigated theoretically. We find that in the forward direction the fluorescence signal exhibits characteristic intensity modulations dominated by an orders of magnitude faster, sped-up initial decay signal. This feature can be exploited for the optical determination of the isomeric transition energy. In order to obtain a unmistakable signature of the isomeric nuclear fluorescence, we put forward a novel scheme for the direct measurement of the transition energy v…
We report the results of a direct search for the $^{229}$Th ($I^{p} = 3/2^+\leftarrow 5/2^+$) nuclear isomeric transition, performed by exposing $^{229}$Th-doped LiSrAlF$_6$ crystals to tunable vacuum-ultraviolet synchrotron radiation and observing any resulting fluorescence. We also use existing nuclear physics data to establish a range of possible transition strengths for the isomeric transition. We find no evidence for the thorium nuclear transition between $7.3 {eV}$ and $8.8 {eV}$ with transition lifetime $(1-2){s} \lesssim τ\lesssim (2000-5600){s}$. This measurement excludes roughly half…
The 7.6 eV electromagnetic transition between the nearly degenerate ground state and first excited state in the Th-229 nucleus may be very sensitive to potential changes in the fine-structure constant, $α= e^2/\hbar c$. However, the sensitivity is not known, and nuclear calculations are currently unable to determine it. We propose measurements of the differences of atomic transition frequencies between thorium atoms (or ions) with the nucleus in the ground state and in the first excited (isomeric) state. This will enable extraction of the change in nuclear charge radius and electric quadrupole…
We consider the excitation of the nuclear transition ^{229g}Th - ^{229m}Th near 7.6 eV in singly ionized thorium via an electronic bridge process. The process relies on the excitation of the electron shell by two laser photons whose sum frequency is equal to the nuclear transition frequency. This scheme allows to determine the nuclear transition frequency with high accuracy. Based on calculations of the electronic level structure of Th^+ which combine the configuration-interaction method and many-body perturbation theory, we estimate that a nuclear excitation rate in the range of 10 s^{-1} can…
The 7.8 eV nuclear isomer transition in 229 Thorium has been suggested as an etalon transition in a new type of optical frequency standard. Here we discuss the construction of a "solid-state nuclear clock" from Thorium nuclei implanted into single crystals transparent in the vacuum ultraviolet range. We investigate crystal-induced line shifts and broadening effects for the specific system of Calcium fluoride. At liquid Nitrogen temperatures, the clock performance will be limited by decoherence due to magnetic coupling of the Thorium nucleus to neighboring nuclear moments, ruling out the common…
We estimate the range of the radiative lifetime and energy of the anomalous, low-energy $3/2^+(7.8 \pm 0.5$ eV) state in the $^{229}$Th nucleus. Our phenomenological calculations are based on the available experimental data for the intensities of $M1$ and $E2$ transitions between excited levels of the $^{229}$Th nucleus in the $K^π[Nn_ZΛ]=5/2^+[633]$ and $3/2^+[631]$ rotational bands. We also discuss the influence of certain branching coefficients, which affect the currently accepted measured energy of the isomeric state. From this work, we establish a favored region where the transition lifet…
Excitation of the isomeric nuclear state 229m Th in the process of thorium atom irradiation by two-color femtosecond pulse of Ti: Sa laser at the fundamental wavelength and second harmonic is analyzed. It is shown that the rate of isomeric state excitation can be enhanced significantly with respect to other nucleus excitation processes in laser plasma or by an external coherent source at the resonance wavelength. This enhancement is due to the process of nonlinear laser nuclear excitation based on the following. First, the atomic current associated with the motion of valence electrons in stron…
We investigate the process of nuclear excitation via a two-photon electron transition (NETP) for the case of the doubly charged thorium. The theory of the NETP process has been devised originally for heavy helium-like ions. In this work, we study this process in the nuclear clock isotope $^{229}$Th in the $2+$ charge state. For this purpose, we employ a combination of configuration interaction and many-body perturbation theory to calculate the probability of NETP in resonance approximation. The experimental scenario we propose for the excitation of the low lying isomeric state in $^{229}$Th is…
A cryogenic Paul trap for probing the nuclear isomeric excited state $^{229\text{m}}$Th$^{3+}$
LMU München（慕尼黑大学）；Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University（哈马德·本·哈利法大学科学与工程学院量子计算中心）；MPIK Heidelberg（海德堡马克斯·普朗克核物理研究所）；Justus-Liebig-Universität Gießen（吉森尤斯图斯-李比希大学）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（达姆施塔特重离子研究中心）；Tsinghua University（清华大学）；Johannes Gutenberg-Universität（美因茨约翰内斯·古腾堡大学）；Helmholtz Institute Mainz（美因茨亥姆霍兹研究所）
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 $γ$-ray. Together with the cross-band transition energy (29.2 keV$\to$ground) and the branching ratio of the 29.2-keV st…
As a unique feature, the $^{229}$Th nucleus has an isomeric transition in the vacuum ultraviolet that can be accessed by optical lasers. The interference effects occurring in the interaction between coherent optical light and an ensemble of $^{229}$Th nuclei are investigated theoretically. We consider the scenario of nuclei doped in vacuum ultraviolet-vacuum ultraviolet transparent crystals and take into account the effect of different doping sites and therefore different lattice fields that broaden the nuclear transition width. This effect is shown to come in interplay with interference effec…
The hyperfine splitting of the ground and low-energy $3/2^+(7.8 \pm 0.5$ eV) levels in the $^{229}$Th nucleus in muonic atom ($μ^-_{1S_{1/2}}{}^{229}$Th$)^*$ has been calculated considering the distribution of the nuclear magnetization in the framework of collective nuclear model with the wave functions of the Nilsson model for the unpaired neutron. It is shown that (a) the hyperfine splitting of the $3/2^+$ isomeric state is anomalously weak, and the reduction of hyperfine structure in comparison with the model of a point nuclear magnetic dipole is close to 100\%, (b) partial inversion of lev…
We describe a novel approach to directly measure the energy of the narrow, low-lying isomeric state in $^{229}$Th. Since nuclear transitions are far less sensitive to environmental conditions than atomic transitions, we argue that the $^{229}$Th optical nuclear transition may be driven inside a host crystal with a high transition Q. This technique might also allow for the construction of a solid-state optical frequency reference that surpasses the precision of current optical clocks, as well as improved limits on the variability of fundamental constants. Based on analysis of the crystal lattic…
We investigate the deexcitation of the $^{229}$Th nucleus via the excitation of an electron. Detailed calculations are performed for the enhancement of the nuclear decay width due to this so called electron bridge (EB) compared to the direct photoemission from the nucleus. The results are obtianed for triply ionized thorium by using a B-spline pseudo basis approach to solve the Dirac equation for a local $x_α$ potential. This approach allows for an approximation of the full electron propagator including the positive and negative continuum. We show that the contribution of continua slightly inc…
$^{229}$Th Nuclear Spectroscopy in an Opaque Material: Laser-Based Conversion Electron Mössbauer Spectroscopy of $^{229}$ThO$_2$
University of California, Los Angeles（加州大学洛杉矶分校）；University of Manchester（曼彻斯特大学）；University of Nevada, Reno（内华达大学雷诺分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Eckert & Ziegler Analytics, Inc.（埃克特&齐格勒分析公司）；Johannes Gutenberg-Universität Mainz（美因茨约翰内斯古腾堡大学）；Ludwig-Maximilians-Universität München（慕尼黑路德维希-马克西米利安大学）
We review the ideas and concepts for a clock that is based on a radiative transition in the nucleus rather than in the electron shell. This type of clock offers advantages like an insensitivity against field-induced systematic frequency shifts and the opportunity to obtain high stability from interrogating many nuclei in the solid state. Experimental work concentrates on the low-energy (about 8 eV) isomeric transition in Th-229. We review the status of the experiments that aim at a direct optical observation of this transition and outline the plans for high-resolution laser spectroscopy experi…
Previously we proposed a new approach of exciting the $^{229}$Th nucleus using laser-driven electron recollision [W. Wang et al., Phys. Rev. Lett. 127, 052501 (2021)]. The current article is aimed to elaborate the method by explaining further theoretical details and presenting extended new results. The method has also been improved by adopting the electronic excitation cross sections calculated recently by Tkalya [E. V. Tkalya, Phys. Rev. Lett. 124, 242501 (2020)]. The new cross sections are obtained from Dirac distorted-wave calculations instead of from Dirac plane-wave calculations as we use…
Electronic bridge excitation of the 76 eV nuclear isomeric state in $^{235}$U is shown to be strongly enhanced in the U$^{7+}$ ion, potentially enabling laser excitation of this nucleus. This is because the electronic spectrum has a very high level density near the nuclear transition energy that ensures the resonance condition is fulfilled. We present a quantum statistical theory based on many-body quantum chaos to demonstrate that typical values for the electronic factor increase the probability of electronic bridge in $^{235}$U$^{7+}$ by many orders of magnitude. We also extract the nuclear …
The nucleus of 229Thorium presents a unique isomer state of very low energy and long lifetime, current estimates are around 7.8 eV and seconds to hours respectively. This nuclear transitions therefore is a promising candidate for a novel type of frequency standard and several groups worldwide have set out to investigate this system. Our aim is to construct a "solid state nuclear clock", i.e. a frequency standard where Thorium ions are implanted into Calciumfluoride crystals transparent in vacuum ultraviolet range. As a first step towards an accurate determination of the exact energy and lifeti…
