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An alternative method to determine the excitation energy of the 229m Th isomer via the laser-induced electronic bridge is investigated theoretically. In the presence of an optical or ultra-violet laser at energies that fulfill a two-photon resonance condition, the excited nuclear state can decay by transfering its energy to the electronic shell. A bound electron is then promoted to an excited state by absorption of a laser photon and simultaneous de-excitation of the nucleus. We present calculated rates for the laser-induced electronic bridge process and discuss the experimental requirements for the corresponding setup. Our results show that depending on the actual value of the nuclear transition energy, the rate can be very high, with an enhancement factor compared to the radiative nuclear decay of up to 10 8 . 1 1 , 6 J J J J f t i n

When Th nuclei are doped in CaF 2 crystals, a set of electronic defect states appear in the crystal band gap which would otherwise provide complete transparency to vacuum-ultraviolet radiation. The coupling of these defect states to the 8 eV 229m Th nuclear isomer in the CaF 2 crystal is investigated theoretically. We show that although previously viewed as a nuisance, the defect states provide a starting point for nuclear excitation via electronic bridge mechanisms involving stimulated emission or absorption using an optical laser. The rates of these processes are at least 2 orders of magnitude larger than direct photoexcitation of the isomeric state using available light sources. The nuclear isomer population can also undergo quenching when triggered by the reverse mechanism, leading to a fast and controlled decay via the electronic shell. These findings are relevant for a possible solid-state nuclear clock based on the 229m Th isomeric transition.

The process of internal conversion from excited electronic states is investigated theoretically for the case of the vacuum-ultraviolet nuclear transition of 229 Th. Due to the very low transition energy, the 229 Th nucleus offers the unique possibility to open the otherwise forbidden internal conversion nuclear decay channel for thorium ions via optical laser excitation of the electronic shell. We show that this feature can be exploited to investigate the isomeric state properties via observation of internal conversion from excited electronic configurations of Th + and Th 2+ ions. A possible experimental realization of the proposed scenario at the nuclear laser spectroscopy facility IGISOL in Jyväskylä, Finland is discussed.

The unique isomeric transition at 7.8 eV in 229 Th has a magnetic dipole (M 1) and an electric quadrupole (E2) multipole mixing. So far, the E2 component has been widely disregarded. Here, we investigate the nuclear physics nature and the impact of the E2 decay channel for the nuclear coupling to the atomic shell based on the newest theoretical predictions for the corresponding reduced nuclear transition probabilities. Our results show that the contribution of the E2 channel is dominant or at least of the same order of magnitude for internal conversion or electronic bridge transitions involving the atomic orbitals 7p, 6d and 5f . Notable exceptions are the internal conversion of the 7s electron and the electronic bridge between the electronic states 7s and 7p, for which the M 1 component dominates by two to three orders of magnitude. Caution is therefore advised when considering isomeric excitation or decay via nuclear coupling to the atomic shell, as the involved orbitals determine which multipole transition component dominates. * Electronic address: Pavlo.Bilous@mpi-hd.mpg.de † Electronic address: nminkov@inrne.bas.bg ‡ Electronic address: Palffy@mpi-hd.mpg.de

A comprehensive theoretical study of direct laser excitation of a nuclear state based on the density matrix formalism is presented. The nuclear clock isomer 229m Th is discussed in detail, as it could allow for direct laser excitation using existing technology and provides the motivation for this work. The optical Bloch equations are derived for the simplest case of a pure nuclear two-level system and for the more complex cases taking into account the presence of magnetic sub-states, hyperfine-structure and Zeeman splitting in external fields. Nuclear level splitting for free atoms and ions as well as for nuclei in a solid-state environment is discussed individually. Based on the obtained equations, nuclear population transfer in the low-saturation limit is reviewed. Further, nuclear Rabi oscillations, power broadening and nuclear twophoton excitation are considered. Finally, the theory is applied to the special cases of 229m Th and 235m U, being the nuclear excited states of lowest known excitation energies. The paper aims to be a didactic review with many calculations given explicitly.

We carry out necessary theoretical justifications for the method of recoil nuclei in application to direct observation of the 229m Th 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 229m Th decay photons.