Thorium-doped CsI: Implications for the thorium nuclear clock transition

For ${}^{229m}\mathrm{Th}$ isomer nucleus with an anomalously low nuclear excitation energy, $E^{★}$ (currently accepted value of $7.8\pm 0.5\mathrm{eV}$), the bound internal conversion (BIC) decay process is caused by the excitation of a valence electron that is sensitive to the electronic structure of the atomic-sized neighborhood. We analyze an experiment where an impacting Th ion is neutralized by a negatively charged ion-receiving cesium iodide (CsI) surface, to obtain the minimal nuclear excitation energy $E_{\min }^{★}$ necessary for BIC promotion of a Th-impurity valence electron in a CsI matrix. We analyze two cases: CsI with Th deposited into the bulk and with Th deposited on the CsI surface. In the bulk we consider band gap effects while on the surface we consider the work function. The energy to pull the electron to the surface is $1.5–2.2\mathrm{eV}$ depending on the surface plane, while to promote to the conduction band in the bulk it is $1.5\mathrm{eV}$. Therefore we conclude that the Th-surface interaction can significantly reduce the lower $E^{★}$ bound of 6.3 eV, as estimated from the direct observation of the Th-clock transition [von der Wense et al., Nature (London) 533, 47 (2016)]. We suggest coating the multichannel plate with differing materials leading to different Th-impurity gaps and work functions can further narrow the $E^{★}$ uncertainty interval.

Figure 1

Th:CsI optimized at GGA level of theory for 12.5% doping. The planar iodine atoms (purple, large spheres labeled I) form quasimolecular ${\mathrm{ThI}}_4$, which helps with the stability, but the planar cesium atoms (red, slightly smaller spheres labeled Cs) form four balancing positive charges which helps to keep the thorium atom (green, small sphere labeled Th) in the neutral state which has four electrons.

Figure 2

Th:CsI electronic density of states at the $G_0{W}_0$ level of theory for the bulk. The gap has a magnitude of $\mathrm{\Delta }=1.2\mathrm{eV}$. The gap from the Th $s$ band (light red, short-dashed lines) is $E^{★}=2.0\mathrm{eV}$ in the spin-up channel and $E^{★}=1.5\mathrm{eV}$ in the spin-down channel. The upper (lower) panel is for spin up (down). The insets show the localization of the Th-$s$ orbital below the Fermi level which is set to 0 eV. Th $d$ orbitals are medium-dashed, brown lines. Th $f$ orbitals are long-short-dashed, dark-brown lines. Cs $s$ orbitals are labeled with medium-dashed, blue lines. Cs $p$ orbitals are labeled with a short-gap-dashed, cyan line. I $p$ orbitals are labeled with a medium-short-dashed, bright-green line. I $d$ orbitals have a short-long-dashed, thicker dark-green line. Finally, the total density of states is a given by a solid black line.